Answer:
125a^3 + 300a^2b + 240ab^2 + 64b^3
Step-by-step explanation:
The volume of a cube is the cube of the side length.
V = s^3
Here, the side length of the cube is 5a + 4b, so we cube 5a + 4b.
V = (5a + 4b)^3
V = (5a + 4b)(5a + 4b)(5a + 4b)
V = (25a^2 + 20ab + 20ab + 16b^2)(5a + 4b)
V = (25a^2 + 40ab + 16b^2)(5a + 4b)
V = 125a^3 + 100a^2b + 200a^2b + 160ab^2 + 80ab^2 + 64b^3
V = 125a^3 + 300a^2b + 240ab^2 + 64b^3
Answer:
x = 4
Explanation:
3x - 4y = 36
5x + 2y = 8 ( multiply all by two )
3x - 4y = 36
10x + 4y = 16
13x = 52
Divide by 13
x = 4 hope this helps
<h3>
Answer: True</h3>
Explanation:
This theorem doesn't have a name unfortunately. So searching it out is a bit tricky if you don't know the right way to word things. Luckily it wasn't too hard of a find, and I managed to track it down in a linear algebra textbook.
Check out the screenshot below for the snippet of the theorem and the corresponding proof. The book simply refers to it as "theorem 1.9", which again, is an unfortunate choice of naming.
<span>At t = 1:
The radius is 3(1) = 3
The volume is 4/3 π(3)^3 = 113
At t = 4:
The radius is 3(4) = 12
The volume is 4/3 π(12)^3 = 7238
We can find the change in the volume:
The change in volume is 7238 - 113 = 7125
The change in volume occurred during a time of 3 seconds. To find the average rate of change in the volume, we need to divide the change in the volume by the time.
average rate of change = 7125 / 3 = 2375
The average rate of the change in the volume is 2375
(The units should be (m^3/s) or (ft^3/s) or (cm^3/s) etc...)</span>