Use the drawing tools to form the correct answer on the provided graph.
Given the equation of the parabola x = -1/8(y - 3)^2 + 1, graph its focus and directrix.
Answers
Using drawing tools parabola graph has been made and uploaded in answer for the given equation.
Standard form of parabola having vertical axis of symmetry given by:
[tex](y - k)^2 = 4p(x - h)[/tex]
where (h, k): vertex and p: distance between the vertex and the focus or directrix.
Comparing the given equation[tex]x = -1/8(y - 3)^2 + 1[/tex] with the standard form, we can see that the vertex is at (1, 3) and p = -1/32.
Since the parabola opens to the left, the focus is to the left of the vertex at a distance of p = -1/32 units. Thus, the focus is located at (-1/32, 3).
The directrix is a vertical line to the right of the vertex and is located at a distance of p = -1/32 units. Thus, the directrix is the vertical line x = 33/32.
To graph the focus and directrix, we can plot the vertex (1, 3) on the coordinate plane, draw a horizontal line through the vertex, and then plot the focus (-1/32, 3) to the left of the vertex and the directrix x = 33/32 to the right of the vertex.
Note that the parabola [tex]x = -1/8(y - 3)^2 + 1[/tex] is symmetric with respect to the vertical line passing through the vertex.
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Related Questions
PLEASE HELP!
What is the remainder of the quantity 5 x cubed plus 7 x plus 5 end quantity divided by the quantity x plus 2 end quantity? Show all necessary steps.
Answers
We can use polynomial long division to find the remainder of the expression (5x^3 + 7x + 5) divided by (x + 2). The steps are as follows:
5x^2 - 3x + 19
____________
x + 2 | 5x^3 + 7x + 5
- (5x^2 + 10x)
______________
-3x + 5
-(-3x - 6)
________
11
Therefore, the remainder of (5x^3 + 7x + 5) divided by (x + 2) is 11.
Answer:
The remainder of the polynomial equation is -49
Step-by-step explanation:
Si le nombre x est choisi est un nombre entier, le résultat obtenu est un multiple de 8.
Answers
Answer:
i don't know
Step-by-step explanation:
you didn't put that answers
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answers
In response to the query, we can state that therefore, the three angle statements that are always true regarding the diagram are: m∠5 + m∠3 = m∠4 and m∠3 + m∠4 + m∠5 = 180° and m∠5 + m∠6 =180°
what are angles?An angle is a shape in Euclidean geometry made composed of two rays, referred to as the angle's sides, that come together at a centre point known as the angle's vertex. An angle that is in the plane where the rays are placed can be produced by two rays. Another angle is produced when two planes collide. Dihedral angles are the name given to them. In planar geometry, an angle is the form made by two rays or lines that share a termination. The English word "angle" derives from the Latin word "angulus," which means "horn." The vertex, also known as the angle's sides, is where the two rays' common terminals meet.
To answer this question, we can use the following facts about the angles in a triangle:
The sum of the interior angles of a triangle is always 180 degrees.
An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Using these facts, we can analyze the diagram and make the following conclusions:
m∠5 + m∠3 = m∠4 is always true because angle 4 is the exterior angle at angle 3, so m∠4 = m∠3 + m∠5.
m∠3 + m∠4 + m∠5 = 180° is always true because the sum of the three exterior angles of a triangle is always 360 degrees (i.e., one full rotation), so m∠3 + m∠4 + m∠5 = 360°. Also, we know that m∠3 + m∠5 = m∠4, so substituting this gives m∠4 + m∠4 = 360°, which simplifies to 2m∠4 = 360°, or m∠4 = 180° - m∠3 - m∠5. Substituting this into the original equation gives m∠3 + m∠4 + m∠5 = 180°.
m∠5 + m∠6 =180° is always true because angle 6 is the exterior angle at angle 5, so m∠6 = m∠5 + m∠3. Substituting this into the equation gives m∠5 + m∠5 + m∠3 = 180°, which simplifies to m∠5 + m∠6 = 180°.
Therefore, the three statements that are always true regarding the diagram are:
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
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15. Write the inequality system that is represented in the graph.
Answers
The inequality system that is represented in the graph are-
y < -x -1 and y ≤ x + 2.
How to find inequality system from the graph?We plot both equations in the very same coordinate system in order to visually solve any system of linear equations. The intersection of the two lines is where the system's answer will be found.Graph the resultant line by replacing the inequality sign with just an equal sign.Consider two point on dotted line.
(-1, 0) and (-2, 1)
Fine slope m:
m = (1 - 0)/(-2 + 1)
m = -1
Equation of line:
y - 0 = (-1)(x + 1)
y = -x -1
In the inequality system.
y < -x -1
Consider two point on bold line.
(0,2) and (-2, 0)
Fine slope m:
m = (0 - 2)/(-2 -0)
m = 1
Equation of line:
y - 2 = (1)(x + 0)
y = x + 2
In the inequality system.
y ≤ x + 2
Thus, the inequality system that is represented in the graph are-
y < -x -1 and y ≤ x + 2.
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2. Graph the piecewise function.
Answers
..
I will solve this equation! Just provide the x value.
Write and solve an equation to represent the hanger.
Answers
Answer:
x = 3
Step-by-step explanation:
We know that the mass of 5x's and 2 is the same as 17, so we can represent this in the equation:
5x + 2 = 17
To solve for x, we need to isolate x and move everything else to the other side, so:
5x = 17 - 2
When 2 moves to the right side, the operation is the opposite (so the + turns into a - )
So we know that:
5x = 15
5 multiplied by x is 15, so, to move 5 to the other side, we need to divide:
x = 15/5
So:
x = 3
You and a friend both work two different jobs. The system of linear equations represents the total earnings (in dollars) for x hours worked at the first job and y hours worked at the second job. Your friend earns twice as much as you.
4x+8y=64 You
8x + 16y - 128 Your Friend
a. One week, both of you work 4 hours at the first job. How many hours do you and your friend work at the second job?
b. Both of you work the same number of hours at the second job. Compare the numbers of hours you and your friend work at the first job.
Answers
Answer:
Step-by-step explanation:
a. We can start by substituting y = 2x into the second equation to get an equation in terms of x only:
8x + 16y - 128 = 8x + 16(2x) - 128 = 0
Simplifying this equation, we get:
24x = 128
Solving for x, we get:
x = 128/24 = 32/6 = 16/3
So you and your friend work 16/3 hours (or approximately 5.33 hours) each at the second job.
b. If both of you work the same number of hours at the second job, then we can set x = y in the first equation and solve for y:
4x + 8y = 64
4x + 8x = 64
12x = 64
x = 64/12 = 16/3
So both you and your friend work 16/3 hours (or approximately 5.33 hours) at the second job.
To compare the number of hours worked at the first job, we can substitute x = 16/3 into the first equation to find:
4(16/3) + 8y = 64
64/3 + 8y = 64
8y = 64 - 64/3 = 128/3
y = 16/3
So your friend works 16/3 hours (or approximately 5.33 hours) at the first job, which is twice the amount of time you work at the first job.
The budget for the summer soccer program in Milltown is $20,000. How much is spent on staff salaries?
$10,000
$8,000
$5,000
$4,000
$2,000
Answers
Answer: 4k
Step-by-step explanation:
What is the measure of angle B?
Answers
Answer:
58 degrees
Step-by-step explanation:
find x first
8x+2 + 6x + 80 = 180
14x + 82 = 180
14x = 98
x = 7
then substitute it back into the angle measure of B
angle b = 8x + 2
8(7) + 2 = 58
Which graph shows the line y=-3x+1?
A. Graph A
B. Graph B
C. Graph C
D. Graph D
Answers
The graph that shows the line y = - 3 x + 1 would be B. Graph B.
How to find the graph ?To find the graph, you need to find the x and y values from the given equation of line y=-3x+1.
Then look at the graph that has these points.
For x = -2:
y = -3(-2) + 1
y = 6 + 1
y = 7
For x = -1:
y = -3(-1) + 1
y = 3 + 1
y = 4
For x = 0:
y = -3(0) + 1
y = 0 + 1
y = 1
For x = 1:
y = -3(1) + 1
y = -3 + 1
y = -2
For x = 2:
y = -3(2) + 1
y = -6 + 1
y = -5
For x = 3:
y = -3(3) + 1
y = -9 + 1
y = -8
So, the y values for x = -3 to x = 3 are:
x = -3: y = 10
x = -2: y = 7
x = -1: y = 4
x = 0: y = 1
x = 1: y = -2
x = 2: y = -5
x = 3: y = -8
The graph that has these points is therefore Graph B.
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PLEASE HURRY WILL GIVE BRAINLIEST AND THANKS AND 5 STARS
On the coordinate plane below, square ABCD is dilated by a factor of 2, with the origin as the center of dilation, to form A ′B ′C ′D ′ .
After the dilation, what is the location of C ′ ?
Answers
Answer:
First option, (4, -6)
Step-by-step explanation:
Scaled by 2. Multiply each coordinate of point C by 2.
(2*2, -3*2) = (4, -6)
1. The perimeter of a square field is 64 m. If the field is surrounded by a running path of width 3.5 m, find the area of the path.
Answers
If the perimeter of a square field is 64 m. If the field is surrounded by a running path of width 3.5 m. The area of the path surrounding the square field is 273 square meters.
What is the area?Let's denote the side length of the square field as x meters.
The perimeter of a square is given by the formula: Perimeter = 4 * side length
Write the equation:
4x = 64
Divide both sides by 4:
x = 16
So, the side length of the square field is 16 meters.
Now, we need to find the area of the path surrounding the field.
The new side length of the square including the path is: x + 2 * (width of the path)
Substitute
New side length = 16 + 2 * 3.5 = 23 meters
The area of the path:
Area of path = Area of larger square - Area of original square
Area of larger square = (New side length)^2
= 23²
= 529 square meters
Area of original square = (Side length)²
= 16²
= 256 square meters
Area of path = 529 - 256
= 273 square meters
Therefore the area of the path surrounding the square field is 273 square meters.
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Considering the square field of each side 16 m, once the 3.5 m wide path is added around the square, the total area increases. The difference between the area of the larger square and the original square gives the area of the path as 273 sq m.
Explanation:This problem can be solved focusing on square geometry and area calculations. We begin by understanding that the perimeter of the square is 64 m. Since a square has equal sides, each side measures 16 m (i.e., 64 m divided by 4).
The running path that surrounds the field adds a width of 3.5 m around the square. So the total side length of the larger square (field + path) becomes 16 m + 3.5 m + 3.5 m = 23 m.
The total area of the larger square (field + path) is thus 23 m * 23 m = 529 sq m.
Now we subtract the area of the original field (16 m * 16 m = 256 sq m) from this total. Therefore, the area of the path is 529 sq m - 256 sq m = 273 sq m.
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let x(t)= t2/3 give the distance of a moving particle from its starting point as a function of time t. for what value of t is the instanteous velocity of the particle equal to its average velocity over the interval (0,8)
Answers
To find the value of t at which the instantaneous velocity of the particle is equal to its average velocity over the interval (0,8), we need to first determine the instantaneous velocity and the average velocity.
The instantaneous velocity of the particle is the derivative of the distance function with respect to time, given by:
v(t) = dx/dt = 2/3 * t^(-1/3)
The average velocity of the particle over the interval (0,8) is the total distance traveled divided by the total time elapsed:
average velocity = (distance traveled) / (time elapsed)
= x(8) / 8
We can find x(8) by plugging t = 8 into the distance function:
x(8) = (8^(2/3)) = 4
Therefore, the average velocity over the interval (0,8) is 4/8 = 1/2.
Now, we need to find the value of t for which the instantaneous velocity is equal to 1/2. Setting v(t) equal to 1/2 and solving for t, we get:
2/3 * t^(-1/3) = 1/2
t^(-1/3) = 3/4
Taking the cube of both sides, we get:
t = (4/3)^3 = 64/27
Therefore, the instantaneous velocity of the particle is equal to its average velocity over the interval (0,8) when t = 64/27.
An investor has $60,000 to invest in a CD and a mutual fund. The CD yields 8% and the mutual fund yields 7%. The mutual fund requires a minimum investment of $8,000, and the investor requires that at least twice as much should be invested in CDs as in the mutual fund. How much should be invested in CDs and how much in the mutual fund to maximize the return? What is the maximum return?
Answers
Answer:
Step-by-step explanation:
Let's start by defining some variables to represent the amount invested in the CD and the mutual fund. Let:
C = amount invested in the CD
M = amount invested in the mutual fund
From the problem statement, we know that:
C + M = 60,000 (the total investment amount is $60,000)
C >= 2M (twice as much should be invested in CDs as in the mutual fund)
M >= 8,000 (the mutual fund requires a minimum investment of $8,000)
We can use these constraints to write the objective function that we want to maximize, which is the total return on investment:
R = 0.08C + 0.07M
To solve this problem, we can use the following steps:
Substitute C = 2M into the first equation to get:
3M = 60,000
M = 20,000
Since M >= 8,000, we can invest the minimum required amount in the mutual fund and put the rest in the CD:
M = 8,000
C = 60,000 - M = 52,000
Calculate the total return on investment:
R = 0.08C + 0.07M = 0.08(52,000) + 0.07(8,000) = 4,960 + 560 = 5,520
Therefore, the investor should invest $52,000 in the CD and $8,000 in the mutual fund to maximize the return, and the maximum return is $5,520.
what is the coefficient of y in the equation 3y² - ⅘y + 6 = 0 ?
Answers
Answer: -4/5
Step-by-step explanation: To find the coefficient of y in the equation 3y² - ⅘y + 6 = 0, we need to identify the term in the equation that contains y and then extract the coefficient.
In this equation, the term that contains y is -⅘y. The coefficient of y is the number that is multiplied by y in this term, which is -⅘.
Therefore, the coefficient of y in the equation 3y² - ⅘y + 6 = 0 is -⅘.
An experiment consists of selecting a card at random from a 52-card deck. Refer to this experiment and find the probability of the event. (Enter your answer as a fraction.)
A club or a jack is drawn.
Answers
4/13 is the probability of drawing a club out of the deck of card if a card at random is selected from a 52-card deck.
Probability of an experiment consisting of a cardThere are 13 clubs and 4 jacks in a standard 52-card deck. However, we need to be careful not to double-count the jack of clubs, which is both a club and a jack.
So the number of cards that are either a club or a jack (excluding the jack of clubs) is:
13 (clubs) + 4 (jacks) - 1 (jack of clubs) = 16
Therefore, the probability of drawing a club or a jack (excluding the jack of clubs) is:
P(club or jack) = number of favorable outcomes / total number of outcomes
= 16 / 52
= 4 / 13
So the probability of drawing a club or a jack is 4/13.
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You and two friends go to the ice cream parlor. The flavors available are Strawberry, Mexican Vanilla, Rocky Road, Belgian Chocolate, Salted Caramel, and Bratwurst. Assuming each of you orders one different flavor, how many outcomes are possible?
Answers
Explanation:
There are 6 flavors given. This is the number of choices you have to pick from. After you choose a flavor, the next person has 6-1 = 5 choices. Then there are 5-1 = 4 choices after that. We have this countdown.
Multiply the values mentioned: 6*5*4 = 30*4 = 120
An alternative is to use the nPr permutation formula with n = 6 and r = 3.
The nPr formula is [tex]_nP_r = \frac{n!}{(n-r)!}[/tex] where the exclamation marks mean factorials.
Seven years ago, Grogg's dad was 9 times as old as Grogg, and 6 years ago, his dad was 7 times as old as Grogg. How old is Grogg's dad currently?
Answers
Answer:
From the first piece of information, we can set up an equation:
D - 7 = 9(G - 7)
Simplifying this equation, we get:
D - 7 = 9G - 63
D = 9G - 56
From the second piece of information, we can also set up an equation:
D - 6 = 7(G - 6)
Simplifying this equation, we get:
D - 6 = 7G - 42
D = 7G - 36
Now we can combine the two equations:
9G - 56 = 7G - 36
Solving for G, we get:
2G = 20
G = 10
So currently, Grogg is 10 years old. We can substitute this value back into either equation to find his dad's age:
D = 9G - 56
D = 9(10) - 56
D = 34
Therefore, Grogg's dad is currently 34 years old.
Step-by-step explanation:
35°
y
X
y=[? ]º
25°
Enter
Answers
Answer:
x = 120°
y=60°
These are the answers
What is the value of the expression (Please see Q3 for equation) Show your work.
Answers
The value οf the expressiοn is 343.
What is expressiοn?An expressiοn in math is a sentence with a minimum οf twο numbers οr variables and at least οne math οperatiοn. This math οperatiοn can be additiοn, subtractiοn, multiplicatiοn, οr divisiοn.
An expressiοn cοnsists οf οne οr mοre numbers οr variables alοng with οne mοre οperatiοn.
The expression [tex](7^{12} * 7^9) / 7^{18[/tex] can be simplified as follows:
First, using the rule that states [tex]a^m / a^n =a^{m+n}[/tex], we can combine the two terms in the numerator to get:
[tex]7^{12} * 7^9 = 7^{(12+9) } = 7^{21}[/tex]
So the expression now becomes:
[tex]7^{21} / 7^{18}[/tex]
Next, using the rule that states [tex]a^m / a^n =a^{m-n}[/tex], we can divide the two terms in the denominator from the numerator to get:
[tex]7^{21} /7^{18} = 7^{21-18}= 7^3[/tex]
Therefore, the value of the expression is 343.
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Use the technique of linear regression to find the line of best fit for the given points. Round any intermediate calculations to no less than six decimal places, and round the coefficients to two decimal places.
(1,9)
, (2,9)
, (3,4)
, (4,2)
, (5,4)
, (6,2)
, (7,3)
Answers
The line of best fit for this set of points is y = -1.00x + 9.00.
What is coefficient?Coefficient is a value that is used to indicate the degree or amount of a certain property or characteristic. It is usually used in mathematics and physics, and is a numerical measure of how two variables are related. For example, the coefficient of friction is a number that indicates how much resistance there is between two surfaces when one is sliding over the other. In economics, the coefficient of elasticity is used to measure how much of a change in one variable affects a change in another.
Linear regression is a technique used to find the line of best fit for a given set of points. To use linear regression, we must first calculate the mean of all the x and y coordinates. The mean of the x coordinates is 4, and the mean of the y coordinates is 4.5.
We then calculate the sum of the squared differences between the x and y coordinates and their respective means. This sum is 36.5.
Next, we calculate the sum of the products of the differences between the x and y coordinates and their respective means. This sum is -25.
Using the formula for linear regression, we can calculate the slope of the line of best fit. The slope is -1.00.
To calculate the y-intercept of the line of best fit, we use the slope and the mean of the x and y coordinates. The y-intercept is 9.00.
The line of best fit for this set of points is y = -1.00x + 9.00.
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In the graph shown, suppose that f(x) = 3.5^x and h(x) = 1.5^x. Choose the statement that COULD be true.
g(x) = 4^x
g(x) = 5^x
g(x) = (.9)^x
g(x) = π^x
Answers
A function that could be true based on the given information is g(x) = 5^x.
By examining the presented graph, we can observe that the functions f(x) = 3.5x and h(x) = 1.5x are growing and concave upward, and h(x) has a larger y-axis intercept than f. (x).
Considering these characteristics, the function g(x) = 5x has the potential to be true. This is why:
The rising nature of the function f(x) = 3.5x indicates that its values rise as x rises.
Although the function h(x) = 1.5x is similarly rising, it has a larger y-axis intercept than the function f(x), which means that its values are larger than f(x) for small values of x.
In addition to rising, the function g(x) = 5x also has a larger y-axis intercept than f(x) and h. (x). It is therefore possible that g(x) lies above both functions for all values of x and crosses the graph of f(x) and h(x) at a point to the right of x = 0.
Because they do not have the same characteristics as the functions f(x) and h(x), the functions g(x) = 4, g(x) = (.9), and g(x) = are unlikely to intersect the graph of both functions and remain above them for all values of x. g(x) = 5x is a function that, given the available data, might be true.
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Solve for 'a' in f(x) = ax² + 7x + 2 when ∆ = 33
Answers
The value of a in the function f(x) = ax² + 7x + 2 when differentiated is 13/x
Calculating the value of a in the function when differentiatedGiven that the function is represented as
f(x) = ax² + 7x + 2
Also, we have the differentiated function to be
∆ = 33
This means that we differentiate f(x) and set the value to 33
When f(x) is differentiated, we have
∆ = 2ax + 7
By equating the functions, we have
2ax + 7 = 33
This gives
2ax = 26
So, we have
a = 13/x
Hence, the value of a is 13/x
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HELP ASAP WILL GIVE 100 POINTS AND BRAINLYEST IF YOU DON"T ANSWER WITH THE INTENT TO ANSWER CORRECTLY I WILL REPORT YOU
Answers
Answer:
1.2 x 10^3 = 1,200
1.2 x 10^-2 = 0.012
1.2 x 10^2 = 120
1.2 x 10^-4 = 0.00012
Step-by-step explanation:
Help me please I need this
Answers
Answer:
I believe it's B!
Step-by-step explanation:
To get System B from System A, we can use the operation of replacing one equation with a multiple of the other equation. Specifically, we can multiply the first equation of System A by 4 to get:
{32x - 12y = 0, 2x + 7y = 3}
Now, we can see that the first equation of System B is the same as the first equation of the modified System A. The second equation of System B is also equivalent to the second equation of the modified System A, since we can multiply the second equation of the modified System A by 4/2 to get:
{32x - 12y = 0, 8x + 28y = 12}
Therefore, System B can be obtained from System A by replacing one equation with a multiple of the other equation. The correct answer is B.
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What data values have a frequency of 2 on the line plot
1) 12 and 58
, 1 half and 5 over 8,
2) 316 and 58
, 3 over 16 and 5 over 8,
3) 12 and 316
, , , 1 half and 3 over 16, , ,
4) 12 and 78
Answers
We can identify the data values with a frequency of 2 on the line plot, which are 3/16, 5/8, and 1/2.
A line plot is a visual representation of data that shows the frequency of values in a dataset. In the given line plot, we need to identify the data values that have a frequency of 2.
Firstly, we have a data value of 3/16 that has a frequency of 2. This means that the value 3/16 appears twice in the dataset.
Next, we have a data value of 5/8 that also has a frequency of 2. This means that the value 5/8 appears twice in the dataset.
Lastly, we have a data value of 1/2 that has a frequency of 2. This means that the value 1/2 appears twice in the dataset.
Therefore, the data values that have a frequency of 2 on the given line plot are 3/16, 5/8, and 1/2.
In addition to these, we have some other data values on the line plot. The data value of 4 appears only once, and the data values of 12 and 78 are not present on the line plot. Hence, we cannot determine their frequency from the given information.
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what fraction each person gets when they share equally. 8 people share 1 pizza.
Answers
Answer:
Each person would get 1/8 of the pizza if they were to share it equally.
Step-by-step explanation:
Please help me out are these angles adjacent, vertical, complementary, or supplementary? image attached below! =]
Answers
Answer:
B. adjacent
Step-by-step explanation:
"adjacent" means they are next to each other (like, touching, they share a side).
"complementary" means that together they make a right angle, or 90°.
"supplementary" means that together they make 180° (a straight angle-- a straight line)
"vertical angles" are made by crossing two lines (that makes four angles) the vertical angles are opposite from each other (touching only at one point) and they are equal.
Need help will be much appreciated! I did A already Im just stuck with B, I have an hour before my assignment is due please help. :)
Answers
A. The inverse of the function f(x) = 3 / (7x + 1) is g(x) = (3 - x)/7x
B. The inverse function is verified, such that f(g(x)) = x
How to find the inverse of the functionThe inverse of the function is solved as follows
f(x) = 3 / (7x + 1)
let f(x) = y, so that y = 3 / (7x + 1)
writing the equation by isolating x
y (7x + 1) = 3
7x + 1 = 3/y
7x = 3/y - 1
7x = (3 - y)/y
x = (3 - y)/7y
interchanging the variables
y = (3 - x)/7x
hence g(x) = (3 - x)/7x
solving for f(g(x)), to verify
f(g(x)) = 3 / (7((3 - x)/7x) + 1)
f(g(x)) = 3 / ((3 - x)/x) + 1)
f(g(x)) = 3 / ((3 - x + x)/x)
f(g(x)) = 3 / 3/x
f(g(x)) = (3 / 3) * x
f(g(x)) = x
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Betsy called the post office to find out about the shipping tubes that she could buy there. The person helping her told her that the tubes had a surface area of 172 in2 and a radius of 2 inches. What is the height of the tube? Hint: Shipping tubes are shaped like cylinders. Use the formula for the surface area of a cylinder. SA = 2 × × radius2 + 2 × height × radius × A. 41 inches B. 20.5 inches C. 82 inches D. 164 inches
Answers
The height of the tubes is 11.68 inch
The surface area of the cylinder:The formula for the surface area of a cylinder is:
SA = 2πr² + 2πrhWhere
SA = Surface area r = Radius of the cylinder h = Height of the cylinderHere we have
The surface area of the tube is 172 in² and the radius is 2 inches.
Using the formula,
Surface area of Tube = 2π (2) (2+ h)
= 4π(2 + h)
From the given data,
The surface area of the tube = 172
=> 4π(2 + h) = 172
=> π(2 + h) = 43
=> 44/7 + 22h/7 = 43
=> 44 + 22h = 301
=> 22h = 257
=> h = 11.68 inch
Therefore,
The height of the tubes is 11.68 inch
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