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2 years ago

A spear has a diameter of 14 ft which equation finds the volume of the sphere

Mathematics

1 answer:

fiasKO [112]2 years ago

6 0

The volume of the sphere is 1437.33 ft³

<h3></h3><h3>What is volume of sphere?</h3>

A sphere's volume V is four-thirds of pi times the radius cubed. A hemisphere's volume is half of the volume of the associated sphere.

The volume of a spherical.

V= 4/3 πr³

radius= 7ft

So,

V= 4/3*22/7*7*7*7

V= 30184/21

V = 1437.33 ft³

Learn more about this concept here:

brainly.com/question/8549007

#SPJ1

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3 years ago

If 180° < α < 270°, cos⁡ α = −817, 270° < β < 360°, and sin⁡ β = −45, what is cos⁡ (α + β)?

eduard

Answer:

$cos(\alpha+\beta)=-\frac{84}{85}$

Step-by-step explanation:

we know that

$cos(\alpha+\beta)=cos(\alpha)*cos(\beta)-sin(\alpha)*sin(\beta)$

Remember the identity

$cos^{2} (x)+sin^2(x)=1$

step 1

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we have that

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Find the value of sine

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substitute

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$sin^2(\alpha)=1-\frac{64}{289}$

$sin^2(\alpha)=\frac{225}{289}$

$sin(\alpha)=-\frac{15}{17}$

step 2

Find the value of $cos(\beta)$

we have that

The angle beta lie on the IV Quadrant

The value of the cosine is positive and the value of the sine is negative

$sin(\beta)=-\frac{4}{5}$

Find the value of cosine

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substitute

$(-\frac{4}{5})^{2}+cos^2(\beta)=1$

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$cos^2(\beta)=\frac{9}{25}$

$cos(\beta)=\frac{3}{5}$

step 3

Find cos⁡ (α + β)

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we have

$cos(\alpha)=-\frac{8}{17}$

$sin(\alpha)=-\frac{15}{17}$

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substitute

$cos(\alpha+\beta)=-\frac{8}{17}*\frac{3}{5}-(-\frac{15}{17})*(-\frac{4}{5})$

$cos(\alpha+\beta)=-\frac{24}{85}-\frac{60}{85}$

$cos(\alpha+\beta)=-\frac{84}{85}$

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