Interpreting Composite Functions in the Real World
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The volume of air in a balloon is represented by the function von = = nr?, where r is the radius of the balloon, in
inches. The radius of the balloon increases with time, in seconds, by the function rt) = 42
Write a composite function that can be used to determine the volume of the balloon after t seconds. Then, select the
two true statements
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Answer:
Answer is A and C on edge
Step-by-step explanation:
The composite function that can be used to determine the volume of the balloon after t seconds, when V is composed with r is 1/48πt⁶ and after 6 second it is 972π.
What is composite function?When the two or more than two functions are written in the form of single function. Then such function is called the composite function.
Let suppose there is a function f(x) and another function g(x). Then the composite function can be given as,
[tex]f[g(x)][/tex]
The volume of air in a balloon is represented by the function,
[tex]V(r)=\dfrac{4}{3}\pi r^3[/tex]
Here, r is the radius of the balloon, in inches.
The radius of the balloon increases with time, in seconds, by the function,
[tex]r(t) = \dfrac{1}{4}t^2[/tex]
The composite function that can be used to determine the volume of the balloon after t seconds is,
[tex]V(r(t))=\dfrac{4}{3}\pi (\dfrac{1}{4}t^2)^3\\V(r(t))=\dfrac{4}{3}\pi (\dfrac{1}{64}t^6)\\V(r(t))=\dfrac{1}{48}\pi t^6[/tex]
After the 6 seconds,
[tex]V(r(6))=\dfrac{1}{48}\pi (6)^6\\V(r(6))=\dfrac{1}{48}\pi \times46656\\V(r(6))=972\pi[/tex]
Thus, the composite function that can be used to determine the volume of the balloon after t seconds, when V is composed with r is 1/48πt⁶ and after 6 second it is 972π.
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Related Questions
Bernie had $30 in his bank account. Today, he withdrew d dollars but tomorrow he will
bank account after tomorrow.
deposit $15. Write an expression to represent how much money Bernie will have in his
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Answer:
Step-by-step explanation:
Bernie had $30 in his bank account.
Today he withdrew $d
Now he has = $30 — $d
Because from $30 he took away $d that’s why $d have to subtract from the $30.
Tomorrow he’ll deposit $15 and that will be added up with current balance $30 —$d.
So, the expression to represent how much money Bernie will have in his bank account is $30 —$d + 15
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5. Laura just became a personal trainer and is finalizing her pricing plans. One plan is to charge
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Answer:
Step-by-step explanation:
Tod did not want the answer?
All the edges of the object in the diagram are equal in length. The object is cut by a vertical plane containing A and B and bisecting two of the horizontal edges. What is the shape of the cross-section resulting from the cut?.
Answers
The shape of the cross-section resulting from the cut is Rhombus.
Given that,
All the edges of the object in the diagram are equal in length.
The object is cut by a vertical plane containing A and B and bisecting two of the horizontal edges.
We have to determine,
What is the shape of the cross-section resulting from the cut?
According to the question,
All the edges of the object in the diagram are equal in length.
The length of all edges is equal in the rhombus.
The object is cut by a vertical plane containing A and B and bisecting two of the horizontal edges.
When the midpoints of all the four sides of a rhombus are joined with each other, you will obtain a rectangle whose length and width will measure half of the value of the prime diagonal.
Moreover, the area of the rectangle formed in this case will be half of the rhombus.
Hence, The shape of the cross-section resulting from the cut is Rhombus.
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Answer: C. A rhombus
Step-by-step explanation:
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The revenue earned when the shovel is sold for $20 is the same when the shovel is sold for $60.
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Domain and Range of {(0,2), (2,4), (-1,1)}
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Range = {0,1,4)
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Answer:
B. slope -5, y-intercept (0, 7)
Step-by-step explanation:
The y-intercept is the first (x, y) pair shown in the table: (0, 7). (This eliminates choices C and D.)
The slope is ...
change in y / change in x
(-13 -7) / (4 -0) = -20/4 = -5 . . . slope
This matches choice B.
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
i think because f(2) : f(x)= 5+2x = 7
Write an equation in point-slope form of the line that passes through the point (-6,6) and has a slope of m=3/2
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Answer:
y=3/2 x+15
Step-by-step explanation:
In mosquito, more itchy bites are dominate to less itchy bites. If a male mosquito with a heterogeneous, more itchy bite mates with a less itchy, homologous female, what will the offspring likely be like?
4 Points Total:
Key (assign letters and traits) 1
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Answer:
a rash
Step-by-step explanation:
Answer the ones you want to. Answer at least one.
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Answer:
I will answer one of them! Let's do... number 2.
Step-by-step explanation:
Conjecture: Each number increases by 5 each time.
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Step-by-step explanation:
Given that D, E, and F are the midpoints of their respective sides, which of the following is a true statement?
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Answer:
I'm pretty sure its the 1st one.
Step-by-step explanation:
1) -64÷16+[12x{6÷(16÷10-2)}]
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Answer:
= -30[tex]x^{6}[/tex]-4
i hope that helps and is right
If that is a multiplication sign then it is -184
if that is an x then it would be -4 -180x
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try it use your brain you can do it
Step-by-step explanation:
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Answer:
[tex]\frac{3^{12}}{3^{10}}[/tex]
Step-by-step explanation:
+ or x you plus the indices
- or divide you minus the indices
so 3^8 x 3^4 would be 3^12
and 3^2 x 3^8 would be 3 ^10
Simplify:
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Answers
Answer:
7x+3
Step-by-step explanation:
-5x+6x+14+12x-20-6x+9
combine like terms
7x+3
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
a train goes 25 kilometers in 45 minutes, how fast would it go in 27 minutes?
Answers
Answer:
15km
Step-by-step explanation:
45mins = 25km
1 min =25/45
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27mins=5/9×27
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Jane went to get her hair cut and colored before Christmas. The hair stylist told her it would cost $80, but Jane wanted to leave a 15% tip how much would her tip amount be how much will it cost her including the tip
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Answer:
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Step-by-step explanation:
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Write the equation of the line that is parallel to the line y=−14x−3 through the point (4,4).
Answers
Hello there! :)
Parallel lines have the same slope, so if one line has a slope of -14, then the line parallel to it has a slope of -14 as well.
We are also given a point that the line passes through.
That's enough information to find the equation of the line.
First, we write the equation in point-slope form, which looks like so:
y-y1=m(x-x1)
y1 is the y-coordinate of the point, m is the slope of the line and x1 is the x-coordinate of the point.
y-4=-14(x-4)
y-4=-14x+56
y=-14x+60
Hence, that's the equation. Hope it helps.
~A lonely teen who helps others with a smile
-Grace
Good luck.
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Answers
7x - 2 = 5x + 14
7x - 5x = 14 + 2
2x = 16
x = 16/2
x = 8
______
Hope it helps ⚜
Answer:
x = -8
Step-by-step explanation:
[tex]7x - 2 = 5x + 14 \\ 5x - 7x = 14 + 2 \\ - 2x = 16 \\ \frac{ - 2x}{ - 2} = \frac{16}{ - 2} \\ x = - 8[/tex]
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Answer:
1) 1600cm² 2 )4095cm² 3) 550cm²
Step-by-step explanation:
Because area is length times width, you can use that on these problems.
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Answer:
1. they both are the same length and diameter, the difference is thw diameter is a different direction.
2. 4 cm
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Step-by-step explanation:
Diameter is the length of the circle aross, hope this helps!
Jack was the science Museum in sabotage the recycling plant had an average speed of 26KM/H. Sometime later Aaliyah love traveling in the opposite direction with an average speed of 57KM/H. After Jack had traveled for four hours they were 332KM a part. How long did Aaliyah travel?
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Note : to find the squareroot of any number follow the steps : find the log ( lowest common factor )
Which statement is true about the equation f(x)=g(x) given f(x)=2x+3 and g(x)=x^2? please help
Answers
Answer:
x=3 and x=-1
Step-by-step explanation:
If f(x)=g(x), then 2x+3=x^2:
x^2-2x-3=0
(x-3)(x+1)=0
x=3 and x=-1
We can conclude that the statement:
There are values of x for which f(x) = g(x)" is true.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To determine which statement is true about the equation f(x) = g(x) given f(x) = 2x + 3 and g(x) = x²,
We can substitute the expressions for f(x) and g(x) into the equation and simplify:
f(x) = g(x)
2x + 3 = x^2
Now we have a quadratic equation.
We can rearrange it to standard form and solve for x using the quadratic formula:
x² - 2x - 3 = 0
a = 1, b = -2, c = -3
x = (-b ± √(b² - 4ac)) / 2a
x = (2 ± √(16)) / 2
x = (2 ± 4) / 2
x = -1 or x = 3
Therefore,
The equation f(x) = g(x) is true for some values of x, namely x = -1 and x = 3.
Thus,
Based on this, we can conclude that the statement "There are values of x for which f(x) = g(x)" is true.
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