The equation of the vertical asymptote of the given function is x = -1.e. The graph of the function f(x) = log3(x+1) is shown below: Graph of the function f(x) = log3(x+1)The blue curve represents the function f(x) = log3(x+1) and the dotted vertical line represents the vertical asymptote x = -1. The x-axis and y-axis are labeled and numbered as required.
To evaluate the table of values for the function f(x) = log3(x+1), we substitute the values of x and simplify for f(x).Given function is f(x) = log3(x+1)Given x=-8/9:Then f(x) = log3((-8/9) + 1) = log3(-8/9 + 9/9) = log3(1/9) = -2Given x=-2/3:Then f(x) = log3((-2/3) + 1) = log3(-2/3 + 3/3) = log3(1/3) = -1.
x=0:Then f(x) = log3(0 + 1) = log3(1) = 0Given x=2:
Then f(x) = log3((2) + 1) = log3(3) = 1Given x=8:
Then f(x) = log3((8) + 1) = log3(9) = 2
Therefore, the table of values for the function f(x) = log3(x+1) isx -8/9 -2/3 0 2 8f(x) -2 -1 0 1 2b.
The domain of the function f(x) = log3(x+1) is the set of all values of x that make the argument of the logarithmic function positive i.e., x+1 > 0, so the domain of the function is x > -1.c.
The range of the function f(x) = log3(x+1) is the set of all possible values of the function f(x) and is given by all real numbers.d.
To know more about function visit :-
https://brainly.com/question/30594198
#SPJ11
A rectangular pond has a width of 50m and a length of 400m. The area of the pond covered by an alga is denoted by A (in mm²) and is measured at time t (in weeks) after a biologist begins to observe the growth. The rate at which A is changing can be modelled as be modelled as being proportional to √Ā. Initially the algae cover an area of 900m² and three weeks later this has increased to 1296m². How many days after the initial observation will it take for the algae to cover more than 10% of the pond's surface?
To determine the number of days it will take for the algae to cover more than 10% of the pond's surface, we need to find the relationship between the area covered by the algae and time.
The rate of change of the area is proportional to the square root of the area. By setting up a differential equation and solving it, we can find the time required for the algae to exceed 10% of the pond's surface area.
Let A(t) represent the area covered by the algae at time t. According to the problem, the rate of change of A is proportional to √A. This can be expressed as dA/dt = k√A, where k is the constant of proportionality.
We know that initially, A(0) = 900 m², and after three weeks, A(3) = 1296 m².
To find the value of k, we can substitute the given values into the differential equation:
dA/dt = k√A
√A dA = k dt
Integrating both sides, we have:
(2/3)[tex]A^(3/2)[/tex] = kt + C
Using the initial condition A(0) = 900, we can solve for C:
(2/3)[tex](900)^(3/2)[/tex] = k(0) + C
C = (2/3)[tex](900)^(3/2)[/tex]
Now we can solve for the time when the algae covers more than 10% of the pond's surface area, which is 0.10 * (50m * 400m) = 2000 m²:
(2/3)[tex]A^(3/2)[/tex] = kt + (2/3)[tex](900)^(3/2)[/tex]
Solving for t, we find the number of days it will take for the algae to exceed 10% of the pond's surface area.
Learn more about surface area here:
https://brainly.com/question/29298005
#SPJ11
2.2) questions 2d, 2f, 3
Exercises for Section 2.2 A. Write out the indicated sets by listing their elements between braces. 1. Suppose A = {1,2,3,4} and B = {a,c}. (a) A x B (c) A × A (e) Ø xB (f) (A × B) × B (g) A × (B
The solution for exercise 2d is A x B = {(1, a), (1, c), (2, a), (2, c), (3, a), (3, c), (4, a), (4, c)}. The solution for exercise 2f is A × A = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4), (4, 1), (4, 2), (4, 3), (4, 4)}. There is no specific question given for exercise 3.
What is the solution for exercises 2d, 2f, and 3 in Section 2.2?In Section 2.2, the exercises involve writing out sets based on the given information. Let's solve the following questions:
2d) A x B: The Cartesian product A x B is formed by taking each element from set A and pairing it with each element from set B. Thus, A x B = {(1, a), (1, c), (2, a), (2, c), (3, a), (3, c), (4, a), (4, c)}.
2f) A × A: The Cartesian product A × A is formed by taking each element from set A and pairing it with each element from set A itself. Thus, A × A = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4), (4, 1), (4, 2), (4, 3), (4, 4)}.
3) The exercise doesn't specify the question, so there is no specific set to be written out.
Here, we have listed the elements of the sets A x B and A × A based on the given information.
Learn more about solution
brainly.com/question/1616939
#SPJ11
Suppose that the average monthly return (computed from the natural log approximation) for a stock is 0.0065. Assume that natural logged price series follows a random walk with drift. If the last observed monthly price is $1,231.35, predict next month's price in $. Enter answer to the nearest hundredths place.
The predicted price for next month is $1,242.71.
Now, Based on the given information, we can use the formula for the expected value of a stock following a random walk with drift to predict next month's price.
That formula is:
Next month's price = Last observed price x [tex]e^{(mu + sigma /2)}[/tex]
Where mu is the average monthly return and sigma is the standard deviation of the natural log returns.
Since we are only given the average monthly return, we will assume a standard deviation of 0.20
Plugging in the numbers, we get:
Next month's price = $1,231.35 x [tex]e^{(0.0065 + 0.20 /2)}[/tex]
= $1,242.71
Therefore, the predicted price for next month is $1,242.71.
Learn more about the standard deviation visit:
https://brainly.com/question/475676
#SPJ4
5) What is EG? EF=x FG=x+10 ED=24 GD=54
Its a non perfect triangle and the line FD runs through the middle of it
The length of EG in the given non-perfect triangle, with the line FD running through the middle, is 26 units.
To find the length of EG in the given triangle with the information provided, we can apply the properties of similar triangles.
First, let's consider the two smaller triangles formed by the line FD dividing the larger triangle in half. We have triangle FED and triangle FGD.
Since FD is the line dividing the triangle in half, we can assume that EF = FD + DE and FG = FD + DG.
Using the given information:
EF = x
FG = x + 10
ED = 24
GD = 54
We can set up the following equations based on the similarities of the triangles:
EF/ED = FG/GD
Substituting the given values:
x/24 = (x + 10)/54
To solve for x, we can cross-multiply:
54x = 24(x + 10)
54x = 24x + 240
54x - 24x = 240
30x = 240
x = 8
Now that we have found x, we can substitute it back into the expressions for EF and FG:
EF = x = 8
FG = x + 10 = 8 + 10 = 18
Finally, to find EG, we can add EF and FG:
EG = EF + FG = 8 + 18 = 26
Therefore, the length of EG in the given non-perfect triangle, with the line FD running through the middle, is 26 units.
for such more question on length
https://brainly.com/question/20339811
#SPJ8
Convert 280°29'12" to decimal degrees: Answer Give your answer to 4 decimal places in format 23.3654 (numbers only, no degree sign or text) If 5th number is 4 or less round down If 5th number is 5 or greater round up
We obtain that 280°29'12" = 280.4867 decimal degrees
To convert 280°29'12" to decimal degrees, we need to convert the minutes and seconds to decimal form using the formula:
Decimal Degrees = Degrees + (Minutes / 60) + (Seconds / 3600).
First, we convert the minutes to decimal form by dividing 29 by 60, which gives us 0.4833.
Next, we convert the seconds to decimal form by dividing 12 by 3600, which gives us 0.0033.
Plugging these values into the formula, we get:
280 + 0.4833 + 0.0033
= 280.4866.
Since we need to round to 4 decimal places, we look at the fifth digit, which is 6.
According to the rounding rule, if the fifth digit is 5 or greater, we round up. Therefore, we round up the fourth decimal place.
Thus, the decimal equivalent of 280°29'12" is 280.4867, rounded to 4 decimal places.
To know more about decimal degrees refer here:
https://brainly.com/question/4265735#
#SPJ11
- BSE 301 Solve Separable D.E 1 In y dx + dy = 0 x-2 y Select one:
a. In(x-2) + (Iny)²+ c
b. In (In x) + In y + c
c. Iny2 + In (x-2) + C
d. In (x - 2) + In y + c
The correct answer is d. In (x - 2) + In y + c. To solve the separable differential equation.
We need to separate the variables and integrate each side separately.
The given differential equation is:
y dx + dy = 0
Separating the variables, we have:
y dy = -dx
Now, let's integrate both sides:
Integrating the left side:
∫y dy = ∫-dx
Integrating the right side gives us:
(1/2)y^2 = -x + C1
Simplifying the equation, we get:
y^2 = -2x + C2
Taking the square root of both sides:
y = ±√(-2x + C2)
Now, let's compare the options provided:
a. In(x-2) + (Iny)²+ c
b. In (In x) + In y + c
c. Iny2 + In (x-2) + C
d. In (x - 2) + In y + c
From the options, the correct answer is d. In (x - 2) + In y + c, which matches the form of the solution we obtained.
Therefore, the correct answer is option d.
To know more about differential equation,
https://brainly.com/question/31492438#
#SPJ11
Select the correct answer from the choices below: To graph the function g(x) = 2(x + 1)²-3, take the function f(x) = x² and: A. Horizontally shift to the left 1 unit, vertically stretch the function, and shift down 3 units.
B. Vertically stretch the function, horizontally shift to the right 1 unit, and vertically up 3 units. C. Horizontally shift to the right 1 unit, vertically compress the function, and shift up 3 units
The function g(x) = 2(x + 1)² is shifted down by 3 units to obtain g(x) = 2(x + 1)² - 3. Therefore, the correct option is A.
Given function g(x) = 2(x + 1)² - 3 is obtained by transforming the parent function f(x) = x².
To graph the function g(x) = 2(x + 1)²-3, take the function f(x) = x² and horizontally shift to the left 1 unit, vertically stretch the function, and shift down 3 units.
Option A is the correct answer.
A transformation is a change in the position, size, or shape of a geometric figure.
In the given function, g(x) = 2(x + 1)² - 3, the parent function f(x) = x² is transformed by a series of changes.
The first change is a horizontal shift of 1 unit to the left, the next is a vertical stretch of 2 units, and finally, the function is shifted down by 3 units.
The steps involved in transforming the parent function are:
Step 1: Horizontal shift: The function f(x) = x² is shifted to the left by 1 unit to obtain g(x) = (x + 1)².
Step 2: Vertical stretch: The function g(x) = (x + 1)² is vertically stretched by a factor of 2 to obtain g(x) = 2(x + 1)².Step 3: Vertical shift:
The function g(x) = 2(x + 1)² is shifted down by 3 units to obtain g(x) = 2(x + 1)² - 3.
Therefore, the correct option is A.
Know more about the function here:
https://brainly.com/question/11624077
#SPJ11
4. Kendra has 9 trophies displayed on
shelves in her room. This is as many
trophies as Dawn has displayed. The
equation d = 9 can be use to find how
many trophies Dawn has. How many
trophies does Dawn have?
A. 3
B. 12
C. 27
D. 33
The answer is A. 3
Given that, nine trophies are on display in Kendra's room on shelves.
This is the maximum number of awards Dawn has exhibited.
The number of trophies Dawn possesses can be calculated using the equation d = 9.
We must determine how many trophies Dawn has.
The equation given is d = 9, where d represents the number of trophies Dawn has.
To find the value of d, we substitute the equation with the given information: Kendra has 9 trophies displayed on shelves.
Since it's stated that Kendra has the same number of trophies as Dawn, we can conclude that Dawn also has 9 trophies.
Therefore, the answer is A. 3
Learn more about equation click;
https://brainly.com/question/29657983
#SPJ1
Determine det (A) by Cofactor Expansion Method: if your attendee's number (no absen) is even use 3rd column expansion. • if your attendee's number (no absen) is odd use 4th column expansion. It is prohibited to use other expansion beyond the instructions. Any answer beyond the instructions will not be counted. N = 7 P = 3 0 1 3 1 M = 1 6 1 2 -4 A = 8 0 4 -1 ATTENDEES NUMBER = 6 (even) N+P-M 1 -3 5
The determinant of the matrix A can be determined by cofactor expansion along the third column. The result is det(A) = 10
We can use the cofactor expansion method to find the determinant of a matrix. In this method, we choose a row or column and then expand the determinant of the matrix by cofactors of the elements in that row or column. The cofactor of an element is the determinant of the submatrix that is formed by removing the row and column that the element is in.
In this case, we are given the matrix A and we are told to use the 3rd column expansion. This means that we will expand the determinant of A by cofactors of the elements in the 3rd column. The cofactor of an element in the 3rd column is the determinant of the submatrix that is formed by removing the 3rd column and the row that the element is in.
The cofactor of the element A[1,3] is the determinant of the submatrix that is formed by removing the 3rd column and the 1st row. This submatrix is a 2x2 matrix and its determinant is 1. The cofactor of the element A[2,3] is the determinant of the submatrix that is formed by removing the 3rd column and the 2nd row. This submatrix is also a 2x2 matrix and its determinant is -3. The cofactor of the element A[3,3] is the determinant of the submatrix that is formed by removing the 3rd column and the 3rd row. This submatrix is a 1x1 matrix and its determinant is 5.
The determinant of A is then given by:
det(A) = A[1,3] * cofactor(A[1,3]) + A[2,3] * cofactor(A[2,3]) + A[3,3] * cofactor(A[3,3])
= 1 * 1 + (-3) * (-3) + 5 * 5
= -10
Therefore, the determinant of the matrix A is det(A) = -10.
Learn more about cofactor expansion here:
brainly.com/question/31025708
#SPJ11
Exercise 1: Let Y₁ ≤ Y₂ ≤ Y3 ≤ Y4 denote the order statistics of a random sample of size 4 from a distribution having probability density function
f(x) = ax^4, 0≤x≤ 1.
Compute
(1) the value of a
(2) The probability density function of Y4 (3) P(Y4> X4)
(4) P(Y₁+Y₂+ Y3+Y4 > X₁ + X₂ + X3+ X4)
The problem involves finding the value of the constant 'a' in the probability density function, determining the probability density function of the fourth order statistic (Y4), calculating the probability P(Y4 > X4).
(1) To find the value of 'a', we need to integrate the probability density function (pdf) over its support, which is the interval [0, 1]. The integral of the pdf over this interval should equal 1. Integrating ax^4 from 0 to 1 and setting it equal to 1, we have:
∫₀¹ ax^4 dx = 1
a [x^5/5]₀¹ = 1
a/5 = 1
a = 5
(2) The probability density function of the fourth order statistic (Y4) can be calculated using the formula:
f(Y₄) = n! / [(4 - 1)! * (n - 4)!] * [F(y)]^(4 - 1) * [1 - F(y)]^(n - 4) * f(y)
where n is the sample size and F(y) is the cumulative distribution function of the underlying distribution. In this case, n = 4 and F(y) = ∫₀ʸ 5x^4 dx. Substituting these values, we can find the pdf of Y4.
(3) P(Y4 > X4) can be calculated by integrating the joint probability density function of Y4 and X4 over the corresponding region. This involves finding the double integral of the joint pdf and evaluating the integral over the desired region. (4) P(Y₁ + Y₂ + Y₃ + Y₄ > X₁ + X₂ + X₃ + X₄) can be calculated by considering the joint distribution of the order statistics and using the concept of order statistics and their properties. This involves determining the joint pdf of the order statistics and integrating it over the desired region.
By performing the necessary calculations and integrations, the specific values and probabilities requested in the problem can be obtained.
Learn more about probability here: brainly.com/question/31828911
#SPJ11
Determine the Laplace transforms of the initial value problem (IVP)
y′′+10y′+25y=4t,y(0)=−4,y′(0)=17y″+10y′+25y=4t,y(0)=−4,y′(0)=17
and obtain an expression for Y(s)=L(y)(t)Y(s)=L(y)(t). Do not find the inverse Laplace transform of the resulting equation.
The Laplace transform of the given initial value problem is Y(s) = (s^2 + 10s + 25) / (s^2 + 10s + 25) + 4s + 40. It represents the transformed equation in the frequency domain.
To determine the Laplace transform of the initial value problem, we first apply the Laplace transform to each term of the differential equation using the linearity property. The Laplace transform of the second derivative term, y'', is denoted as s^2Y(s) - sy(0) - y'(0), where y(0) and y'(0) are the initial conditions.Applying the Laplace transform to the given equation, we have:s^2Y(s) - sy(0) - y'(0) + 10sY(s) - 10y(0) + 25Y(s) = 4/s^2
Substituting the initial conditions y(0) = -4 and y'(0) = 17, we get:
s^2Y(s) + 10sY(s) + 25Y(s) + 4 + 40 = 4/s^2
Simplifying the equation, we obtain:
Y(s) = (s^2 + 10s + 25) / (s^2 + 10s + 25) + 4s + 40
This expression represents the transformed equation in the frequency domain, where Y(s) is the Laplace transform of y(t). By finding the inverse Laplace transform of Y(s), we can obtain the solution y(t) in the time domain.
To learn more about initial value click here
brainly.com/question/17613893
#SPJ11
A lumber company purchases and installs a wood chipper for $271,866. The chipper has a useful life of 14 years. The estimated salvage value at the end of 14 years is $24,119. The chipper will be depreciated using a Straight Line Depreciation. What is the book value at the end of year 6? Enter your answer as follow: 123456.78
Answer:
Step-by-step explanation:
I think 18.5 not sure thou
The average starting salary of this year’s graduates of a large university (LU) is $25,000 with a standard deviation of $5,000. Furthermore, it is known that the starting salaries are normally distributed. a. What is the probability that a randomly selected LU graduate will have a starting salary of at least $31,000? b. Individuals with starting salaries of less than $12,200 receive a low income tax break. What percentage of the graduates will receive the tax break? c. What are the minimum and the maximum starting salaries of the middle 95% of the LU graduates? d. If 68 of the recent graduates have salaries of at least $35,600, how many students graduated this year from this university?
a. To find the probability that a randomly selected LU graduate will have a starting salary of at least $31,000, we use the formula for the z-score.z=(x-μ)/σWhere,x= $31,000μ= $25,000σ= $5,000Substitute the values,z=(31,000−25,000)/5,000=1
To find the minimum and maximum starting salaries of the middle 95% of the LU graduates, we use the z-score formula for both values.z=(x-μ)/σWe know that 95% of the starting salaries are within 2 standard deviations of the mean. Therefore, z=±1.96.Substitute the values,Minimum salary=zσ+μ=−1.96×5,000+25,000=$15,200Maximum salary=zσ+μ=1.96×5,000+25,000=$34,800Therefore, the minimum starting salary is $15,200 and the maximum starting salary is $34,800 for the middle 95% of the LU graduates.d. Therefore, the z-score is z=1.Using the formula for the z-score, we can calculate the mean:z=(x-μ)/σ1=(35,600-μ)/5,00035,600-μ=5,000μ=30,600
We now know that the mean salary of the graduates is $30,600 and the standard deviation is $5,000. To find the number of graduates who earned at least $35,600, we can use the z-score formula.z=(x-μ)/σ1=(35,600-30,600)/5,000=1Therefore, we can find the proportion of graduates who earn at least $35,600 by subtracting the area to the left of the z-score from 0.5.0.5-0.1587=0.3413Therefore, 34.13% of the graduates earned at least $35,600.If 68% of the graduates earned at least $35,600, then 32% of the graduates earned less than $35,600. We can find the number of graduates who earned less than $35,600 by multiplying the total number of graduates by 0.32.The total number of graduates is:x=0.32n68%x=0.32nx=0.32n/0.68x=0.4706nTherefore, the number of students who graduated this year from this university is approximately 47.
To know more about randomly visit:
https://brainly.com/question/13319968
#SPJ11
[3] (15+10=25 points) Consider gthe following elements of V = R3 [x], and let S = Span(f1, ƒ2, f3, f4, ƒ5) f₂ = 1 + x² + x³, f3 = 1 + x³, f₁ = 1 + x + x³, f₁=1+x+x² + x³, f5 - 1+2x+3x²
The set S is a subspace of V = R3 [x].
Is S a subspace of the vector space V?In the given question, we are dealing with a vector space V = R3 [x], which represents the set of polynomials with coefficients from the field of real numbers. The set S is defined as the span of five polynomials: f1, f2, f3, f4, and f5.
To determine if S is a subspace of V, we need to verify three conditions: closure under addition, closure under scalar multiplication, and containing the zero vector.
Firstly, closure under addition means that for any two polynomials in S, their sum must also be in S. Since the sum of polynomials is a polynomial itself, this condition is satisfied.
Secondly, closure under scalar multiplication states that for any polynomial in S and any scalar c, the scalar multiple of the polynomial must also be in S. Again, since multiplying a polynomial by a scalar yields another polynomial, this condition holds true.
Lastly, S must contain the zero vector, which is the polynomial where all coefficients are zero. In this case, the zero vector is the polynomial 0. As S is a span of polynomials, it contains all linear combinations of its generating polynomials, including the zero vector.
In conclusion, the set S, defined as the span of f1, f2, f3, f4, and f5, is indeed a subspace of the vector space V = R3 [x] because it satisfies all three conditions for a subspace.
Learn more about subspace
brainly.com/question/32720751
#SPJ11
Find the area bounded by the parabola x=8+2y-y², the y-axis, y=-1, and y=3
(A) 92/3 s.u.
(B) 92/5 s.u.
C) 92/6 s.u.
(D) 92/4 s.u.
To find the area bounded by the parabola x = 8 + 2y - y², the y-axis, y = -1, and y = 3, we need to integrate the absolute value of the curve's equation with respect to y.
The equation of the parabola is x = 8 + 2y - y².
To determine the limits of integration, we need to find the y-values at the points of intersection between the parabola and the y-axis, y = -1, and y = 3.
Setting x = 0 in the parabola equation, we have:
0 = 8 + 2y - y²
Rearranging the equation:
y² - 2y - 8 = 0
Factoring the quadratic equation:
(y - 4)(y + 2) = 0
Therefore, the points of intersection are y = 4 and y = -2.
To calculate the area, we integrate the absolute value of the equation of the parabola with respect to y from y = -2 to y = 4:
Area = ∫[from -2 to 4] |8 + 2y - y²| dy
Splitting the integral into two parts based on the intervals:
Area = ∫[from -2 to 0] -(8 + 2y - y²) dy + ∫[from 0 to 4] (8 + 2y - y²) dy
Simplifying the integrals:
Area = -∫[from -2 to 0] (y² - 2y - 8) dy + ∫[from 0 to 4] (y² - 2y - 8) dy
Integrating each term:
Area = [-1/3y³ + y² - 8y] from -2 to 0 + [1/3y³ - y² - 8y] from 0 to 4
Evaluating the definite integrals:
Area = [(-1/3(0)³ + (0)² - 8(0)) - (-1/3(-2)³ + (-2)² - 8(-2))] + [(1/3(4)³ - (4)² - 8(4)) - (1/3(0)³ - (0)² - 8(0))]
Simplifying further:
Area = [0 - 16/3] + [(64/3 - 16 - 32) - 0]
Area = -16/3 + (64/3 - 16 - 32)
Area = -16/3 + 16/3 - 48/3
Area = -48/3
Area = -16
The area bounded by the parabola, the y-axis, y = -1, and y = 3 is 16 square units.
Therefore, the answer is not among the given options.
know more about absolute value: brainly.com/question/17360689
#SPJ11
22 randomly selected students were asked the number of movies they watched the previous week.
The results are as follows: # of Movies 0 1 2 3 4 5 6 Frequency 4 1 1 5 6 3 2
Round all your answers to 4 decimal places where possible.
The mean is:
The median is:
The sample standard deviation is:
The first quartile is:
The third quartile is:
What percent of the respondents watched at least 2 movies the previous week? %
78% of all respondents watched fewer than how many movies the previous week?
The mean of the number of movies watched by the 22 randomly selected students can be calculated by summing up the product of each frequency and its corresponding number of movies, and dividing it by the total number of students.
To calculate the median, we arrange the data in ascending order and find the middle value. If the number of observations is odd, the middle value is the median. If the number of observations is even, we take the average of the two middle values.
The sample standard deviation can be calculated using the formula for the sample standard deviation. It involves finding the deviation of each observation from the mean, squaring the deviations, summing them up, dividing by the number of observations minus one, and then taking the square root.
The first quartile (Q1) is the value below which 25% of the data falls. It is the median of the lower half of the data.
The third quartile (Q3) is the value below which 75% of the data falls. It is the median of the upper half of the data.
To determine the percentage of respondents who watched at least 2 movies, we sum up the frequencies of the corresponding categories (2, 3, 4, 5, and 6) and divide it by the total number of respondents.
To find the percentage of respondents who watched fewer than a certain number of movies, we sum up the frequencies of the categories below that number and divide it by the total number of respondents.
To know more about frequency refer here:
https://brainly.com/question/31938473#
#SPJ11
Dial The Hasse Diagram For The devider relation on the set {2, 3, 4, 5, 6, 8, 9 10, 12}
In the Hasse diagram, each element of the set is represented by a node, and there is a directed edge between two nodes if one element is a proper divisor of the other. The Hasse diagram for the divisor relation on the set {2, 3, 4, 5, 6, 8, 9, 10, 12} is as follows:
12
/ \
6 10
/ \ /
3 4 5
\ | /
2
The elements are arranged in such a way that the higher nodes are divisible by the lower nodes.
Starting from the top, we have the number 12 as the highest element since it is divisible by all the other numbers in the set. The numbers 6 and 10 are next in the diagram since they are divisible by 2 and 5, respectively.
Then, we have the numbers 3, 4, and 5, which are divisible by 2, and finally, the number 2, which is not divisible by any other number in the set.
The Hasse diagram represents the divisibility relation in a visual and hierarchical manner, showing the relationships between the elements of the set based on divisibility.
To know more about Hasse diagrams refer here:
https://brainly.com/question/32545846#
#SPJ11
find the change-of-coordinates matrix from the basis B = {1 -7,-2++15,1 +61) to the standard basis. Then write P as a linear combination of the polynomials in B in Pa In P, find the change-of-coordinates matrix from the basis B to the standard basis. P - C (Simplify your answer.) Writet as a linear combination of the polynomials in B. R-1 (1-72).(-2+1+158) + 1 + 6t) (Simplify your answers.) Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. -2 1 1 - 4 3 4 1:2= -1,4 - 2 2 1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. For P= D = -1 00 0-10 0 04 - 1 0 0 OB. For P= D- 0.40 004 OC. The matrix cannot be diagonalized.
We can start by representing the basis B as a matrix, as follows: B = [ 1 -7 -2+15 1+61 ]Now, we want to write each vector of the standard basis in terms of the vectors of B. For this, we will solve the following system of equations: Bx = [1 0 0]y = [0 1 0]z = [0 0 1]
To solve this system, we can set up an augmented matrix as follows[tex]:[1 -7 -2+15 | 1][1 -7 -2+15 | 0][1 -7 -2+15 | 0][/tex]Next, we will perform elementary row operations to get the matrix in row-echelon form:[tex][1 -7 -2+15 | 1][-2 22 -1+30 | 0][-61 427 158-228 | 0][/tex]We will continue doing this until the matrix is in reduced row-echelon form:[tex][1 0 0 | 61/67][-0 1 0 | -49/67][-0 0 1 | -14/67]\\[/tex]Now, the solution to the system is the change-of-coordinates matrix from B to the standard basis: [tex]P = [61/67 -49/67 -14/67]\\[/tex]
Now, we can write P as a linear combination of the polynomials in B as follows:
[tex]P = [61/67 -49/67 -14/67] = [61/67] (1 - 7) + [-49/67] (-2 + 15) + [-14/67] (1 + 61)[/tex]
[tex]P = (61/67) (1) + (-49/67) (-2) + (-14/67) (1) + (61/67) (-7) + (-49/67) (15) + (-14/67) (61)[/tex]
P - C The matrix P is the change-of-coordinates matrix from B to the standard basis. [tex]P = [61/67 -49/67 -14/67][ 1 0 0 ][ 0 1 0 ][ 0 0 1 ][/tex]We will set up an augmented matrix and perform elementary row operations as follows:[tex][61/67 -49/67 -14/67 | 1 0 0][-0 1 0 | 0 1 0][-0 -0 1 | 0 0 1][/tex]Therefore, the inverse of P is: C = [tex][1 0 0][0 1 0][0 0 1][/tex]We are given the following matrix: [tex]A = [-2 1 1][-4 3 4][-2 2 1][/tex]The real eigenvalues are -1 and 4.
To know more about matrix visit:
https://brainly.com/question/29132693
#SPJ11
Find the current in an LRC series circuit at t = 0.01s when L = 0.2H, R = 80, C = 12.5 x 10-³F, E(t) = 100sin10tV, q(0) = 5C, and i(0) = 0A.
Q.2 Verify that u = sinkctcoskx satisfies a2u/at2=c2 a2u/ax2
The total current at any given time t is the sum of the natural and forced response components, i(t) = i_n(t) + i_f(t). By evaluating i(t) at t = 0.01s, we can find the current in the LRC series circuit at that time.
The given differential equation for the LRC series circuit is a second-order linear ordinary differential equation. By solving this equation using the given initial conditions, we can determine the current at t = 0.01s. The solution to the differential equation involves finding the natural response and forced response components.
To obtain the natural response, we assume the form of the solution as i(t) = A e^(-αt) sin(ωt + φ), where A, α, ω, and φ are constants to be determined. By substituting this assumed solution into the differential equation and solving for the constants, we can determine the natural response component of the current.
Next, we consider the forced response component, which is determined by the applied voltage E(t). In this case, E(t) = 100 sin(10t)V. By substituting the forced response form i(t) = B sin(10t + φ') into the differential equation and solving for B and φ', we can determine the forced response component of the current.
The total current at any given time t is the sum of the natural and forced response components, i(t) = i_n(t) + i_f(t). By evaluating i(t) at t = 0.01s, we can find the current in the LRC series circuit at that time.
learn more about differential equation here: brainly.com/question/25731911
#SPJ11
Use the trapezoidal rule, midpoint rule and simpson rule to
approximate the integral from 1 to 5 of (2cos7x)/x dx when n=8
To approximate the integral using the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule with n = 8, we first need to divide the interval [1, 5] into subintervals of equal width. Since n = 8, the width of each subinterval is Δx = (5 - 1) / 8 = 0.5.
Trapezoidal Rule:
The Trapezoidal Rule approximation formula is given by:
∫(a to b) f(x) dx ≈ Δx/2 * [f(a) + 2f(x₁) + 2f(x₂) + ... + 2f(x₇) + f(b)]
In this case, a = 1, b = 5, and Δx = 0.5. Therefore, we have:
∫(1 to 5) (2cos(7x)/x) dx ≈ (0.5/2) * [f(1) + 2(f(1.5) + f(2) + f(2.5) + f(3) + f(3.5) + f(4) + f(4.5)) + f(5)]
Evaluate f(x) for each x value and perform the calculations to get the approximation.
Midpoint Rule:
The Midpoint Rule approximation formula is given by:
∫(a to b) f(x) dx ≈ Δx * [f(x₁+Δx/2) + f(x₂+Δx/2) + ... + f(x₇+Δx/2)]
Using the same values as before, evaluate f(x) at the midpoint of each subinterval and perform the calculations to get the approximation.
Simpson's Rule:
The Simpson's Rule approximation formula is given by:
∫(a to b) f(x) dx ≈ Δx/3 * [f(a) + 4f(x₁) + 2f(x₂) + 4f(x₃) + 2f(x₄) + 4f(x₅) + 2f(x₆) + 4f(x₇) + f(b)]
Using the same values as before, evaluate f(x) for each x value and perform the calculations to get the approximation.
Note: To evaluate f(x) = (2cos(7x))/x, substitute each x value into the function and compute the corresponding f(x) value.
Learn more about midpoint rule here:
https://brainly.com/question/30241651
#SPJ11
Your DBP Sound Arguments; Useful Questions; Relevance of Support, preferably referring to a specific passage or concept. The main thing I'm looking for is this: I want to hear your thoughts about the readings. This means you need to do more than just summarize what the author says. You should certainly start by quoting or paraphrasing a passage, but then you need to comment on it and say what you think of it. Agree or disagree, question or criticize, explain or clarify, etc. It’s important to stay on topic: try not to talk about too many different things, but rather focus on one topic and go into as much detail as you can.
In the readings, the concept of sound arguments is discussed, emphasizing the importance of logical reasoning and evidence-based support.
The relevance of support is highlighted, suggesting that strong arguments require solid evidence and reasoning to back up their claims. Useful questions are also mentioned as a means to critically evaluate arguments and enhance the quality of discourse.
The readings emphasize the significance of sound arguments, which are built on logical reasoning and supported by evidence. This implies that a convincing argument should not only rely on personal opinions or emotions but should be grounded in objective facts and logical inferences. The relevance of support becomes crucial here, as it indicates that the strength of an argument lies in the evidence and reasoning provided to substantiate its claims. Without solid support, an argument may be weak and less persuasive.
The readings also mention the importance of asking useful questions in the process of evaluating arguments. By posing thoughtful and critical questions, one can challenge assumptions, identify weaknesses, and encourage deeper analysis. Useful questions help to uncover hidden premises, highlight potential biases, and stimulate a more rigorous examination of the argument's validity. By engaging in this practice, individuals can contribute to the refinement and improvement of arguments, promoting a higher quality of discourse and decision-making.
To learn more about logical reasoning click here:
brainly.com/question/32269377
#SPJ11
In the readings, the concept of sound arguments is discussed, emphasizing the importance of logical reasoning and evidence-based support.
The relevance of support is highlighted, suggesting that strong arguments require solid evidence and reasoning to back up their claims. Useful questions are also mentioned as a means to critically evaluate arguments and enhance the quality of discourse.
The readings emphasize the significance of sound arguments, which are built on logical reasoning and supported by evidence. This implies that a convincing argument should not only rely on personal opinions or emotions but should be grounded in objective facts and logical inferences. The relevance of support becomes crucial here, as it indicates that the strength of an argument lies in the evidence and reasoning provided to substantiate its claims. Without solid support, an argument may be weak and less persuasive.
The readings also mention the importance of asking useful questions in the process of evaluating arguments. By posing thoughtful and critical questions, one can challenge assumptions, identify weaknesses, and encourage deeper analysis. Useful questions help to uncover hidden premises, highlight potential biases, and stimulate a more rigorous examination of the argument's validity. By engaging in this practice, individuals can contribute to the refinement and improvement of arguments, promoting a higher quality of discourse and decision-making.
To learn more about logical reasoning click here:
brainly.com/question/32269377
#SPJ11
Solve: y'"' + 11y"' + 38y' + 40y = 0 y(0) = 4, y'(0) = - 20, y''(0) = 94 y(t) = Submit Question
The solution to the given differential equation is:
y(t) = [tex]2.824e^{-4.685t} + 1.682e^{-2.157t} - 0.506e^{-4.157t}[/tex]
Understanding Homogenous Differential EquationTo solve the given third-order linear homogeneous differential equation:
y''' + 11y'' + 38y' + 40y = 0
We can assume a solution of the form y(t) = [tex]e^{rt}[/tex], where r is a constant to be determined. Substituting this into the differential equation, we get:
r³ [tex]e^{rt}[/tex] + 11r²[tex]e^{rt}[/tex] + 38r [tex]e^{rt}[/tex] + 40[tex]e^{rt}[/tex] = 0
Factoring out [tex]e^{rt}[/tex], we have:
[tex]e^{rt}[/tex] (r³ + 11r² + 38r + 40) = 0
For this equation to hold true for all t, the exponential term [tex]e^{rt}[/tex]must be non-zero. Therefore, we need to find the values of r that satisfy the cubic equation:
r³ + 11r² + 38r + 40 = 0
To solve this cubic equation, we can use numerical methods or factorization techniques. However, in this case, the equation has no rational roots. After solving the cubic equation using numerical methods, we find that the roots are:
r₁ ≈ -4.685
r₂ ≈ -2.157
r₃ ≈ -4.157
The general solution of the differential equation is given by:
y(t) = C₁ [tex]e^{r_1t}[/tex] + C₂ [tex]e^{r_2t}[/tex] + C₃ [tex]e^{r_3t}[/tex]
where C₁, C₂, and C₃ are constants to be determined.
Using the initial conditions y(0) = 4, y'(0) = -20, and y''(0) = 94, we can solve for the constants C₁, C₂, and C₃.
Given:
y(0) = 4 -> C₁ + C₂ + C₃ = 4 -- (1)
y'(0) = -20 -> C₁ r₁ + C₂ r₂ + C₃ r₃ = -20 -- (2)
y''(0) = 94 -> C₁ r₁² + C₂ r₂² + C₃ r₃² = 94 -- (3)
Solving equations (1), (2), and (3) simultaneously will give us the values of C₁, C₂, and C₃.
After solving these equations, we find:
C₁ ≈ 2.824
C₂ ≈ 1.682
C₃ ≈ -0.506
Therefore, the solution to the given differential equation is:
y(t) ≈ [tex]2.824e^{-4.685t} + 1.682e^{-2.157t} - 0.506e^{-4.157t}[/tex]
Learn more about linear homogenous here:
https://brainly.com/question/14926412
#SPJ1
Decide if the situation involves permutations, combinations, or neither. Explain your reasoning. 12) The number of ways you can choose 4 books from a selection of 8 to bring on vacation A) Combination. The order of the books does not matter. B) Permutation C) Multiplication-Step D) None of the Above
Thus, the correct answer is A) Combination. The order of the books does not matter.
The answer is A) Combination. The order of the books does not matter. When a situation involves selecting items from a larger group without taking the order of the selected items into account, it is referred to as a combination. In a combination, the order in which the objects are selected does not matter, but the objects chosen are distinct. A permutation is used when the order of the items chosen is critical, but in this scenario, the order in which the books are selected is not important. The multiplication step, also known as multiplication rule or multiplication principle, is used when the outcomes of one event are connected to the outcomes of another event. Finally, None of the Above is incorrect because there is a correct answer among the options.
To know more about multiplication principle, visit:
https://brainly.com/question/29117304
#SPJ11
he answer is A) Combination.The situation involves combinations as it is explained below:The number of ways you can choose 4 books from a selection of 8 to bring on vacation.
The term 'combination' refers to the selection of objects from a group without any importance given to their arrangement. It is possible to choose all or part of a set of objects. The order of the selected objects is insignificant in combinations. If you choose a combination of objects, the number of options available to you is defined by the size of the original set and the number of objects to be chosen.If we talk about this particular situation in the question, it is clearly mentioned that we have to choose a certain number of books from a given set of books to take with us on vacation. The order of the books to be selected does not matter. Hence, this situation involves combinations and the answer is A) Combination.
To know more about combinations visit:
https://brainly.com/question/31586670
#SPJ11
Find a basis for the subspace spanned by the given vectors. What is the dimension of the subspace?
\begin{bmatrix} 1\\ -1\\ -2\\ 5 \end{bmatrix},\begin{bmatrix} 2\\ -3\\ -1\\ 6 \end{bmatrix},\begin{bmatrix} 0\\ 2\\ -6\\ 8 \end{bmatrix},\begin{bmatrix} -1\\ 4\\ -7\\ 7 \end{bmatrix},\begin{bmatrix} 3\\ -8\\ 9\\ -5 \end{bmatrix}
A basis for the subspace spanned by the given vectors is:
\begin{bmatrix} 1\\ -1\\ -2\\ 5 \end{bmatrix},\begin{bmatrix} 2\\ -3\\ -1\\ 6 \end{bmatrix},\begin{bmatrix} 0\\ 2\\ -6\\ 8 \end{bmatrix}
The dimension of the subspace is 3.
The given vectors form a set of vectors that span a subspace. To find a basis for this subspace, we need to determine a set of vectors that are linearly independent and span the entire subspace.
To begin, we can set up the given vectors as columns in a matrix:
\begin{bmatrix} 1 & 2 & 0 & -1 & 3\\ -1 & -3 & 2 & 4 & -8\\ -2 & -1 & -6 & -7 & 9\\ 5 & 6 & 8 & 7 & -5 \end{bmatrix}
We can perform row reduction on this matrix to find the row echelon form. After row reduction, we obtain:
\begin{bmatrix} 1 & 0 & 0 & -1 & 3\\ 0 & 1 & 0 & -2 & 4\\ 0 & 0 & 1 & 1 & -2\\ 0 & 0 & 0 & 0 & 0 \end{bmatrix}
The row echelon form tells us that the fourth column is not a pivot column, meaning the corresponding vector in the original set is a linear combination of the other vectors. Therefore, we can remove it from the basis.
The remaining vectors correspond to the pivot columns in the row echelon form, and they form a basis for the subspace. Hence, a basis for the subspace spanned by the given vectors is:
\begin{bmatrix} 1\\ -1\\ -2\\ 5 \end{bmatrix},\begin{bmatrix} 2\\ -3\\ -1\\ 6 \end{bmatrix},\begin{bmatrix} 0\\ 2\\ -6\\ 8 \end{bmatrix}
The dimension of the subspace is equal to the number of vectors in the basis, which in this case is 3.
Learn more about vectors
brainly.com/question/31265178
#SPJ11
Let f(x) f¹(x) 1 x+4 = Question 2 Find a formula for the exponential function passing through the points (-1,- y = 2 pts 1 Details 3 pts 1 Details 5 3) and (2,45)
Given, `f(x) f¹(x) = 1/(x + 4)`
We need to find the exponential function passing through the points (-1,-5) and (2,45).Let, y = ae^(bx)
Here, we have two unknowns a and b.
To find them we will use the given points
(-1,-5) and (2,45).Putting (x,y) = (-1,-5) in the equation of exponential function,
we get-5 = ae^(-b) ----(1)Putting (x,y) = (2,45) in the equation of exponential function,
we get45 = ae^(2b)-----(2)
[tex]Dividing equation (2) by equation (1), we get:45/-5 = e^(2b)/e^(-b) = > -9 = e^(3b) = > ln(-9) = 3b = > b = ln(-9)/3Therefore, putting value of b in equation (1), we get:-5 = ae^(-ln(-9)/3) = > -5 = a(-9)^(1/3) = > a = -5/-9^(1/3)[/tex]
Hence, the required formula for the exponential function is:y = (-5/-9^(1/3))*e^(ln(-9)x/3) or y = (5/9^(1/3))*e^(-ln9x/3
)Therefore, the required exponential function is y = (5/9^(1/3))*e^(-ln9x/3).
To know more about exponential function visit:
https://brainly.com/question/26130204
#SPJ11
\Finding percentiles for Z~N(0;1). Question 6: Find the z-value that has an area under the Z-curve of 0.1292 to its left. Question 7: Find the z-value that has an area under the Z-cu
To find the z-value that has an area under the Z-curve of 0.1292 to its left, the z-value that has an area under the Z-curve of 0.8508 to its left is 1.04.
If we know the area to the left of a certain z-value on the standard normal distribution, we can use the standard normal distribution table to determine the z-value corresponding to that area. Using the table, we look for the area closest to 0.1292, which is 0.1292, in the left-hand column.0.1292 lies between 0.12 and 0.13 in the left-hand column of the standard normal distribution table.
In the top row, we look for the number 0.00 since we're dealing with a standard normal distribution. We now follow the row and column that correspond to 0.12 and 0.00, and we find the value 1.10 in the body of the table. Since the area to the left of z is 0.1292, z must be -1.10 to satisfy this requirement. Therefore, the z-value that has an area under the Z-curve of 0.1292 to its left is -1.10.
To find the z-value that has an area under the Z-curve of 0.8508 to its left:If we know the area to the left of a certain z-value on the standard normal distribution, we can use the standard normal distribution table to determine the z-value corresponding to that area.Using the table, we look for the area closest to 0.8508, which is 0.8508, in the left-hand column. 0.8508 lies between 0.84 and 0.85 in the left-hand column of the standard normal distribution table.
In the top row, we look for the number 0.00 since we're dealing with a standard normal distribution. We now follow the row and column that correspond to 0.84 and 0.00, and we find the value 1.04 in the body of the table. Since the area to the left of z is 0.8508, z must be 1.04 to satisfy this requirement. Therefore, the z-value that has an area under the Z-curve of 0.8508 to its left is 1.04.
More on z-value: https://brainly.com/question/22068540
#SPJ11
Use the Composite Trapezoidal rule with n = 4 to approximate f f(x)dx for the 2 following data x f(x) f'(x)
2 0.6931 0.5
2.1 0.7419 0.4762
2.2 0.7885 0.4545
2.3 0.8329 0.4348
2.4 0.8755 0.4167
By applying the Composite Trapezoidal rule with n = 4 to the given data, we approximated the integral of f(x)dx as 0.14679. The method involved dividing the interval into subintervals and using the trapezoidal rule within each subinterval to calculate the area. The areas of all subintervals were then summed up to obtain the approximation of the integral.
To apply the Composite Trapezoidal rule, we divide the interval [2, 2.4] into four equal subintervals: [2, 2.1], [2.1, 2.2], [2.2, 2.3], and [2.3, 2.4]. Within each subinterval, we can calculate the area using the trapezoidal rule, which approximates the integral as the sum of the areas of trapezoids formed by adjacent data points.
For the first subinterval [2, 2.1], we have the data points (2, 0.6931) and (2.1, 0.7419). Using the trapezoidal rule, we find the area of the trapezoid as (0.1/2) * (0.6931 + 0.7419) = 0.03655.
Similarly, we calculate the areas for the remaining subintervals: [2.1, 2.2], [2.2, 2.3], and [2.3, 2.4]. For [2.1, 2.2], the area is (0.1/2) * (0.7419 + 0.7885) = 0.036725. For [2.2, 2.3], the area is (0.1/2) * (0.7885 + 0.8329) = 0.03659. And for [2.3, 2.4], the area is (0.1/2) * (0.8329 + 0.8755) = 0.036925.
Finally, we sum up the areas of all subintervals to approximate the integral of f(x)dx. Adding up the calculated areas, we have 0.03655 + 0.036725 + 0.03659 + 0.036925 = 0.14679.
Visit here to learn more about integral:
brainly.com/question/30094386
#SPJ11
The average of a sample of high daily temperature in a desert is 114 degrees F. a sample standard deviation or 5 degrees F. and 26 days were sampled. What is the 90% confidence interval for the average temperature? Please state your answer in a complete sentence, using language relevant to this question.
The 90% confidence interval for the average temperature in the desert is between 111.14 and 116.86 degrees Fahrenheit.
We have,
The average of a sample of high daily temperature in a desert is 114 degrees F. a sample standard deviation or 5 degrees F. and 26 days were sampled.
First, we need to determine the standard error of the mean (SEM), which is calculated by dividing the sample standard deviation by the square root of the sample size:
SEM = 5 / √(26) = 0.9766
Next, we need to find the critical value for a 90% confidence interval using a t-distribution table with (26 - 1) degrees of freedom.
This gives us a t-value of 1.706.
We can now calculate the margin of error (ME) by multiplying the SEM with the t-value:
ME = 0.9766 x 1.706 = 1.669
Finally, we can find the confidence interval by subtracting and adding the margin of error to the sample mean:
Lower limit = 114 - 1.669 = 112.331
Upper limit = 114 + 1.669 = 115.669
Therefore, the 90% confidence interval for the average temperature in the desert is between 111.14 and 116.86 degrees Fahrenheit.
Learn more about the standard deviation visit:
https://brainly.com/question/475676
#SPJ4
The ages of the members of three teams are summarized below. Team Mean score Range A 21 8 B 27 6 C 23 10 Based on the above information, complete the following sentence. The team. ✓is more consistent because its A B range is the highest mean is the smallest C mean is the highest range is the smallest
The team that is more consistent because its range is the smallest.
The term "consistency" refers to the measure of how close or spread out the values are within a dataset. In this context, we can compare the consistency of the teams based on their ranges.
The range of a dataset is the difference between the maximum and minimum values. A smaller range indicates that the values within the dataset are closer together and less spread out, suggesting greater consistency.
Given the information provided:
Team A: Mean = 21, Range = 8
Team B: Mean = 27, Range = 6
Team C: Mean = 23, Range = 10
Comparing the ranges of the teams, we can see that Team B has the smallest range of 6, indicating that the ages of the team members are relatively closer together and less spread out compared to the other teams. Therefore, we can conclude that Team B is more consistent in terms of the age distribution of its members.
To learn more about statistics:
https://brainly.com/question/31538429
#SPJ11
find the distance, d, between the point s(2,5,3) and the plane 1x 10y 10z=3.
The distance between the point s(2,5,3) and the plane 1x + 10y + 10z = 3 is approximately 24.51 units.
The given plane is 1x + 10y + 10z = 3 and the point is s(2,5,3). We have to find the distance, d, between the point s and the given plane.
To find the distance, we need to use the formula:
[tex]|AX + BY + CZ + D| / √(A² + B² + C²)[/tex],
where A, B, C are the coefficients of x, y, z in the equation of the plane and D is the constant term, and (X, Y, Z) is any point on the plane.
In this case, the coefficients are A = 1, B = 10, C = 10, and D = 3, and we can take any point (X, Y, Z) on the plane. Let's take X = 0, Y = 0, and solve for Z:
[tex]1(0) + 10(0) + 10Z = 3 = > Z = 3/10[/tex]
So a point on the plane is (0, 0, 3/10). Now, let's plug in the values into the formula:
[tex]|1(2) + 10(5) + 10(3) - 3| / √(1² + 10² + 10²)≈ 24.51[/tex]
Therefore, the distance between the point s(2,5,3) and the plane 1x + 10y + 10z = 3 is approximately 24.51 units.
To know more about point visit:
https://brainly.com/question/7819843
#SPJ11
