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Basile [38]
3 years ago
10

2

Mathematics
1 answer:
goldfiish [28.3K]3 years ago
4 0

Answer:

The volume of can A is half the volume of can B.

Step-by-step explanation:

Given

Can A and Can B

Required

The true statement

For Can A, we have:

h =8

r = 0.5

The volume is:

Volume = \pi r^2h

This gives:

V_A = \pi * 0.5^2 * 8

V_A = \pi * 2

V_A = 2\pi

For Can B, we have:

h =4

r = 1

The volume is:

Volume = \pi r^2h

This gives:

V_B = \pi * 1^2 * 4

V_B = \pi  * 4

V_B = 4\pi

So, we have:

V_A = 2\pi

V_B = 4\pi

By comparison, (d) is correct

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The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new functio
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Answer:

The new function is (x + 7)² - 47 ⇒ the 3rd answer

Step-by-step explanation:

* Lets put the function f(x) in the vertex form at first and then make

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∵ The y-coordinate of the vertex of the function is f(-b/2a)

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∵ f(x) = x² + 22x + 58

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∵ x-coordinate of the vertex = -b/2a

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* lets revise the rules of the translation

- If the function f(x) translated horizontally to the right  

 by m units, then the new function g(x) = f(x - m)

- If the function f(x) translated horizontally to the left  

 by m units, then the new function g(x) = f(x + m)

- If the function f(x) translated vertically up  

 by n units, then the new function g(x) = f(x) + n

- If the function f(x) translated vertically down  

 by n units, then the new function g(x) = f(x) – n

∵ f(x) will translate 4 units to the right

∴ m = 4

∵ f(x) ⇒ f(x - m)

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∵f(x) will translate 16 units up

∴ -63 will add by 16

∴ n = 16

∴ f(x) ⇒ f(x) + n

∵ -63 + 16 = -47

∴ The new function is (x + 7)² - 47

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