Answer:
m= 1/2 or 1 over 2 or m=0.5
Answer:
Three non-collinear points determine a plane.
Step-by-step explanation:
This statement means that if you have three points not on one line, then only one specific plane can go through those points. The plane is determined by the three points because the points show you exactly where the plane is
Answer:
15
Step-by-step explanation:because u add them all up
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.
Given this equation:

That represents t<span>he height of a tree in feet over (x) years. Let's analyze each statement according to figure 1 that shows the graph of this equation.
</span>
The tree's maximum height is limited to 30 ft.
As shown in figure below, the tree is not limited, so this statement is false.
<span>
The tree is initially 2 ft tall
The tree was planted in x = 0, so evaluating the function for this value, we have:
</span>

<span>
<span>So, the tree is initially

tall.
</span>
Therefore this statement is false.
</span>
Between the 5th and 7th years, the tree grows approximately 7 ft.
<span>
if x = 5 then:
</span>

<span>
</span>if x = 7 then:

So, between the 5th and 7th years the height of the tree remains constant
:

This is also a false statement.
<span>
After growing 15 ft, the tree's rate of growth decreases.</span>
It is reasonable to think that the height of this tree finally will be 301ft. Why? well, if x grows without bound, then the term

approaches zero.
Therefore this statement is also false.
Conclusion: After being planted this tree won't grow.