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Black_prince [1.1K]

3 years ago

14

Find the value of x. Please help!

1 answer:

Mars2501 [29]3 years ago

8 0

Answer:

x = 3

Step-by-step explanation:

Using the triangle similarity theorem

x/x+3 = x+3/12

Cross multiply

12x = (x+3)(x+3)

12x = x²+3x+3x+9

12x = x²+6x+9

x²+6x+9-12x = 0

x²-6x+9 = 0

Factorize

x²-3x-3x+9 = 0

x(x-3)-3(x-3) = 0

x - 3 = 0

x = 3 twice

Hence the value of x is 3

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Answer:

1. 170.083 in³

2. 126π in³

3. 92.106 m³

4. 2412.74 in³

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Step-by-step explanation:

1.

Cylinder:

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$(3.14)(2.5)^{2}(7)$ *Square 2.5*

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Sphere:

$V = \frac{4}{3}\pi r^{3}$ *Plug in numbers*

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2.

Cylinder:

$V = \pi r^{2}h$ *Plug in numbers*

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$\pi (9)(10)$ *Multiply*

$90\pi$

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$V = \frac{4}{3}$ π $r^{3}$ *Plug in numbers*

$\frac{4}{3}\pi (3)^{3}$ *Cube 3*

$\frac{4}{3} \pi (27)$ *Multiply*

$36\pi$

Add both Volumes to get total

$90\pi + 36\pi = 126in^{3}$

3.

Sphere:

$V = \frac{4}{3}\pi r^{3}$ *Plug in numbers*

$\frac{4}{3} (3.14)(3)^{3}$ *Cube 3*

$\frac{4}{3} (3.14)(27)$ *Multiply*

$113.04m^{3}$

Cone:

$V = \frac{\pi r^{2}h}{3}$ *Plug in numbers*

$\frac{(3.14)(2)^{2}(5)}{3}$ *Square 2*

$\frac{(3.14)(4)(5)}{3}$ *Solve*

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Subtract the volumes to get the volume of the blue area

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$\frac{4}{3}\pi (8)^{3}$ *Cube 8*

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$V = \frac{\pi r^{2}h}{3}$ *Plug in numbers*

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$\frac{\pi (64)(20)}{3}$ *Multiply and Divide*

$1340.41 in^{3}$

Add both volumes

$1072.33 + 1340.41 = 2412.74in^{3}$

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$\pi (6)^{2}(16)$ *Square 6*

$\pi (36)(16)$ *Multiply*

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