Find the surface area of the figure below.
1 answer:
Answer:
261 cm²
Step-by-step explanation:
To find the surface area of a square pyramid, you must first recognize all of the shapes.
There are four triangles and one square.
- To find the area of a square, multiply the side by itself twice.
- To find the area of a triangle, multiply the base and the height, then multiply the product by 1/2.
The triangles have a base of 9 and a height of 10.
Multiply the product by 1/2.
There are four triangles.
The area of all three triangles is 180 centimeters; the area of a single triangle is 45 centimeters.
There square has sides of 9 centimeters.
The area of the square is 81 centimeters.
Lastly, we add the areas of the shapes.
Therefore, the surface area of this square prism is 261 cm².
You can use this layout to find the surface area of a square pyramid.
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Answer:
1)f(x)=2(3)^x
2)f(x)=10(2)^x
3)Graph attached
4) Amber will have 192 and 3145728 shares on day 3rd and 10th respectively
Ben will have 54 and 118,098 shares on day 3rd and 10th respectively
Carter will have 80 and 10240 shares on day 3rd and 10th respectively
5)the graph has moved 45 unit up
6)Amber's posts will travel fastest
7)Amber' function
Step-by-step explanation:
1)
Ben shares posts with two friends and then they share with 3 more everyday, so her the growth rate is 3
f(x)=2(3)^x
x=number of days
2)
Carter shares posts with ten friends and then they share with 2 more everyday, so her the growth rate is 2
f(x)=10(2)^x
x=number of days
3)
Graph attached contain graph's of following
Ben's f(x)=2(3)^x in red
Carter's f(x)=10(2)^x in blue
Amber's f(x)=3(4)^x in green
4)
Finding how many shares each student will get on day 3 and day 10:
For Amber:
substituting x=3,
f(x)=3(4)^3
= 192
Now substituting x=10,
f(x)= 3(4)^10
= 3145728
Amber will have 192 and 3145728 shares on day 3rd and 10th respectively
For Ben:
substituting x=3,
f(x)=2(3)^3
= 54
Now substituting x=10,
f(x)= 2(3)^10
= 118,098
Ben will have 54 and 118,098 shares on day 3rd and 10th respectively
For Carter:
substituting x=3,
f(x)=10(2)^3
= 80
Now substituting x=10,
f(x)= 10(2)^10
= 10240
Carter will have 80 and 10240 shares on day 3rd and 10th respectively
5)
If Amber's graph changes to
f'(x)=3(4)^x +45
then as per translation, it means the graph has moved 45 unit up from original position as shown in attached graph
original f(x)=3(4)^x in green
translated f'(x)=3(4)^x +45 in blue
6)
In exponential function the base of function effects the growth and in given cases of Amber, Ben and Carter; base of Amber's function is greatest i.e 4 other two have 2 and 3.
So Amber's posts will travel fastest
7) A post with fewer friends initially and then more shares like Amber. Because at the end of the day the growth rate is important and as explain above the number of shares i.e base of exponential function is important.
Hence for more shares and likes Amber' function is the best choice !
