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tamaranim1 [39]
3 years ago
9

A wedge of cheese in the shape of a triangular prism is shown below.

Mathematics
1 answer:
BabaBlast [244]3 years ago
7 0

Answer:

144 ft^2

Step-by-step explanation:

Back (vertical):  (4 ft)(8 ft) = 32 ft^2

Right side (vert.):  (4 ft)(6 ft) = 24 ft^2

Front (vert.):  (4 ft)(10 ft) = 40 ft^2

Top (horizontal):  A = (1/2)(6 ft)(8 ft) = 48 ft^2 total (top and bottom)

Total surface area is (32 + 24 + 40 + 48) ft^2, or 144 ft^2

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How do you factor 125-x^3?
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Step-by-step explanation:

We have

125 - x {}^{3}

First, 125 is a perfect cube because

5 \times 5 \times 5 = 125

and

x^3 is a perfect cube because

x \times  x \times x = x {}^{3}

so we can use the difference of cubes identity

( {x}^{3}  -  {y}^{3} ) = (x - y)( {x}^{2}  + xy +  {y}^{2} )

Let say we have two perfect cubes:

64 because 8×8×8=64

and 27 because 3×3×3=27 and let subtract

64 - 27

we know that

64 - 27 = 37

but using the difference of cubes identity we should get the same thing.

Remeber cube root of 64 is 4 and cube root of 27 is 3 so we have

(4 - 3)( {4}^{2}  + 4(3) + 3 {}^{2} )

1(16 + 12 + 9) = 1(37) = 37

So the difference of cubes works for real numbers. This is a good way to help remeber the identity using real numbers.

Back on to the topic,

we know that 5 is cube root of 125 and x is the cube root of x^3 so we have

(5 - x)( {5}^{2}  + 5x +  {x}^{2} ) =

(5 - x)(25 + 5x +  {x}^{2} )

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