Answer:
17.5
Step-by-step explanation:
Given that the variables x and y have a proportional relationship.
i.e. y is directly proportional to x or can be written as
y = mx where m is the constant of proportionality.
When x =2, y =7
Substitute this to get the value of m.
7 =2m or m = 3.5
Thus the relationship between x and y is
y = 3.5x
So when x=5, y = 3.5(5) = 17.5
Answer:
see explanation
Step-by-step explanation:
Calculate the distance (d) using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 1,4) and (x₂, y₂ ) = (- 5, 3)
d = 
= 
=
=
≈4.12 ( to 2 dec. places )
To find the midpoint use the midpoint formula
[0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]
Using the same points as above then
midpoint = [0.5(- 1- 5), 0.5(4 + 3 ) ] = [0.5(- 6), 0.5(7) ] = (- 3, 3.5 )
Answer:
A) A[p(t)] = 36πt²
B) 7234.56 square units
Step-by-step explanation:
<u>Given functions</u>:

<u>Part A</u>
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}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DA%28p%29%20%26%20%3D%20%5Cpi%20p%5E2%5C%5C%5C%5C%20%5Cimplies%20A%5Bp%28t%29%5D%20%26%20%3D%20%5Cpi%20%5Bp%28t%29%5D%5E2%5C%5C%26%20%3D%20%5Cpi%20%286t%29%5E2%5C%5C%26%20%3D%20%5Cpi%206%5E2%20t%5E2%5C%5C%26%20%3D%2036%5Cpi%20t%5E2%5Cend%7Baligned%7D)
<u>Part B</u>
Given
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}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DA%5Bp%288%29%5D%20%26%20%3D%2036%5Cpi%20t%5E2%5C%5C%26%20%3D%2036%20%5Ccdot%203.14%20%5Ccdot%208%5E2%5C%5C%26%20%3D%2036%20%5Ccdot%203.14%20%5Ccdot%2064%5C%5C%26%20%3D%20113.04%20%5Ccdot%2064%5C%5C%26%20%3D%207234.56%5C%3A%5C%3A%20%5Csf%20square%5C%3Aunits%5Cend%7Baligned%7D)
Therefore, the area of spilled paint after 8 minutes if 7234.56 square units.
terminating................. because the number does not repeat