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tangare [24]
3 years ago
5

The radius of a circular pond is increasing at a constant rate, which can be modeled by the function , where t is time in months

. The area of the pond is modeled by the function . The area of the pond with respect to time can be modeled by the composition . Which function represents the area with respect to time? A. B. C. D.
Mathematics
1 answer:
horrorfan [7]3 years ago
5 0

Answer:

B. A(r(t)) = 25πt²

Step-by-step explanation:

Find the completed question below

The radius of a circular pond is increasing at a constant rate, which can be modeled by the function r(t) = 5t where t is time in months. The area of the pond is modeled by the function A(r) = πr². The area of the pond with respect to time can be modeled by the composition . Which function represents the area with respect to time? A. B. C. D.

Given

A(t) = πr²

r(t) = 5t

We are to evaluate the composite expression A(r(t))

A(r(t)) = A(5t)

To get A(5t), we will replace r in A(t) with 5t and simplify as shown

A(5t) = π(5t)²

A(5t) = π(25t²)

A(5t) = 25πt²

A(r(t)) = 25πt²

Hence the composite expression A(r(t)) is 25πt²

Option B is correct.

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Sindrei [870]

Step-by-step explanation:

all we need to do is find the surface area, deduct windows and door areas.

that gives us the m² to be covered, which we have to multiply by $12.50 to get the total price.

what is the problem ? there are only trivial multiplications (with a calculator), additions and subtractions.

the house surface area is like for a box, but we don't care about the top and the bottom. only about the walls.

the "box" is 18 m × 14 m × 4 m.

so, the front and the back walls are each

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each side wall is

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both sides : 2×56 = 112 m²

now for the deductions.

each window is

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7 0
2 years ago
What is x? 3x+43=100​
jenyasd209 [6]

Answer:

x = 19

Step-by-step explanation:

Solve for x:

3 x + 43 = 100

Subtract 43 from both sides:

3 x + (43 - 43) = 100 - 43

43 - 43 = 0:

3 x = 100 - 43

100 - 43 = 57:

3 x = 57

Divide both sides of 3 x = 57 by 3:

(3 x)/3 = 57/3

3/3 = 1:

x = 57/3

The gcd of 57 and 3 is 3, so 57/3 = (3×19)/(3×1) = 3/3×19 = 19:

Answer:  x = 19

8 0
3 years ago
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3 years ago
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