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elixir [45]
2 years ago
11

Two similar triangular prisms have volumes of 27 square meters and 64 square meters.

Mathematics
1 answer:
Inessa [10]2 years ago
8 0

Answer:

9/16

Step-by-step explanation:

First we need to know that the dimensions ratio, the surface area ratio and the volume ratio have the following relation:

volume ratio = dimension ratio ^3

surface area ratio = dimension ratio ^2

The volume ratio between small prism and the large prism is 27 / 64.

To find the dimensions ratio, we need to take the cubic root of the volume scale:

dimension ratio = 3√(27/64) = 3/4

Now, to find the surface area ratio, we just need to make the square of the dimension ratio:

surface area ratio = (3/4)^2 = 9/16

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Given sin(u)= -7/25 and cos(v) = -4/5, what is the exact value of cos(u-v) if both angles are in quadrant 3
solmaris [256]

Given:

\sin (u)=-\dfrac{7}{25}

\cos (v)=-\dfrac{4}{5}

To find:

The exact value of cos(u-v) if both angles are in quadrant 3.

Solution:

In 3rd quadrant, cos and sin both trigonometric ratios are negative.

We have,

\sin (u)=-\dfrac{7}{25}

\cos (v)=-\dfrac{4}{5}

Now,

\cos (u)=-\sqrt{1-\sin^2 (u)}

\cos (u)=-\sqrt{1-(-\dfrac{7}{25})^2}

\cos (u)=-\sqrt{1-\dfrac{49}{625}}

\cos (u)=-\sqrt{\dfrac{625-49}{625}}

On further simplification, we get

\cos (u)=-\sqrt{\dfrac{576}{625}}

\cos (u)=-\dfrac{24}{25}

Similarly,

\sin (v)=-\sqrt{1-\cos^2 (v)}

\sin (v)=-\sqrt{1-(-\dfrac{4}{5})^2}

\sin (v)=-\sqrt{1-\dfrac{16}{25}}

\sin (v)=-\sqrt{\dfrac{25-16}{25}}

\sin (v)=-\sqrt{\dfrac{9}{25}}

\sin (v)=-\dfrac{3}{5}

Now,

\cos (u-v)=\cos u\cos v+\sin u\sin v

\cos (u-v)=\left(-\dfrac{24}{25}\right)\left(-\dfrac{4}{5}\right)+\left(-\dfrac{7}{25}\right)\left(-\dfrac{3}{25}\right)

\cos (u-v)=\dfrac{96}{625}+\dfrac{21}{625}

\cos (u-v)=\dfrac{1 17}{625}

Therefore, the value of cos (u-v) is 0.1872.

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