Hello!
To find surface area, all you need to do is add up the areas of all the faces of the prism. Let’s start by remembering some basic area formulas:
Area of a triangle= 1/2*base*height
Area of a rectangle= length*width
First, find the area of each of the little triangles on the sides of the net. The base is 3 ft, and the height is 4 ft. So:
1/2*3*4= 6 ft
There are two triangles of the same size, so multiply that number by 2.
6*2=12
Now, find the area of the top rectangle:
3*8= 24
And the area of the bottom rectangle:
5*8= 40
Finally, add all of those numbers together:
12+24+40= 76 ft^2
That should be your answer!
That picture tho fiejfjejdjwjdhehfhueuxhrhfjsjdjrjr :)
Its 9m-9(2) make sure to think of the minus sign as a negative because it will equal 9m-18 not 9m+18
Answer:
Given the statement: if y =3x+6.
Find the minimum value of ![(x^3)(y)](https://tex.z-dn.net/?f=%28x%5E3%29%28y%29)
Let f(x) = ![(x^3)(y)](https://tex.z-dn.net/?f=%28x%5E3%29%28y%29)
Substitute the value of y ;
![f(x)=(x^3)(3x+6)](https://tex.z-dn.net/?f=f%28x%29%3D%28x%5E3%29%283x%2B6%29)
Distribute the terms;
![f(x)= 3x^4 + 6x^3](https://tex.z-dn.net/?f=f%28x%29%3D%203x%5E4%20%2B%206x%5E3)
The derivative value of f(x) with respect to x.
![\frac{df}{dx} =\frac{d}{dx}(3x^4+6x^3)](https://tex.z-dn.net/?f=%5Cfrac%7Bdf%7D%7Bdx%7D%20%3D%5Cfrac%7Bd%7D%7Bdx%7D%283x%5E4%2B6x%5E3%29)
Using ![\frac{d}{dx}(x^n) = nx^{n-1}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%28x%5En%29%20%3D%20nx%5E%7Bn-1%7D)
we have;
![\frac{df}{dx} =(12x^3+18x^2)](https://tex.z-dn.net/?f=%5Cfrac%7Bdf%7D%7Bdx%7D%20%3D%2812x%5E3%2B18x%5E2%29)
Set ![\frac{df}{dx} = 0](https://tex.z-dn.net/?f=%5Cfrac%7Bdf%7D%7Bdx%7D%20%3D%200)
then;
![(12x^3+18x^2) =0](https://tex.z-dn.net/?f=%2812x%5E3%2B18x%5E2%29%20%3D0)
![6x^2(2x + 3) = 0](https://tex.z-dn.net/?f=6x%5E2%282x%20%2B%203%29%20%3D%200)
By zero product property;
and 2x + 3 = 0
⇒ x=0 and x = ![-\frac{3}{2} = -1.5](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B2%7D%20%3D%20-1.5)
then;
at x = 0
f(0) = 0
and
x = -1.5
![f(-1.5) = 3(-1.5)^4 + 6(-1.5)^3 = 15.1875-20.25 = -5.0625](https://tex.z-dn.net/?f=f%28-1.5%29%20%3D%203%28-1.5%29%5E4%20%2B%206%28-1.5%29%5E3%20%3D%2015.1875-20.25%20%3D%20-5.0625)
Hence the minimum value of
is, -5.0625
Answer:
2520
Step-by-step explanation: