Let say radius is r
<span>its height is h </span>
<span>its lateral area = y </span>
<span>y = 2 pi r h </span>
<span>since the cylinder is inscribed in the sphere </span>
<span>So (2r )^2 + h^2 = 64 </span>
<span>then 4 (r^2) = 64 - h^2 </span>
<span>since y^2 = 4 (pi)^2 r^2 h^2 </span>
<span>then y^2 = (pi)^2 *h^2 * (64 -h^2) </span>
<span>y^2 = 64 (pi)^2 * h^2 - (pi)^2 * h^4 </span>
<span>2 y y' = 128 (pi)^2 * h - 4 (pi)^2 * h^3 </span>
<span>putting y' = 0 </span>
<span>4 (pi)^2 h ( 32 - h^2)=0 </span>
<span>ether h = 0 testing this value (changing of the sign of y' before and after ) y is minimum </span>
<span>or h = 4 sqrt(2) </span>
<span>testing this value (changing of the sign of y' before and after ) y is maximum </span>
<span>So the maximum value of y^2 = (pi)^2 *32 *( 64 - 32) </span>
<span>y^2 = (pi)^2 * (32)^2 </span>
<span>y = 32 (pi) square feet
hope this helps</span>
Answer:
k = -5
Step-by-step explanation:
The function f(x) passes through the points (-4,0) and (-2,2).
Therefore, the equation of the straight line is given by
⇒ 
⇒ y = x + 4
⇒ f(x) = x + 4 ......... (1)
Now, g(x) passes through the points (-4,0) and (-2,-10).
Then the equation will be
⇒ 
⇒ y = - 5x - 20 = - 5 (x + 4)
⇒ g(x) = -5 (x + 4) ....... (2)
Therefore, from equations (1) and (2) we get k = -5 (Answer)
Answer:
An angle degree and a side measure
Step-by-step explanation:
SAS means side angle side
so in order to prove that the triangles are congruent, you need to find out if one of the angle degree and a side measure are the same
Answer:
v = 15/7, or 2.14
Step-by-step explanation:
Find a common denominator, or multiply both denominators by each other, and well as the numerator.
v/5 = 3/7 can be written as 7v/35 = 15/35
multiplying both sides with 35, we are left with 7v = 15
v = 15/7, or 2.14
