Answer:
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To find the 'maximum height' we will need to take the derivative of h(t) = –16t² + 32t + 6 then set it equal to zero, then solve for t. this t will be the time at which the ball reaches it's maximum height.
d<em>y</em>/d<em>x</em> = 4 + √(<em>y</em> - 4<em>x</em> + 6)
Make a substitution of <em>v(x)</em> = <em>y(x)</em> - 4<em>x</em> + 6, so that d<em>v</em>/d<em>x</em> = d<em>y</em>/d<em>x</em> - 4. Then the DE becomes
d<em>v</em>/d<em>x</em> + 4 = 4 + √<em>v</em>
d<em>v</em>/d<em>x</em> = √<em>v</em>
which is separable as
d<em>v</em>/√<em>v</em> = d<em>x</em>
Integrating both sides gives
2√<em>v</em> = <em>x</em> + <em>C</em>
Get the solution back in terms of <em>y</em> :
2√(<em>y</em> - 4<em>x</em> + 6) = <em>x</em> + <em>C</em>
You can go on to solve for <em>y</em> explicitly if you want.
√(<em>y</em> - 4<em>x</em> + 6) = <em>x</em>/2 + <em>C</em>
<em>y</em> - 4<em>x</em> + 6 = (<em>x</em>/2 + <em>C </em>)²
<em>y</em> = 4<em>x</em> - 6 + (<em>x</em>/2 + <em>C </em>)²
Answer:
23/3
Step-by-step explanation:
They already give you the area of one base, which is great! The volume of a rectangular prism is l · w · h, and they've already done h · l for you.
All you do is multiply the two values you see on screen.
4/3 · 23/ 4
= 23/3
(Since there is a 4 both on top and on the bottom, you can cross them out, instead of multiplying everything across)
I hope this helped!
