The formula for the volume of a prism is V=Bh, where B is the base area and h is the height.The base of the prism is a rectangle.The length of a rectangle is 9cm and the width is 7cm.
Answer:
The line has no slope. I hope this helps
Answer:
1
Step-by-step explanation:
x+y=1 if x=0, then y=1
Answer:
The inner function is
and the outer function is
.
The derivative of the function is
.
Step-by-step explanation:
A composite function can be written as
, where
and
are basic functions.
For the function
.
The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.
Here, we have
inside parentheses. So
is the inner function and the outer function is
.
The chain rule says:
![\frac{d}{dx}[f(g(x))]=f'(g(x))g'(x)](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%3Df%27%28g%28x%29%29g%27%28x%29)
It tells us how to differentiate composite functions.
The function
is the composition,
, of
outside function: ![g(x)=3x^5](https://tex.z-dn.net/?f=g%28x%29%3D3x%5E5)
inside function: ![h(x)=4x^2 + 8](https://tex.z-dn.net/?f=h%28x%29%3D4x%5E2%20%2B%208)
The derivative of this is computed as
![\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=3\frac{d}{dx}\left(\left(4x^2+8\right)^5\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\f=u^5,\:\:u=\left(4x^2+8\right)\\\\3\frac{d}{du}\left(u^5\right)\frac{d}{dx}\left(4x^2+8\right)\\\\3\cdot \:5\left(4x^2+8\right)^4\cdot \:8x\\\\120x\left(4x^2+8\right)^4](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%283%5Cleft%284x%5E2%2B8%5Cright%29%5E5%5Cright%29%3D3%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%28%5Cleft%284x%5E2%2B8%5Cright%29%5E5%5Cright%29%5C%5C%5C%5C%5Cmathrm%7BApply%5C%3Athe%5C%3Achain%5C%3Arule%7D%3A%5Cquad%20%5Cfrac%7Bdf%5Cleft%28u%5Cright%29%7D%7Bdx%7D%3D%5Cfrac%7Bdf%7D%7Bdu%7D%5Ccdot%20%5Cfrac%7Bdu%7D%7Bdx%7D%5C%5Cf%3Du%5E5%2C%5C%3A%5C%3Au%3D%5Cleft%284x%5E2%2B8%5Cright%29%5C%5C%5C%5C3%5Cfrac%7Bd%7D%7Bdu%7D%5Cleft%28u%5E5%5Cright%29%5Cfrac%7Bd%7D%7Bdx%7D%5Cleft%284x%5E2%2B8%5Cright%29%5C%5C%5C%5C3%5Ccdot%20%5C%3A5%5Cleft%284x%5E2%2B8%5Cright%29%5E4%5Ccdot%20%5C%3A8x%5C%5C%5C%5C120x%5Cleft%284x%5E2%2B8%5Cright%29%5E4)
The derivative of the function is
.
Answer:
40 ft²
Step-by-step explanation:
Let the length of the original rectangle be L and original Breadth be B
it is given that the original area is 5/8 ft²
i.e.
Original Length x Original Breadth = Original Area, or,
LB = 5/8 ft² ------------------(1)
Given that the dilation factor is 8,
Hence,
New Length = 8L and New Breadth = 8B
THerefore,
New Area = 8L x 8B
= 64 LB (from (1) above , we know that LB = 5/8 ft², substitute into expression)
= 64 (5/8)
= 40 ft²