Answer:
1176π m³
Step-by-step explanation:
The formula for the volume of a cylinder is:
V = πr²h
Let's substitute the values given into this equation:
V = πr²h
V = (π)(14²)(6)
Solve:
V = (π)(14²)(6)
V = (π)(196)(6)
V = 1,176π
Therefore, the volume of the cylinder is 1176π cubic meters.
Answer:
dx/dt = 5√5/2
Step-by-step explanation:
Given:
dx/dt = 25 feet per second
According to Pythagoras theorem:
x² + 90² = y²
We know that x = 30 ft
So,
x² + 90² = y²
30² + 90² = y²
y = 30√10
So,
x² + 90² = y²
By taking differentiate:
2x dx/dt = 2y dy/dt
[x/y][dx/dt] = dy/dt
dx/dt = 5√5/2
Answer:
Step-by-step explanation:
To get maximum product we need to optimize how we break down the numbers
Its obvious we don't want number 1 to be used as it won't change the product
Also we don't want to use big numbers, we can have four 5's instead of two 10's as it would give greater product, 5*5 > 10
<u>What is best number?</u>
- 2 and 3 are the smallest, 4 can be written as two 2's
- 5 = 2+ 3 and 2*3 = 6, so it is better to use 2's and 3's instead of 5
- 6 = 2+2+2, 2^3 = 8 and 6 = 3+ 3, 3^2 = 9, so it is better to use two 3's for 6
- 7 = 2+2+3, 2*2*3= 12, again 2's and 3's make greater product
<u>So the best is to break the number down to 2's and 3's</u>
- 23 = 2*10 + 3 ⇒ 2^10*3 = 3072
- 23 = 3*7 + 2 ⇒ 3^7*2 = 4374
As we see the maximum product we can get is 4374 with seven 3's and one 2.
<u>Hence the numbers are:</u>
Step-by-step explanation:
equation y =
When x = -1
y = = (Answer)
When x = 0,
y = = 1 (Answer)
When x = 3,
y = = 216 (Answer)