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alexandr402 [8]
3 years ago
12

Nathan has a sculpture in the shape of a pyramid. The height of the sculpture is 3 centimeters less than the side length,x,of it

s square base. Nathan uses the formula for the volume of a pyramid to determine the dimesnsioms of the sculpture.
V=1/3 a^2h
Here, a is the side length of the pyramids square base and h is it’s height.

If 162 cubic centimeters of clay were used to make the sculpture, the equation x^3+_x^2+_=0 can be used to find that the length of the sculptures base is _ centimeters.
Mathematics
1 answer:
Eduardwww [97]3 years ago
7 0

Answer:

side length of sculpture = 9 cm

height of sculpture = 6cm

Step-by-step explanation:

Given that,

volume of sculpture = 162cm³

side length of sculpture = x

height of sculpture = x-3

formula for volume of sculpture

<h3>V=1/3 a²h</h3>

by putting values, the equation can be used to find the length of the sculpture’s base

162 = 1/3 (x)² (x-3)

162(3) =  (x)² (x-3)

486 = x²(x-3)

486 = x³ - 3x²

x³ - 3x² - 486 = 0

x = 9 <em>(using a graph tool / calculator equation mode)</em>

side length of sculpture = 9 cm

height of sculpture = 9 - 3

                                 = 6cm

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3 years ago
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Find the coordinates of the midpoint M of the segment with the given endpoints. Then find the distance between the two points. R
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Answer:

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PQ midpoint = (x2 + x1)/2, (y2 + y1)/2

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Givens

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Question 2

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