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MrMuchimi
3 years ago
5

Find the volume of the following solid:

Mathematics
1 answer:
goblinko [34]3 years ago
5 0

Answer:

93214.28 cm³

Step-by-step explanation:

The area of the given solid in the front side is = area of the rectangle + area of the semi circle.

= ( 40 × 30 ) + 0.5 × π × r²

= (40 \times 30) + 0.5 \times  \frac{22}{7} \times 15^{2} {Since radius = 0.5 × Diameter = 0.5 × 30 = 15 cm}

= 1553.57 cm².

Now the volume of the solid is given by (Area of the vertical surface × horizontal length) = 1553.57 × 60 = 93214.28 cm³ (Answer)

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What is the factorization of 3x2 – 8x + 5?
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we have

3x^{2} -8x+5

Equate the expression to zero to find the roots

3x^{2} -8x+5=0

Group terms that contain the same variable, and move the constant to the opposite side of the equation

3x^{2} -8x=-5

Factor the leading coefficient

3(x^{2} -(8x/3))=-5

Complete the square. Remember to balance the equation by adding the same constants to each side.

3(x^{2} -(8x/3)+(16/9))=-5+(16/3)

3(x^{2} -(8x/3)+(16/9))=(1/3)

Rewrite as perfect squares

3(x-(4x/3))^{2}=(1/3)

(x-(4x/3))^{2}=(1/9)

square roots both sides

(x-\frac{4}{3})=(+/-) \sqrt{\frac{1}{9}}

x=\frac{4}{3}(+/-) \frac{1}{3}

the roots are

x=\frac{4}{3}+ \frac{1}{3}=\frac{5}{3}

x=\frac{4}{3}- \frac{1}{3}=\frac{3}{3}=1

so

3x^{2} -8x+5=3(x-\frac{5}{3})(x-1)=(3x-5)(x-1)

therefore

<u>the answer is the option</u>

(3x-5)(x-1)

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3 years ago
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What is the rate of change for the linear function f(x)=-2x-5 over any interval?
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To solve this problem you must apply the proccedure shown below:

1. By definition, the rate of change of a linear function is the slope of the line and it is constant. Based on this, you must find the slope of the given function.

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3. Then, you have that the slope of the function f(x)=-2x-5 is:

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