can someone please help mee

Mathematics

1 answer:

Finger [1]2 years ago

4 0

Answer:

$\frac{\sqrt{731}}{30}$

Step-by-step explanation:

We first observe that the angle is located in quadrant III

This allows us to draw a triangle as attached in the attachments.

Using this triangle, we can find sin( $\theta_1$ ).

Remembering that sin(theta) = $\frac{opp}{hypo}$ , we can see from the attached image that it is $\frac{\sqrt{30^2 - 13^2}}{30}$ , then simplifying $\sqrt{30^2 - 13^2}$ using a calculator, we get $\sqrt{731}$ .

So our final answer is the answer shown above.

You may be wondering how did the side lengths appear on the triangle.

From cos(theta_1), we remember that cos(theta) = adj/hypo, so, we can draw our triangle using that the adjacent of the theta = -13 (another reason why is because the angle is in quadrant three), and hypo is 30.

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Hello,how do I calculate the the volume of this compound shape?

Setler [38]

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The volume of a rectangular prism is given by the product between its 3 different dimensions, width, length and height. The green prism is the easiest to see the its dimensions, it has a width equals to 3, a length equals to 3 and a height equal to 1/2, therefore, its volume is

$V_g=3\times3\times\frac{1}{2}=9\times\frac{1}{2}=\frac{9}{2}=4\frac{1}{2}$

Since the width of the green prism is 3 and the red prism is 1 1/2 apart from the corner of the green prism, the width of the red prism is the difference between those values.

$3-1\frac{1}{2}=\frac{6}{2}-\frac{3}{2}=\frac{6-3}{2}=\frac{3}{2}=1\frac{1}{2}$

The length and the height of the red prism are also easy to see on the image, both of those values are 1, which means the volume of the red prism is

$V_r=1\frac{1}{2}\times1\times1=1\frac{1}{2}$

Finally, the last prism is the blue prism. The height of the green prism and the blue prism combined is equal to 3/4. Since the height of the green prism is 1/2, the height of the blue prism is