Answers
Answer:
Step-by-step explanation:
(a) We can find the position vectors of the points L, M, and N by taking the average of the position vectors of the points they lie between.
The midpoint of AB is given by:
N = (A + B)/2 = (41 + (41 + 21))/2 = (41 + 62)/2 = 51.5i
The midpoint of AD is given by:
L = (A + D)/2 = (41 + 6k)/2 = 23i + 3k
The midpoint of BD is given by:
M = (B + D)/2 = (41 + 21 + 6k)/2 = 31i + 3.5k
Now, we can find the vector MN by subtracting the position vectors of M and N:
MN = M - N = (31i + 3.5k) - (51.5i) = -20.5i + 3.5k
The angle between the directions of MN and OB can be found using the dot product:
cos(θ) = (MN . OB) / (|MN| * |OB|)
where θ is the angle between the two vectors. We can find the dot product and the magnitudes of the vectors as follows:
MN . OB = -20.5i + 3.5k . 41i + 21j = -20.5 * 41 + 3.5 * 21 = -847.5
|MN| = √((-20.5)^2 + (3.5)^2) = 21
|OB| = √(41^2 + 21^2) = √(1764) = 42
Substituting these values into the formula for cos(θ), we get:
cos(θ) = (-847.5) / (21 * 42) = -0.5
The angle θ can be found from the cosine inverse:
θ = cos^-1(-0.5) = 120 degrees
So, the angle between the directions of MN and OB is 120 degrees.
(b) To find the value of p, we can use the intersection of the lines through P and B and the lines through C and L. Let's call the intersection point R.
The line through P and B can be represented as P + t(B - P) = R
where t is a scalar and R is the position vector of the intersection point. Similarly, the line through C and L can be represented as:
C + s(L - C) = R
where s is a scalar. Setting these two expressions equal to each other, we get:
P + t(B - P) = C + s(L - C)
Expanding and simplifying, we get:
P + t(41i + 21j + 6k) = 21i + 6s(23i + 3k)
Comparing the i, j, and k components, we get:
P + 41t = 21 + 6s * 23
t = (21 - P)/41
6s = (P - 21)/23
s = (P - 21)/138
Substituting s back into the equation for C + s(L - C), we get:
C + (P - 21)/138 * (L - C) = R
21i + 6k + (P - 21)/138 * (23i + 3k - 6k) = R
Expanding, we get:
21i + 6k + (23/138) * Pi + (3/138) * k = R
Comparing the i and k components, we get:
21 + (23/138) * P = Ri
6 + (3/138) * P = Rk
Solving for P, we get:
P = 138 * (Ri - 21)/23 = 138 * (Rk - 6)/3
So the value of p for which the line through P and B intersects the line through C and L is given by the above formula.
Related Questions
a tire of a moving bicycle has a diameter of 18 inches, if the tire is making 4 rotations per second find the bicycle's speed in miles per hour.
Answers
Speed of bicycle in miles per hour will be 12.85 mi/h.
What is the definition of speed?
The following is the definition of speed:
The rate at which the position of an item changes in any direction.
The ratio of distance travelled to time spent travelling is described as speed. Speed is a scalar number since it has just one direction and no magnitude.
Formula for Speed
The speed formula is as follows:
s=d/t
Where,
s denotes the speed in metres per second, d the distance travelled in metres, and t the time in seconds.
Now,
Given Diameter=18 inch
then distance covered by cycle in 4 rotation in one second =4*π*diameter
=4*22/7*18
=226.28
Then Speed=226.28 in/s
As 1 mike=63360 inch and 1 hour= 3600 seconds
then Speed in miles/hour=226.28*3600/63360
=12.85 mi/h
hence,
Speed of bicycle in miles per hour will be 12.85 mi/h.
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In a particular metal mixture there are:
1 part mercury to 5 parts copper,
3 parts tin to 10 parts copper,
You would need how many parts mercury to how many parts tin?
A) 1:3
B) 2:3
C) 6:13
D) 4:15
Answers
Answer:
B) 2:3
Step-by-step explanation:
If you have mercury : copper = 1 : 5 and tin : copper = 3 : 10, you want the ratio of mercury to tin.
RatioThe ratios can be compared or combined when common components are represented by the same number. Doubling the values in the first ratio, we will have two ratios that both have 10 parts copper.
mercury : copper = 1 : 5 = 2 : 10
Then ...
mercury : tin : copper = 2 : 3 : 10
You need 2 parts mercury to 3 parts tin.
mercury : tin = 2:3 . . . . . . choice B
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Having hard tiMe finding function
Answers
The local maximums are at x = -4 and x = 4, and the value of the local maximum is f(x) = 1.
How to find the local maximums?For a function f(x), we define a local maximum as a value of x = c such that:
f(c) ≥ f(x)
for any value of x in a given interval.
Here we can see two local maximums on the graph, and we can see that these are at:
x = -4 and x = 4
b) And the local maximum value of f is the value that the function takes in the maximum, we can see that:
f(-4) = f(4) = 1
The value of the local maximum is y = 1.
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Find the sum of 4√5 and √5 in simplest form. Also, determine whether the result is
rational or irrational and explain your answer.
Answers
Answer:
See below
Step-by-step explanation:
[tex]4\sqrt{5}+\sqrt{5}=(4+1)\sqrt{5}=5\sqrt{5}[/tex]
This sum is irrational because [tex]\sqrt{5}[/tex] was irrational to begin with.
I need help solving part b)
Answers
The answers to the questions are:
a) P(A|B) = 1/3
b) P(B|A) = 1.15
c) A. A student given a $1 bill is more likely to have kept the money.
What is the probability?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Because the probability of 0.659 is almost two times greater than 0.341
Assuming the following table:
Purchased Gum Kept the Money Total
Students Given 4 Quarters 25 19 44
Students Given $1 Bill 13 26 39
Total 38 45 83
a. find the probability of randomly selecting a student who spent the money, given that the student was given a $1 bill.
For this case let's define the following events
B= "student was given $1 Bill"
A="The student spent the money"
For this case we want this conditional probability:
P(A|B) = P(A And B) / P(B)
We have that
P(A) = 38/83, P(B) = 39/83
P(A And B) = 13/83
And if we replace we got:
P(A|B) = (13/83)/(45/83) = 13/39 = 1/3
b. find the probability of randomly selecting a student who kept the money, given that the student was given a $1 bill.
For this case let's define the following events
B= "student was given a $1 Bill"
A="The student kept the money"
P(A|B) = P(A And B) / P(B)
We have that
P(A) = 45/83, P(B) = 39/83
P(A And B) = 26/83
And if we replace we got:
P(B|A) = (45/83)/(39/83) = 45/39 = 1.15
c. what do the preceding results suggest?
For this case the best solution is:
A. A student given a $1 bill is more likely to have kept the money.
Because the probability of 0.659 is almost two times greater than 0.341
Hence, The answers to the questions are:
a) P(A|B) = 1/3
b) P(B|A) = 1.15
c) A. A student given a $1 bill is more likely to have kept the money.
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Question 3
Sam built the model shown below. It is composed of two rectangular prisms. What is the volume of the figure?
Answers
Answer:
44 in^2
Step-by-step explanation:
V = L×W×H
Bottom rectangle prism
L= 6 W= 4 H= 1
V = 6×4×1
V=24
Top rectangle prism
L= 2 W= 2 H= 5
V=2×2×5
V= 20
Add both of the rectangle prisms
24+25= 44
Kate had some stickers.
She kept 2/5 of them for herself and gave 5/6 of the remaining stickers to 6 of her
friends equally.
(a) What fraction of her stickers did Kate give to her 6 friends?
(b) What fraction of Kate's stickers did each of her 6 friends receive?
Answers
a) The fraction of the stickers that Kate gave to her 6 friends was 1/2.
b) The fraction of Kate's stickers that each friend received from the 1/2 of stickers was 1/12.
What is the fraction?The fraction is the portion or part of a whole.
Fractions can be proper, improper, and complex fractions, depending on the relative value of the numerator and the denominator.
The total number of stickers that Kate possesses = 1/1
The fraction Kate kept for herself = 2/5
The remaining portion of Kate's stickers = 3/5 (1 - 2/5)
The fraction Kate gave to her 6 friends to share equally = 5/6 of 3/5 = 1/2
The fraction of Kate's stickers that each friend received = 1/2 ÷ 6 = 1/12
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By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 299 mg of cholesterol. If the child eats 3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol. By eating 3 eggs and 1 cupcake, a child consumes 834 mg of cholesterol. How much cholesterol is in each item? The quantity of cholesterol in an egg is.....mg, the quantity of cholesterol in a cupcake is.....mg, and the quantity of cholesterol in a slice of pizza is.....mg. (Simplify your answers. Type mixed numerals, if possible. Otherwise, type integers or fractions.)
Answers
The quantity of cholesterol in an egg is 272 mg
The quantity of cholesterol in a cupcake is 18 mg
The quantity of cholesterol in a slice of pizza is 9 mg
How to find the amount of cholesterol in each itemLet the amount of egg be e
Let the amount of cupcake be c
Let the amount of pizza be p
By eating 1 egg, 1 cupcake, and 1 slice of pizza, a child consumes 299 mg of cholesterol
e + c + p = 299
The child eats 3 cupcakes and 4 slices of pizza, he or she takes in 90 mg of cholesterol
3c + 4p = 90
By eating 3 eggs and 1 cupcake, a child consumes 834 mg of cholesterol
3e + c = 834
e + c + p = 299
3c + 4p = 90
3e + c = 834
solving the simultaneous equation gives
e = 270
c = 18
p = 9
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Which equation shows how to rewrite the sum of 42 and 54 using their greatest common factor?
Answers
Answer:69
Step-by-step explanation:
31+38=69
Graph the system of inequalities.
y> 4x-2
2y-x≤8
Answers
The solution of inequalities is (1.714 , 4.857).
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
y > 4x-2
2y-x ≤ 8
Now, solving the inequalities.
y > 4x-2 is given by purple region and 2y-x ≤ 8 is shown by Grey region.
The two lines of inequalities intersect at (1.714 , 4.857).
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Please help question below
Answers
The required equation that Nandita used to make the given graph is y = -3x + 2. Option B is correct.
What is the intercept in the equation?In the equation intercept is the value of the linear function where either of the variables is zero.
Here,
From the graph, we need to identify the y-intercept and then match that intercept with each given in the options So,
From the graph, the y-intercept is ordered where the x coordinate of the pair is zero, So,
(0, y) = (0, 2)
Thus, the required equation among the option is y = -3x + 2.
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A recent study reported the mean body mass index (BMI) for adults in the United States was 26. 8. A researcher believes the mean BMI of marathon runners is less than 26. 8. A random sample of 35 marathon runners had a mean BMI of 22. 7 with a standard deviation of 3. 1. The researcher will conduct a one-sample t-test for a population mean. Have the conditions for inference been met
Answers
Since the samples of the study are independent, the condition for inference have been met
The body mass index for adults in the United States = 26.8
BMI stands for Body Mass Index
Body mass index of marathon runners = less than 26.8
The random samples = 35
The body mass index of the random samples = 22.7
Standard deviation = 3.1
Then the researchers will conduct a one sample t test for a population mean.
The one sample t-test is is defined as the hypothesis test that check whether the unknow population mean is different from the specific value
Here the samples are independent
Therefore, the condition for inference have been met
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The function represented by the data in the table could
model the perimeter of a square whose area is x.
Explain how the function in the table models this
relationship. Be sure to identify how the function
represents area, perimeter, and the length of a side. Then
generalize the pattern in the table.
Type your response in the box.
Answers
Note that the pattern in the table is that the perimeter of a square with area x is four times the square root of x. We can express this relationship as:
f(x) = 4 * √(x)
What is the rationale for the above response?We know that the area of a square is calculated as the square of its side length, which means that the side length of a square with area x is the square root of x. Therefore, the length of the side of the square can be expressed as:
s = √(x)
To calculate the perimeter of the square, we simply add up the lengths of all four sides:
P = 4s = 4 * √(x)
So, the function f(x) in the table represents the perimeter of a square with area x, which can be calculated using the equation:
f(x) = 4 * √(x)
To verify this, let us take these examples:
when x = 1, the area of the square is 1, and the side length is 1. Therefore, the perimeter of the square is 4 * 1 = 4, which matches the value in the first row of the f(x) column.when x = 4, the area of the square is 4, the side length is 2, and the perimeter of the square is 4 * 2 = 8, which matches the value in the second row of the f(x) column, and so on.Learn more about Square Roots:
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A growing giant pumpkin weighs 40.5 pounds on day 18 and 496.3 pounds on day 50. Which equation can be
used to find the weight gain of the giant pumpkin, (pounds), from day 18 to day 50, and what is the value of x?
Answers
The equation of line is y = 14.24375x + 296.8875 , where x is the number of days and y is the total weight gain in x days
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 18 , 40.5 )
Let the second point be Q ( 50 , 496.3 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 496.3 - 40.5 ) / ( 50 - 18 )
Slope m = 455.8 / 32
Slope m = 14.24375
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 40.5 = 14.24375 ( x - 18 )
On simplifying the equation , we get
y - 40.5 = 14.24375x - 256.3875
Adding 40.5 on both sides of the equation , we get
y = 14.24375x + 296.8875
where x is the number of days
Hence , the equation of line is y = 14.24375x + 296.8875
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consider the following: Point (3,5), and Line y-1=0. Write the slope intercept form of the equation of the line through the given point an parallel to the given line.
Answers
Step-by-step explanation:
please see the attached picture
Add a term to the expression so tha it becomes a perfect square trinomial. Y^2-13y+
Answers
The term that should be added to the expression to make the expression perfect square trinomial is 169/4. The expression then becomes : (y - 13/2)²
What is meant by a perfect square trinomial?
By multiplying a binomial by another binomial, perfect square trinomials—algebraic equations with three terms—are created. A number can be multiplied by itself to produce a perfect square. Algebraic expressions known as binomials are made up of simply two words, each of which is separated by either a positive (+) or a negative (-) sign. Similar to polynomials, trinomials are three-term algebraic expressions.
A perfect square trinomial expression can be created by taking the binomial equation's square. If and only if a trinomial satisfying the criterion b² = 4ac has the form ax² + bx + c, it is said to be a perfect square.
Given expression y² - 13y + ?
Comparing with the general equation
a = 1
b = -13
For perfect square trinomial
b² = 4ac
(-13)² = 4 * 1 * c
169 = 4c
c = 169/4
So the expression becomes,
y² - 13y + 169/4 = (y - 13/2)²
Therefore the term that should be added to the expression to make the expression perfect square trinomial is 169/4.
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In how many ways 4-digits numbers can be formed using the digits 1,2,3,7,8,9 without repetition? How many of these are even numbers?How many of these are even numbers?
Answers
We can form 15 different 4-digit numbers using the digits 1, 2, 3, 7, 8, and 9, without repetition. Out of these, 30 are even numbers. We used the concept of combination to find these numbers.
Combination is a mathematical technique used to calculate the number of ways in which a group of objects can be selected from a larger set, without considering their order.
We can use the combination formula to find the total number of possible combinations:
C(4, 3) = 4! / (3! * 1!) = 4
This means that we can form four different 3-digit numbers using the digits 1, 2, 3, and 4, without repetition.
Now, coming back to our original problem, we need to form 4-digit numbers using the digits 1, 2, 3, 7, 8, and 9, without repetition. Using the same combination formula, we can find the total number of possible combinations:
C(6, 4) = 6! / (4! * 2!) = 15
This means that we can form a total of 15 different 4-digit numbers using the given digits.
Next, we need to find out how many of these numbers are even. An even number is a number that is divisible by 2, and in our case, this means that the last digit of the number must be either 2, 8, or a combination of 1 and 7.
To find the number of even 4-digit numbers, we can use the same combination formula, but this time we have to consider only 3 digits (2, 8, and a combination of 1 and 7) for the last digit:
C(3, 1) * C(5, 3) = 3 * 10 = 30
This means that we can form a total of 30 different 4-digit even numbers using the given digits.
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this problem is very confusing pls help me, I will give brainliest
Answers
The required value of the trigonometric function is sin (α - β) = - 10.96/15.
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
The trigonometric ratios are given in the question, as follows:
sin α = -2/5 and cos β = -1/3
So cos α = √1 - (-2/5)² = √(1 - 4/25) = √21/5
And sin β = √1 - (-1/3)² = √(1 - 1/9) = √8/3
We have to determine the value of sin (α - β).
According to trigonometric identity,
sin (α - β) = sinα cos β - cos α sin β
Substitute the values of sin α = -2/5 and cos β = -1/3,
sin (α - β) = (-2/5)( -1/3) - (√21/5)(√8/3)
sin (α - β) = 2/15 - (√21×8)/15
sin (α - β) = 2/15 - (√168)/15
sin (α - β) = 2/15 - 12.96/15
sin (α - β) = - 10.96/15
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what is v=u+at
u=17 a=4 t=8
Answers
Answer: 65
Step-by-step explanation:
17 + 48
Complete the sentence below.
If (3x2 + 22x + 7) = (x + 7) = 3x + 1 , then (x + 7) ( ? )
＝?
The check of the polynomial division problem shows that the product of two polynomials is a polynomial.
This supports the fact that the __________ ?
property is satisfied for polynomial multiplication.
Answers
your answers are
3x + 1 = 3x^2 + 22x + 7
"closure"
Find the slope between the two points.
(2,10) and (6,30)
Please help what’s the slope between the two points
Answers
Answer:
The slope between the two points would be 5.
Answer: The slope would be 5
Step-by-step explanation:
question 4 i need help with
Answers
3+5=8
20/8 =2.50
Answer:
$3.00
Step-by-step explanation:
The drinks for the first family were 4, and the drinks for the second were 3. They were 2 numbers apart in price and so that means that they costed around $1. Minus a drink on the first to get $17.00. Now tell how far apart it is.
Can someone please help me with 83? What is A? full explanation please. Offering lots of points
Answers
Answer: A = 5
Step-by-step explanation:
So, we are given a function, with a point: we can substitute (x,y) from the coordinate into x and f(x) in the function. (recall that f(x) is just a fancy way of saying y).
so:
[tex]-1 = \frac{2(0) + 5}{0 - A}[/tex]
[tex]-1 = \frac{5}{-A}[/tex], (we can drop the negative sign from both sides here)
[tex]\frac{5}{5} = \frac{5}{A}[/tex], (recall 1 = x/x where x is literally any number)
hence we can see that A = 5
Ask questions in the comments if this doesn't make sense :)
please help me :(
where are the vertical asymptotes for y = 6 tan(0.2x)?
Answers
In the case of the tangent function, the vertical asymptotes occur when the argument of the tangent function (0.2x in this case) is equal to an odd multiple of pi/2, since that is when the tangent function becomes undefined.
So we can find the vertical asymptotes by solving the equation:
0.2x = (2n + 1) * pi/2
where n is an integer. Solving for x, we get:
x = (2n + 1) * pi / (2 * 0.2) = 5 * (2n + 1) * pi/2
So the vertical asymptotes occur at x = 5 * pi/2, x = 11 * pi/2, x = 17 * pi/2, and so on.
Note that these are not the only vertical asymptotes, since the function y = 6 tan(0.2x) is periodic with a period of 2 * pi / 0.2, which is much larger than pi. The function will have additional vertical asymptotes at the same values plus or minus 2 * pi / 0.2, and so on.
Three vertices of a parallelogram are located at (-4, 3), (1, -2), and (-1,4). What are two possible locations of the fourth vertex? Explain your reasoning.
Answers
Answer:
(4, -1) and (-6, 9).
Step-by-step explanation:
To find the fourth vertex of a parallelogram, we need to find the vector that represents the displacement from one of the given vertices to another, and then add that vector to the third given vertex. Since parallelograms have opposite sides that are equal in length and parallel, adding the same displacement vector to two of the given vertices will give us the coordinates of the other two vertices.
One possible displacement vector is the difference between the first and second given vertices, or (1 - (-4), -2 - 3) = (5, -5). Adding this vector to the third given vertex, (-1, 4), gives us the fourth vertex at (4, -1).
Another possible displacement vector is the difference between the second and third given vertices, or (-1 - 1, 4 - (-2)) = (-2, 6). Adding this vector to the first given vertex, (-4, 3), gives us the fourth vertex at (-6, 9).
So the two possible locations of the fourth vertex are (4, -1) and (-6, 9).
The angles of a triangle are in the ratio of 2 : 3 : 7. Find the measure of the two greatest angles of the triangle.
Answers
Answer:
Step-by-step explanation:
The measure of the two greatest angles is 105° and 45°
Let the angles be 2x, 3x and 7x ...... (i)
According to the 'Angle Sum Property' of triangle,
2x + 3x + 7x = 180°
12x = 180°
x = 15°
Now, put value of x in (i)
2x = 2 × 15 = 30°
3x = 3 × 15 = 45°
7x = 7 × 15 = 105°
so, the two greatest angles are 105° and 45°
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our jobs are to be done on four different machines. The cost in rupees of
producing ith on the jth machine is given below. Assign the jobs to different machines
so as to minimise the total cost.
Jobs
M1
M2
M3
M4
J1
15
11
13
15
J2
17
12
12
13
J3
14
15
10
14
J4
16
13
11
17
Answers
The total optimal solution based on the information will be 49 rupees.
How to calculate the valueHere, four jobs and four machines are given, with the assignment matrix.
Find out the each row minimum element and subtract it from that row
Find out the each column's minimum element and subtract it from that column.
This assignment problem is being solved using Hungerian Method as the optimal solution is:
J1 to M2, J2 to M4, J3 to M1 and J4 to M3. The total optimal cost is:
= 11 + 13 + 14 + 11
= 49 rupees
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brainliest answr quick tho
Answers
Answer:
BL
Step-by-step explanation:
because it goes in both directions infintely
Hi there, here's your answer:
To find the answer to this question, let us review all the options given in the question.
a) BL
BL being two ends of a given line that extends infinitely along its axis, forms a line.
b) GK
GK being two distinct lines do not join and hence do not form an independent line.
c) EB
E being a point on the line BL and B being one end of a larger line form a ray.
d) HI
HI being two points on a line GJ form a line segment, which is finite and has definite end points.
Thus, the answer to this question is (a).
Hope it helps! Please mark as Brainliest!
3. Hem started to travel at 11:40 and reached to his. destination at 12:20 at the speed of 6 km/hr. Find his distance covered.
Answers
Answer:
4 km
Step-by-step explanation:
There is a period of 40 minutes between 11:40 and 12:20.
[tex]40 \: minutes \: = \frac{2}{3} \: of \: an \: hour[/tex]
[tex] \frac{2}{3} \times \frac{6}{1} kmhr \: = \frac{12}{3} = 4[/tex]
3. Using the equation y = 3x - 5, what would the output be for an input of 2?
Answers
The output of the equation for input of 2 is 1.
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.
Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.
The given equation is:
y = 3x - 5
Here, x is the input value and y is the output value.
Substituting input that is x = 2.
y = 3(2) - 5
y = 6 - 5
y = 1
Hence, the output of the equation for input of 2 is 1.
Learn more about equation here:
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