Answer:
surface area = 136 m^2
Step-by-step explanation:
The prism has 5 faces.
Faces 1 and 2: The front and back faces are two congruent triangles with base 6 m and height 4 m.
Face 3: The bottom face is a rectangle with length 7 m and width 6 m.
Faces 4 and 5: The left and right inclined faces are two congruent rectangles with length 7 m and width 5 m.
area = area of faces 1 and 2 + area of face 3 + area of faces 4 and 5
area of triangle = bh/2
area of rectangle = LW
area = 2 * 6 m * 4 m / 2 + 7 m * 6 m + 2 * 7 m * 5 m
area = 24 m^2 + 42 m^2 + 70 m^2
area = 136 m^2
Answer: surface area = 136 m^2
Answer:
First term=1
Second term=-x
Third term=![2x^2](https://tex.z-dn.net/?f=2x%5E2)
Fourth term =![-\frac{28}{3!}x^3](https://tex.z-dn.net/?f=-%5Cfrac%7B28%7D%7B3%21%7Dx%5E3)
Step-by-step explanation:
We are given that function
![f(x)=(1+3x)^{-1/3}](https://tex.z-dn.net/?f=f%28x%29%3D%281%2B3x%29%5E%7B-1%2F3%7D)
We have to find the first four non zero terms of the Maclaurin series for the binomial.
Maclaurin series of function f(x) is given by
![f(x)=f(0)+f'(0)x+\frac{1}{2!}f''(0)x^2+\frac{1}{3!}f'''(0)x^3+....](https://tex.z-dn.net/?f=f%28x%29%3Df%280%29%2Bf%27%280%29x%2B%5Cfrac%7B1%7D%7B2%21%7Df%27%27%280%29x%5E2%2B%5Cfrac%7B1%7D%7B3%21%7Df%27%27%27%280%29x%5E3%2B....)
![f(0)=(1+3x)^{\frac{-1}{3}}=1](https://tex.z-dn.net/?f=f%280%29%3D%281%2B3x%29%5E%7B%5Cfrac%7B-1%7D%7B3%7D%7D%3D1)
![f'(x)=-\frac{1}{3}(1+3x)^{-\frac{4}{3}}(3)=-(1+3x)^{-\frac{4}{3}}](https://tex.z-dn.net/?f=f%27%28x%29%3D-%5Cfrac%7B1%7D%7B3%7D%281%2B3x%29%5E%7B-%5Cfrac%7B4%7D%7B3%7D%7D%283%29%3D-%281%2B3x%29%5E%7B-%5Cfrac%7B4%7D%7B3%7D%7D)
![f'(0)=-1](https://tex.z-dn.net/?f=f%27%280%29%3D-1)
![f''(x)=\frac{4}{3}\times 3 (1+3x)^{-\frac{7}{3}}](https://tex.z-dn.net/?f=f%27%27%28x%29%3D%5Cfrac%7B4%7D%7B3%7D%5Ctimes%203%20%281%2B3x%29%5E%7B-%5Cfrac%7B7%7D%7B3%7D%7D)
![f''(0)=4](https://tex.z-dn.net/?f=f%27%27%280%29%3D4)
![f'''(x)=-4\times \frac{7}{3}\times 3(1+3x)^{-\frac{10}{3}}](https://tex.z-dn.net/?f=f%27%27%27%28x%29%3D-4%5Ctimes%20%5Cfrac%7B7%7D%7B3%7D%5Ctimes%203%281%2B3x%29%5E%7B-%5Cfrac%7B10%7D%7B3%7D%7D)
![f'''(0)=-28](https://tex.z-dn.net/?f=f%27%27%27%280%29%3D-28)
Substitute the values we get
![(1+3x)^{-\frac{1}{3}}=1-x+\frac{4}{2!}x^2+\frac{-28}{3!}x^3+...](https://tex.z-dn.net/?f=%281%2B3x%29%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%3D1-x%2B%5Cfrac%7B4%7D%7B2%21%7Dx%5E2%2B%5Cfrac%7B-28%7D%7B3%21%7Dx%5E3%2B...)
![(1+3x)^{-\frac{1}{3}}=1-x+2x^2+\frac{-28}{3!}x^3+...](https://tex.z-dn.net/?f=%281%2B3x%29%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%3D1-x%2B2x%5E2%2B%5Cfrac%7B-28%7D%7B3%21%7Dx%5E3%2B...)
First term=1
Second term=-x
Third term=![2x^2](https://tex.z-dn.net/?f=2x%5E2)
Fourth term =![-\frac{28}{3!}x^3](https://tex.z-dn.net/?f=-%5Cfrac%7B28%7D%7B3%21%7Dx%5E3)
The equation would be 12h = 120 - 36
Your answer is h = 7
Because 120 - 36 = 84
and 84 / 12 = 7
Hope this helps!
A circle is a set of points equidistant from a center point. Here's a set of points equidistant from the origin! A common form to write the equation of a circle in is the center-radius form. The center-radius form is: (x−h)2+(y−k)2=r2 Here, the center point is denoted by (h,k) and r is the radius of the circle.