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dlinn [17]
3 years ago
15

What is the total volume of the figure? Pls help

Mathematics
1 answer:
goldfiish [28.3K]3 years ago
3 0

Answer: 58 in

Step-by-step explanation:

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1. The prism-shaped roof has equilateral triangular bases. Create an equation that models the height of one of the roof's triang
Mandarinka [93]
1. Check picture 1. Let the one side of the triangle be a, drop one perpendicular, CD. Then triangle ADB is a right triangle, with hypothenuse a and one side equal to 1/2a. By the Pythegorean theorem, as shown in the picture, the height is \frac{ \sqrt{3} }{2} a

2. if a a=25 ft, then the height is \frac{ \sqrt{3} }{2} a=\frac{ \sqrt{3} }{2} *25= \frac{1.732}{2}*25= 21. 7 (ft)

3. consider picture 2. Let the length of the roof be l feet.

one side of the prism (the roof) is a rectangle with dimensions a and l, so the area of one side is a*l
the lateral Area of the roof is 3a*l

the area of the equilateral surfaces is 2*( \frac{1}{2} *a* \frac{ \sqrt{3} }{2}a )=\frac{ \sqrt{3} }{2} a^{2}

so the total area of the roof is \frac{ \sqrt{3} }{2} a^{2} +3al

4. The total area was the 2 triangular surfaces + the 3 equal lateral rectangular surfaces. Now instead of 3 lateral triangular surfaces, we have 2.
So the total area found previously will be decreased by al


5. so the area now is \frac{ \sqrt{3} }{2} a^{2} +2al

6. now a=25 and l=2a=50

Area=\frac{ \sqrt{3} }{2} a^{2} +2al=\frac{ \sqrt{3} }{2} * 25^{2}+2*25*50=25 ^{2}  (\frac{ \sqrt{3} }{2} +4)=625*4.866

=3041.3 (ft squared)

7 0
4 years ago
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GalinKa [24]

Answer:

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_{Itsbrazts}

<em>Here's the photo... </em>

5 0
3 years ago
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Solve the equation x^5-4x^4+4x^3+2x^2-5x+2=0
sergejj [24]

Answer:

x = 2 or x = 1 or x = -1

Step-by-step explanation:

Solve for x over the real numbers:

x^5 - 4 x^4 + 4 x^3 + 2 x^2 - 5 x + 2 = 0

The left hand side factors into a product with three terms:

(x - 2) (x - 1)^3 (x + 1) = 0

Split into three equations:

x - 2 = 0 or (x - 1)^3 = 0 or x + 1 = 0

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x = 2 or x - 1 = 0 or x + 1 = 0

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x = 2 or x = 1 or x + 1 = 0

Subtract 1 from both sides:

Answer:  x = 2 or x = 1 or x = -1

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Arada [10]

Answer:

Y= -2x - 18

Step-by-step explanation:

Hope it works

4 0
3 years ago
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