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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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Need help thank you very much
Zarrin [17]

Answer:

a)  -    9/2   or   -0,45

b)  -   3/5    or -0,6

c)   -4

d)  1

e)  -2

d)  0

Step-by-step explanation:

4 0
2 years ago
Write a quadratic relation in the form y = ax2 + bx + c with roots 4 and - 3 and
pochemuha

Answer:

y =  2*x^2 - 2*x - 24

Step-by-step explanation:

If we have a quadratic function with roots a and b, we can write the equation for that function as:

y = f(x) = A*(x - a)*(x - b)

Where A is the leading coefficient.

In this case, we know that the roots are: 4 and -3

Then the function will be something like:

f(x) = A*(x - 4)*(x - (-3) )

f(x) = A*(x - 4)*(x + 3)

Now we need to determine the value of A.

We also know that the graph of the function passes through the point (3, -12)

This means that:

f(3) = -12

Then:

-12 = A*(3 - 4)*(3 + 3)

-12 = A*(-1)*(6)

-12 = A*(-6)

-12/-6 = A

2 = A

Then the equation is:

y = f(x) = 2*(x - 4)*(x + 3)

Now we need to write this in standard form, so we just need to expand the equation:

y = f(x) = 2*(x^2 + x*3 - x*4 - 4*3)

y = f(x) = 2*(x^2 - x - 12)

y = f(x) = 2*x^2 - 2*x - 24

Then the relation is:

y =  2*x^2 - 2*x - 24

4 0
3 years ago
Multiply (x - 4)(2x + 3) using the foil method show the foil method products
AVprozaik [17]

(x - 4)(2x + 3)

Using foil:

2x^2 + 3x - 8x - 12

Simplify.

2x^2 - 5x - 12 is the product after using FOIL.

8 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B60%7D%20%7D%7B%5Csqrt%5B3%5D%7B36%7D%20%7D" id="TexFormula1" title=
Margarita [4]
∛60
--------
∛36

=
∛5
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∛3

=∛45
-----------
3

= 1.185
3 0
3 years ago
Read 2 more answers
The arena has come to an agreement with the Sleaford Rockers to pay them according to this formula: b = tp- ( s + 2,000)
Anna35 [415]

if I am not mistaken your answer is 92,000. I hope this helps you good luck with l=your mathematics.

7 0
3 years ago
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