The division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 will have a quotient of 2x³ + x² +3x -5 and a remainder of 47 using the remainder theorem.
What is the remainder theoremThe remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a).
We shall divide the 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 as follows;
x⁴ divided by 3x equals 2x³
3x + 4 multiplied by 2x³ equals 6x⁴ + 8x³
subtract 6x⁴ + 8x³ from 6x⁴ + 11x³ + 13x² - 3x + 27 will give us 3x³ + 13x² - 3x + 27
3x³ divided by 3x equals x²
3x + 4 multiplied by x² equals 3x³ + 4x²
subtract 3x³ + 4x² from 3x³ + 13x² - 3x + 27 will give us 9x² - 3x + 27
9x² divided by 3x equals 3x
3x + 4 multiplied by 3x equals 9x² + 12x
subtract 9x² + 12x from 9x² - 3x + 27 will give us -15x + 27
-15x divided by 3x equals -5
3x + 4 multiplied by -5 equals -15x - 20
subtract -15x - 20 from -15x + 27 will result to a remainder of 47
using the remainder theorem, x = -4/3 from the the divisor 3x + 4
thus:
f(-4/3) = 6(-4/3)⁴ + 11(-4/3)³ + 13(-4/3)² - 3(-4/3) + 27 {putting the value -4/3 for x}
f(-4/3) = (1536/81) - (704/27) + (208/9) + (12/3) + 27
f(-4/3) = (1536 - 2112 + 1872 + 324 + 2157)/81 {simplification by taking the LCM of the denominators}
f(-4/3) = (5919 - 2112)/81
f(-4/3) = 3807/81
f(-4/3) = 47
Therefore, the quotient of after the division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 is 2x³ + x² +3x -5 and there is the remainder of 47 using the remainder theorem.
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2. Dottie needs to learn a total of 24 vocabulary words. She has learned 75% of the words.
How many of her vocabulary words did she learn so far?
A. 3
B. 6
C. 18
D. 21
the formula would be used to find a) the first quartile of a data set using the inclusive method. b) the third quartile of a data set using the exclusive method. c) the first quartile of a data set using the exclusive method. d) the median of a data set using the inclusive method.
The given formula would be used to find the first quartile of a data set using the exclusive method.
What is quartile?
A quartile is a type of quantile used in statistics that divides the total number of data points into four roughly equal parts, or quarters. To compute quartiles, the data must be arranged from smallest to largest; therefore, quartiles are a type of order statistic.
The given formula is [tex]L_P = (n + 1)\frac{25}{100} \\[/tex]
This formula can also be written as,
[tex]R = (n + 1)\frac{25}{100}[/tex]
where 25 is the percentile of the data set.
So, the option (c) is correct.
The first quartile of a data set using the exclusive method.
Hence, the given formula would be used to find the first quartile of a data set using the exclusive method.
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The mean of the data set 5, 10, 2, 1 and x is 5. What is the value of x ?
1 point
A) 5
B) 7
C) 13
D) 18
Answer: b) 7
Step-by-step explanation:
mean = average of the data
[tex]mean = \frac{sum of all terms}{total number of terms}[/tex]
[tex]5 = \frac{5+10+2+1+x}{5}\\ 25 = 18+x\\\\25 - 18 = x\\\\7= x[/tex]
Which of the following is a solution of the equation 3x-7 = 7-4x
Answer:
x = 2
Step-by-step explanation:
⭐What is the solution of an equation?
the value of the variable that makes LHS (the left-hand side) equal RHS (the right-hand side)Thus, we need to solve for x, the variable.
Given:
3x - 7 = 7 - 4x
To solve for x, we need to have all the variables on the LHS (or RHS), and all the constants on the RHS (or LHS).
To do so, first add 4x to the LHS and RHS. This "moves" -4x to the LHS:
3x +4x - 7 = 7 +4x -4x
Add like terms (terms with the same variable) to simplify:
7x - 7 = 7
Next, add 7 to the LHS and RHS. This "moves" -7 to the RHS:
7x +7 -7 = 7 +7
7x = 14
Finally, divide the LHS and RHS by 7 to isolate the variable:
[tex]\frac{7x}{7} = \frac{14}{7}[/tex]
∴ x = 2
⭐ if this response helped you, please mark it the brainliest!⭐
Consider the differential equation: dy/dx=ey(3x2-6x)
a) Sketch a slope field for the given equation and include six points on the graph.
b) FInd y=f(x), the particular solution to the differential equation that passes through (1,0).
c) Write an equation for the tangent line to the graph of f at the point (1,0). Use the tangent line to approximate f(1,2).
F(x)= -ln(-x3+3x-1) is a particular solution to the differential equation that passes through (1, 0). An equation for the tangent line to the graph of f at the point (1,0) = -3.
b.[tex]\frac{dy}{e^y} = (3x^2-6x)dx\\[/tex]
∫[tex]e^{-y} dy =[/tex] ∫[tex](3x^2-6x)dx[/tex]
[tex]-1e^{-y} = x^3-3x^2+C\\e^{-y} = -x^3+3x^2+C_{2}\\ -y= ln(-x^3+3x^2+C_{2}) \\y=-ln(-x^3+3x^2+C_{2}[/tex]
Given (1,0)
[tex]0= -ln (-1+3+C)\\0=ln_{c} (2+C)\\e^{0} = 2+C\\-1=C\\so f(x)= -ln(-x^3+3x^2-1)\\[/tex]
f(1.2)=-.465 as the actual value.
c. tangent line slope at (1,0).[tex]= e^0 (3(1)^2-6(1))\\[/tex]
[tex]=-3[/tex]
Line equation: y= 3(x-1) or y= 3x + 3
with f(1,2)=-3(1.2)+3 =-.6
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Consider the graph of the line y = 1//2x – 4 and the point (−4, 2). The slope of a line parallel to the given line is . A point on the line parallel to the given line, passing through (−4, 2), is . The slope of a line perpendicular to the given line is . A point on the line perpendicular to the given line, passing through (−4, 2), is ✔ (–2, –2) .
For the given line y = 1/2x - 4,
The slope of the line parallel to the given line is m = 0.The point on the line parallel to the given line, passing through (-4, 2) is (0, 4) and its equation is x - 2y + 8 = 0.The slope of the line perpendicular to the given line is m = -2.The point on the line perpendicular to the given line, passes through (-4, 2) is (-2, -2) and its equation is y = -2x - 6.How to calculate the slopes and equations of parallel and perpendicular lines of a line?Consider a line with the equation ax+by+c=0
The slope of the line is m = -b/a.The slope of the line parallel to the given line is m = 0.The slope of the line perpendicular to the given line is m = a/b or the product of their slopes equal to -1.The equation of the line parallel to the given line and passing through the point (x1, y1) is a(x - x1) + b(y - y1) = 0.The equation of the line perpendicular to the given line and passing through the point (x1, y1) is b(x - x1) - a(y - y1) = 0.Calculation:It is given that, the equation of a line is given as y = 1/2x - 4.
The slope of the given line is m = 1/2; (since it is in the form of y=mx+c)
Then, the slope of the line parallel to the given line is m = 0.
And the equation of the parallel line passing through the point (-4, 2) is
a(x - x1) + b(y - y1) = 0; where a = 1; b = -2 (y = 1/2x-4 ⇒ 2y = x - 8)
⇒ 1(x + 4) - 2(y - 2) = 0
⇒ x + 4 -2y + 4 = 0
⇒ x - 2y +8 = 0
So, the point on the parallel line is (0, 4).
The slope of the line perpendicular to the given line is m = -1/1/2 = -2.
And the equation of the perpendicular line passing through the point (-4, 2) is
b(x - x1) - a(y - y1) = 0; where a = 1; b = -2;
⇒ -2(x + 4) - 1(y - 2) = 0
⇒ -2x - 8 - y +2 = 0
⇒ y = -2x - 6
So, the point on the perpendicular line is (-2, -2).
All of these are shown in the graph below:
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Rhett drove 50 miles East then 40 miles North. How many miles would Rhett have driven directly from the starting point to the end point? (Round to the nearest mile)
Answer:
[tex]\sqrt{4100}[/tex]
Step-by-step explanation:
Step 1 Substitute Using Pythagorean Theorem:
x = [tex]\sqrt{50^2+40^2}[/tex]
Step 2 Solve:
[tex]50^2=2500[/tex]
[tex]40^2=1600[/tex]
Therefore,
[tex]\sqrt{50^2+40^2}=\sqrt{4100}[/tex]
before agreeing to purchase a large order of polyethylene sheaths for a particular type of high-pressure oil-filled submarine power cable, a company wants to see conclusive evidence that the true standard deviation of sheath thickness is less than .05mm. what hypotheses should be tested? what are the type i and type ii errors?
Hypothesis is tested as H₀: σ = 0.05 mm versus H₁: σ < 0.05 mm.
The type I error occurs if we accept a shipment that should have been rejected .
A type II error occurs if we reject a shipment that should have been accepted.
Given that,
A corporation wants to see concrete proof that the genuine standard variation of sheath thickness is less than 0.05mm before committing to a significant order of polyethylene sheaths for a certain kind of high-pressure oil-filled submarine power line.
We have to find what theories need to be tested and what exactly are types I and ii errors.
We know that
H₀: σ = 0.05 mm
versus
H₁: σ < 0.05 mm.
In this context,
The type I error occurs if we accept a shipment that should have been rejected .
A type II error occurs if we reject a shipment that should have been accepted.
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if angle A=125 in the parallelogram below, what is the measure of angle B?
Answer:
angle B = 55°
.............
The maker of an automobile advertises that it takes 11 seconds to accelerate from 25 kilometers per hour to 75 kilometers per hour. Assuming constant acceleration, compute the distance, in meters, the car travels during the 11 seconds. Round your answer to two decimal places. 168.06 m 152.78 m 305.56 m 76.39 m 32.73 m
The value of the acceleration is 1.26 m/s² for the automobile advertised by the makers.
Explain the equation of motion?motion is shift in a body's orientation or position over time. Translation is defined as movement across a line or a curve. Rotation is a motion that modifies a body's orientation.Time t = 11 sec
Initial velocity u = 25 kmph
u = (25 × 1000)/(60 × 60) = 6.9 m/s
final velocity v = 75 kmph
v = (75 × 1000)/(60 × 60) = 20.83 m/s
From the first equation of motion;
v = u + at
Put the values;
20.83 = 6.9 + 11a
20.83 - 6.9 = 13a
11a = 13.93
a = 13.93 / 11
a = 1.26 m/s²
Thus, the value of the acceleration is 1.26 m/s² for the automobile advertised by the makers.
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Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.i) 4x² - 3x + 7 ii) y² + √2 iii) 3√t + t√2 iv) y + (2/y) v) x10 + y3 + t50
(A) 4x² - 3x + 7 and (B) y² + √2 are polynomials with one variable and the rest are not.
What are polynomials?A polynomial is a mathematical equation made up of coefficients and indeterminates that exclusively uses the operations of addition, subtraction, multiplication, or powers of positive numbers of the variables.
x² - 4x + 7 is an illustration of a quadratic with a solitary indeterminate x.
(A) 4x² - 3x + 7:
'x' is the only variable in the provided polynomial.
As a result, the polynomial 4x² - 3x + 7 has one variable.
(B) y² + √2:
'Y' is the only variable in the provided polynomial.
y² + √2 is a polynomial in one variable as a result.
(C) 3√t + t√2:
Since the power of the variable in the first term is 1/2, which is not a whole integer, 3√t + t√2 is not a polynomial.
(D) y + (2/y):
Because the power of the variable in the second term is -1, which is not a whole number, y + 2y⁻¹ is not a polynomial.
(E) x¹⁰ + y³ + t⁵⁰
Due to the fact that x, y, and t are all three variables, x¹⁰ + y³ + t⁵⁰ is not a polynomial in one variable.
Therefore, (A) 4x² - 3x + 7 and (B) y² + √2 are polynomials with one variable and the rest are not.
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because of limited space availability and a desire to provide an acceptable level of service, the bank manager would like to have no more than three cars in the system at any time (waiting in line or being served). what is the probability that there are no more than 3 cars in the system?
The probability that there are no more than 3 cars in the system is 0.50
Probability:
In math, the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes is referred as probability.
Given,
Because of limited space availability and a desire to provide an acceptable level of service, the bank manager would like to have no more than three cars in the system at any time.
Here we need to find the probability that there are no more than 3 cars in the system.
Here we know that the present level of service for three or fewer cars is the probability that there are 0, 1, 2, or 3 cars in the system.
As per the Model 1, Exhibit 8A.8, the probability of having more than three cars in the system is 1.0 minus the probability of three or fewer cars => 1.0 − 0.685 = 31.5 percent
And the 95 percent service level of three or fewer cars, this states that
=> P0 + P1 + P2 + P3 = 95 percent.
When we can solve this by trial and error for values of λ/μ.
Therefore, the value of λ/μ = 0.50
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Is (6, 4) a solution to this system of
y = 2x - 8
y = -1/3x + 6
3
yes
no
(This is on IXL)
Answer:
Yes
Step-by-step explanation:
y = 2x - 8 Plug is 6 for x and 4 for y
4 = 2(6) - 8
4 = 12 - 8
4 = 4
(6,4) is a solution for this equation
y = -1/3 x + 6
4 = -1/3(6) + 6
4 = -2 + 6
4 = 4
(6,4) is a solution for this equation too.
How do you solve 2=11+3(m+3)?
Answer: m= -6
Step-by-step explanation: 2 = 11 + 3m + 9
3m = 2 - 11 - 9
3m = -18
Divide both sides by 3.
m= -6
Answer:
m = -6
Step-by-step explanation:
Step by step explanation:
2-11 = 3m+9 ==》3m = -18 ==》m = -18/3 ==》m= -6
a better understanding of how I can solve for 1/2d-3/4d+3f-2f
The simplified form of the given expression is, 1/4d + f.
What is simplified form of the expression?
To simplify an expression, create an equivalent expression without any terms that are similar.
The expression will then be rewritten using the fewest terms possible.
Mathematical operations can be made much simpler by using the right order of operations. Exponents, terms in parentheses, multiplication, division, addition, and finally subtraction are the correct order of operations.
Consider the given expression,
1/2d - 3/4d + 3f - 2f
Here the like terms are '1/2d and 3/4d' and '3f and 2f'.
To simplify the expression,
1/4d + f
Hence, the simplified form of the given expression is, 1/4d + f.
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A prestigious program accepts 2 out of every 9 applicants per yer. if the program accepted 360 applicants, how many applicants were not accepted?
The number of applicants that were not accepted are calculated to be 1260.
The number of applicants that were not accepted can be determined as follows;
Since 2 out of every 9 applicants are accepted; therefore the total number of applicants out of which 360 applicants were accepted can be calculated as follows;
360 × 9 / 2 = 3240 / 2 = 1620
Therefore the total number of applicants is calculated to be 1620, out of these 1620 applicants, 360 were accepted therefore the number of applicants that were not accepted can be determined by subtraction.
The number of applicants that were not accepted can be determined by subtracting the accepted applicants from the total number of applicants as follows;
Applicants not accepted = 1620 - 360
Applicants not accepted = 1260
Therefore 1260 applicants were not accepted by the program.
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Please help soon on functions problem, thanks!
Answer:
g(0) = 3
Step-by-step explanation:
x=0 fits perfectly in the range -1<x<2: -1<0<2 √
Hence:
g(x)=3 when x=0
Since x=0:
g(x) = g(0) = 3
There are 95 green balls and 90 red balls in a box. How many balls must be chosen to
be certain we have the following?
One red and one green?
The number of balls that must be chosen to be certain we have One red and one green is; 5 balls.
What is the probability of selection?We are given;
Number of green balls in box = 95 balls
Number of red balls in box = 90 balls
Thus;
Total number of balls in the box = 95 + 90
Total number of balls in the box = 185 balls
Now, the probability of getting one red from selection = 90/185
Probability of getting one green ball = 95/185
P(Red and Green) = P(R) * P(G)
P(R and G) = = (90/185) * (95/185) = 0.2418
However, in this case we will make use of the unitary method which is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Thus, minimum number of balls to get the given selection = 95 - 90 = 5 balls
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Rectangular prism A is similar to rectangular prism B. The ratio of the surface of A to B is 4:1. If the volume of rectangular prism B is 12 cm3 , what is the volume of rectangular prism A?
The volume of rectangular prism A will be 48 cm³
How to find area of Rectangular Prism?
The volume of a rectangular prism is given by the formula:
A = lwh
Where:
l = length
w = width
h = height.
Since the surface ratio of rectangular prism A to rectangular prism B is 4:1, the ratio of the linear dimensions of A to B must also be 4:1.
This means that if one linear dimension of rectangular prism A is 4 times the size of the corresponding dimension of rectangular prism B, then all of the linear dimensions of A will be 4 times the size of the corresponding dimensions of B.
Since the volume of a rectangular prism is given by the product of its linear dimensions.
The volume of rectangular prism A will be 4 times the volume of rectangular prism B.
Therefore, if the volume of rectangular prism B is 12 cm³, the volume of rectangular prism A will be 4 * 12 cm³ = 48 cm³.
Hence, The volume of rectangular prism A will be 48 cm³.
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suppose s1, 1d is a critical point of a function f with contin- uous second derivatives. in each case, what can you say about f?
In each case, for a) f has local maximum at (1,1) and for b) f has saddle point at (1,1).
a) f_{xx}f_{yy}-(f_{xy})2
=(-4)(-2)-(1)2
=8-1
=7>0
f_{xx}=-4<0
Therefore, f has local maximum at (1,1)
b) f_{xx}f_{yy}-(f_{xy})2
=(-4)(-2)-(3)2
=8-9
=-1<0
Therefore, f has saddle point at (1,1)
A factor at which a feature of variables has partial derivatives identical to 0 however at which the feature has neither a most nor a minimal value.
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Complete question:
Suppose (1, 1) is a critical point of a function f with continuous second derivatives. In each case, what can you say about f?a) f_{xx}f_{yy}-(f_{xy})2 and b) f_{xx}f_{yy}-(f_{xy})2
How many solutions does the equation
-1/2(-8x+14) = 3x +9+x have?
The no: of solutions that the equation -1/2(-8x+14) = 3x +9+x has is 1
What is an example of an equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
What are the 3 types of equations?There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.
The no: of solutions that the equation is -1/2(-8x+14) = 3x +9+x is 1
as the equation is 1 degree polynomial.
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Sarah uses three and one half pounds of clay to make 14 small vases. Use a proportion to find how many pounds of clay she will use to make 31 small vases.
12 and one half pounds
8 and three fourths pounds
7 and three fourths pounds
6 and one half pounds
Sarah needs 7 and three-fourths of pounds of clay to make 31 small vases. By using the proportion of pounds of clay to the number of small vases, the required value is calculated.
What are proportions?Proportions are equations in which two ratios are made equal to each other. By using these we can relate a part to a whole. The formula for the proportions is written as
a : b = c : d or a/b = c/d or ad = bc
Here the variables a and d are said to be the extreme terms and the variables b and c are the mean terms.
Mostly used proportions are inverse proportion, direct proportion, compound proportion, etc.
Calculation:Given that,
Sarah uses 3 and 1/2 pounds of clay to make 14 small vases.
And x pounds of clay to make 31 small vases.
So, applying the proportions formula for finding the x value as
[tex]3\frac{1}{2}:x=14:31[/tex]
Then, we can write them as
bc = ad ⇒ 14x = 7/2 × 31
⇒ 14x = 217/2
⇒ x = 217/28
⇒ x = 7.75 = [tex]7\frac{3}{4}[/tex]
Therefore, Sarah needs 7 and three-fourths pounds of clay to make 31 small vases. So, option C is correct.
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A pyramid has a square base with Side s. The height of the pyramid is 2/3 that if it’s side. What is the expression of the volume of the pyramid
The expression for the volume of the pyramid is V = 2/9s^3
Volume of a pyramid
To find the volume of a pyramid, we multiply the area of its base with the height of the pyramid, and divide by 3. We express this product with the formula V=(1/3)×B×H, where B is the area of the base of the pyramid, and H is its height.
The volume of a pyramid is:
V=1/3(B)(H)
Where
B:Base = s^2
H:Height = 2/3s
Then:
V=1/3(B)(H) = 1/3(s^2)(2/3s) = 2/9s^3
Hence, the expression for the volume of the pyramid is V = 2/9s^3
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Bruno Fruscalzo decided to start a small production facility in Sydney to sell gelato to the local restaurants. His local milk supplier charges $0.5 per kg of milk plus a $15 delivery fee (that is independent of the amount ordered). Bruno’s holding cost is $0.03 per kg per month. He needs 9250 kgs of milk per month.
a. Suppose Bruno orders 9750 kgs each time. What is his average inventory (kgs)? 4,875 kgs
(Round your answer to 1 decimal place.)
b. Suppose Bruno orders 6250 kgs each time. How many orders does he place with his supplier each year? 1.0 orders
c. How many kgs should Bruno order from his supplier with each order to minimize the sum of ordering and holding costs? 15 kgs
(Do not round intermediate calculations. Round your answer to 2 decimal places.)
d. If Bruno’s storage vessel can hold only 2000 kgs of milk, what would be Bruno’s annual ordering and holding costs?
(Do not round intermediate calculations. Round your answer to 2 decimal places.)
e. If Bruno’s storage vessel can hold only 5750 kgs of milk, what would be Bruno’s annual ordering and holding costs?
(Do not round intermediate calculations. Round your answer to 2 decimal places.)
f. Bruno’s supplier’s truck can carry 20,000 kgs of milk. The supplier does not want to deliver to more than 3 customers with each truck. Thus, the supplier requires a minimum order quantity of 6,500 kgs. If Bruno orders the minimum amount, what would be the sum of his annual ordering and holding costs? Assume he has a storage vessel large enough to hold 6,500 kgs.
(Round your answer to 3 decimal places.)
g. Bruno’s supplier offers a 4% discount when a customer orders a full truck, which is 20,000 kgs. Assume Bruno can store that quantity and the product will not spoil. If Bruno orders a full truck, what would be the inventory holding and ordering cost incurred per kg of milk? Assume the discount also applies to the holding cost.
1 decimal places required.
The cost of the milk from the supplier can be calculated as follows:
Cost of milk = (price per kg of milk) * (number of kg of milk) + delivery fee
= $0.5/kg * 9250 kg + $15
= $<<0.5*9250+15=4675>>4675
The holding cost of the milk can be calculated as follows:
Holding cost = (holding cost per kg per month) * (number of kg of milk)
= $0.03/kg/month * 9250 kg
= $<<0.03*9250=277.5>>277.5
Therefore, the total cost of the milk for Bruno's production facility is $4675 for the milk from the supplier and $277.5 for the holding cost, for a total of $4952.5.
A line has a slope of 1 and passes through the point (–3, –13)What is its equation in slope intercept form?
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
The equation of the line is
y = x - 10.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The line has,
Slope = 1
Passes through = (-3, -13)
Now,
The equation of a line is given as,
y = mx + c
Put (-3, -13) = (x, y)
-13 = 1 x (-3) + c
-13 = -3 + c
c = -13 + 3
c = -10
Now,
The equation of the line.
y = 1x - 10
y = x - 10
Thus,
The equation of the line is
y = x - 10.
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for each graph caculate the slope of each line
Answer: -5/4
Step-by-step explanation:
The slope is rise/run or y2 - y1/ x2 - x1
The two points are (-6,-3) (-2, -8)
The y decreases by 5 and the x increase by 4
So the slope is -5/4
evaluate the integral by interpreting it in terms of areas. 0 36 − x2 dx −6
The value of the original integral is 42, as expected.
What must an answer about a indefinite integral of a function include?
A definite integral is an infinitesimal sum derived from a integrable function, that is, a function that exist for all value x within the range of integration.
To evaluate this integral, we can interpret it in terms of the area of a region. To do this, we can rewrite the integral as:
∫0 36 − x2 dx −6
= ∫0 36 x2 dx + ∫0 36 dx
= ∫x2 dx + ∫dx
The first integral on the right-hand side represents the area under the curve y = x^2 from x = 0 to x = 6.
The second integral on the right-hand side represents the area of the rectangle with base 6 and height 1, which is just 6.
Therefore, the original integral can be interpreted as the sum of the area under the curve y = x^2 from x = 0 to x = 6 and the area of the rectangle with base 6 and height 1. This area is equal to 36 + 6 = 42. Thus, the value of the original integral is 42.
We can also verify this result using the formula for the area under a curve:
∫x2 dx = (1/3) x3 + C
Substituting the limits of integration, we get:
∫0 6 x2 dx = (1/3) * 6^3 - (1/3) * 0^3
= (1/3) * 216
= 72
Therefore, The value of the original integral is 42, as expected.
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! if f( n + 1) = f(n) + 2 and f(2) = 4 then f(4) =
explain
Answer: 8
Step-by-step explanation:
From our knowledge, we know two things.
f(n + 1) = f(n) + 2f(2) = 4From here, we can work out what f(3) is by substituting n as 2
f(2 + 1) = f(2) + 2
f(3) = 4 + 2 = 6
And we can work out f(4) by substituting n as 3
f(3 + 1) = f(3) + 2
f(4) = 6 + 2 = 8
Eventually, if you continue doing this, you will see a sequence forming where the next number is the previous number added by 2.
A brick wall 4.3 m by 2.4 m is to be built. How
many bricks will be needed if there are 40 bricks
per m2? (round up to the nearest whole brick)
Help
Please
413 bricks are needed to build a wall whose area is equivalent to 10.32 m².
What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Given is that a brick wall of dimension 4.3 m by 2.4 m is to be built. There are 40 bricks per m².
The area of the wall will be -
[A] = 4.3 x 2.4 = 10.32 m²
[A] = 10.32 m²
Now, for the area of 1 m², 40 bricks are needed. So, for 10.32 m², we can say that -
10.32 x 40
412.8
413 bricks.
Therefore, for the area of 10.32 m², to only 413 bricks are needed to build it.
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Please help asap
The number of people attending Convention A can be modeled by
f(x) = 1200 • 0.95^x, where x is the number of years that the convention has been
occurring. The number of people attending Convention B was 2200 in year 1 and 2100 in year 2. Which convention’s attendance is decreasing at a greater rate? Explain your reasoning.
For the given conditions convention B attendance is decreasing at a greater rate.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that, the number of people attending convention A can be modeled by the function as,
f(x) = 1200 • 0.95ˣ
where x is the number of years that the convention has been occurring.
The number of people attending convention A in year 1,
f(x) = 1200 × 0.95¹
f(x) = 1140
The number of people attending convention A in year 2,
f(x) = 1200 × 0.95²
f(x) = 1083
The number of people decreasing in the Convention A,
=1140 - 1083
=57
If the number of people attending Convention B was 2200 in year 1 and 2100 in year 2. The number of people decreasing in the Convention B,
=2200-2100
=100
Thus, for the given conditions convention B attendance is decreasing at a greater rate.
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