Answer:
4
Step-by-step explanation:
Answer: 132
Step-by-step explanation:
r = 4cm
h = 12cm
therefore, Volume of cylinder = 
h
= 22/7 x 4 x 4 x 12
= 22/7 x 16 x 12
= 22/7 x 192
= 132
Hope it helped u,
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Answer:
Assume that Sn is valid for n = k and prove that Sn is valid for n = k + 1.
Step-by-step explanation:
This is the second step in the principal of mathematical induction. The three steps in the principals of mathematical induction are:
1. show that something works for the first case (base or anchor step)
2. assume that it works for any particular step (inductive hypothesis), and then
3. show that it works for the next case (inductive step)
p. 621 in textbook
It's weird that they put steps 2 & 3 together, but it was correct on the test so ¯\_(ツ)_/¯
Answer:
Step-by-step explanation:
Let the length of one side of the square base be x
Let the height of the box by y
Volume of the box V = x²y
Since the box is opened at the top, the total surface area S = x² + 2xy + 2xy
S = x² + 4xy
Given
S = 7500sq in.
Substitute into the formula for calculating the total surface area
7500 = x² + 4xy
Make y the subject of the formula;
7500 - x² = 4xy
y = (7500-x²)/4x
Since V = x²y
V = x² (7500-x²)/4x
V = x(7500-x²)/4
V = 1/4(7500x-x³)
For us to maximize the volume, then dV/dx = 0
dV/dx = 1/4(7500-3x²)
1/4(7500-3x²) = 0
(7500-3x²) = 0
7500 = 3x²
x² = 7500/3
x² = 2500
x = √2500
x = 50in
Since y = (7500-x²)/4x
y = 7500-2500/4(50)
y = 5000/200
y = 25in
Hence the dimensions of the box that will maximize its volume is 50in by 50in by 25in.
The Volume of the box V = 50²*25
V = 2500*25
V= 62,500in³
Hence the maximum volume is 62,500in³
Answer:
y = -3x - 1
Step-by-step explanation:
y = mx + c
m = (-4-2)/(1-(-1)) = -6/2 = -3
y = -3x + c
When x = -1, y = 2
2 = -3(-1) + c
c = 2 - 3 = -1
y = -3x - 1
