Answer:
The answer to your question is -3, 7
Step-by-step explanation:
Data
x + y = 4 ------------ Equation l
7x + 9y = 42 ----------- Equation ll
Process
1.- Solve the system by elimination
- Multiply equation l by -7
-7x - 7y = - 28
7x+9y = 42
2.- Simplify
0 + 2y = 14
3.- Solve for y
y = 14/2
y = 7
4.- Substitute y in equation l to find x
x + 7 = 4
Solve for x
x = 4 - 7
x = -3
<span>So there are 4 books
=> 1 physics
=> 1 chemistry
=> mathematics
=> Biology
These books needs to be place on a shelf.
Now, let’s find the probability of mathematics book to be placed on top.
Let’s analyze the problem
Probability => 1 mathematics book / 4 total books
P = Probability
P = 1 / 4
P = ¼ or 0.25
Thus, the probability of mathematics book to be placed on top inside the shelf
approximately is ¼ or 0.25.</span>
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:
your question is incomplete! :)
