<span>Generate a function for the height of the cyliner as a function of radius. Use this function to generate a function of r for the material used. Take the derivative of that function, set it to zero, and solve for r.
</span><span>V=πr2h</span>h=d h=d=2r h=2r <span>V=πr22r
</span><span>V(r,h)=180.5=πr2h⟹h=<span>180.5/<span>πr2</span></span></span><span>⟹A(r)=r(r+h)=r2+<span>180.5/<span>πr
</span></span></span><span>A(r)=2r(2r+h)=4r2+<span>361/<span>πr
</span></span></span>
<span>A′(r)=8r−<span>361/<span>π<span>r2</span></span></span></span>
So with this problem, let's first define the given. The city has a budget of 8m which means that it is willing spend 8m on projects and other things for the city's development. Now when the day arrived that they had to account for their spending, they realized they actually spent 12m instead of the 8m. So to solve for the deficit, meaning the amount outside of the budget, we simply subtract 12m to 8m. If we do this, we will get 4m. So the deficit of the city's budget is 4m.
Answer:
x = 80
Step-by-step explanation:
Let x be the unknown number
1/2 x - 10 = 30
Add 10 to each side
1/2x -10+10 = 30+10
1/2x = 40
Multiply each side by 2
1/2x * 2 = 40*2
x = 80
3/6 or 1/2 because there are 3 odd numbers and a cube has 6 sides.
