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3 years ago

Goran is riding his bicycle. He rides for 22.5 kilometers at a speed of 9 kilometers per hour. For how many hours does he ride?

Mathematics

1 answer:

astra-53 [7]3 years ago

6 0

Answer: He rides for 2.5 hours or 2 and a half hours.

Step-by-step explanation:

He needs to complete a trajectory of 22.5 kilometers.

He rides 9 kilometers per hour.

Divide the total by the amount of kilometers that he rides.

$\frac{22.5}{9}=2.5h$

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A) A[p(t)] = 36πt²

B) 7234.56 square units

Step-by-step explanation:

Given functions:

$\begin{cases}p(t)=6t \\ A(p)=\pi p^2 \end{cases}$

Part A

To find the area of the circle of spilled paint as a function of time, substitute the function p(t) into the given function A(p):

$\begin{aligned}A(p) & = \pi p^2\\\\ \implies A[p(t)] & = \pi [p(t)]^2\\& = \pi (6t)^2\\& = \pi 6^2 t^2\\& = 36\pi t^2\end{aligned}$

Part B

Given

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Substitute the given values into the equation for A[p(t)} found in part A:

$\begin{aligned}A[p(8)] & = 36\pi t^2\\& = 36 \cdot 3.14 \cdot 8^2\\& = 36 \cdot 3.14 \cdot 64\\& = 113.04 \cdot 64\\& = 7234.56\:\: \sf square\:units\end{aligned}$

Therefore, the area of spilled paint after 8 minutes if 7234.56 square units.

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