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fgiga [73]
2 years ago
9

How do i work this problem sin(2cos^-1 1/11)

Mathematics
1 answer:
lora16 [44]2 years ago
5 0
\sin\left(2\cos^{-1}\dfrac1{11}\right)=2\sin\left(\cos^{-1}\dfrac1{11}\right)\cos\left(\cos^{-1}\dfrac1{11}\right)

When 0, you have \cos(\cos^{-1}x)=x, so you can simplify the above slightly to get

\sin\left(2\cos^{-1}\dfrac1{11}\right)=\dfrac2{11}\sin\left(\cos^{-1}\dfrac1{11}\right)

Now picture a right triangle and pick one of the non-right angles. Let this angle's cosine be \dfrac1{11}. This means the leg adjacent to this angle must have length 1, while the hypotenuse must have length 11. By the Pythagorean theorem, the length of the remaining leg must be

\sqrt{11^2-1^1}=\sqrt{121-1}=\sqrt{120}=2\sqrt{30}

This means the sine of this angle is \dfrac{2\sqrt{30}}{11}, and so

\sin\left(2\cos^{-1}\dfrac1{11}\right)=\dfrac{4\sqrt{30}}{121}
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24.6967 meters

Step-by-step explanation:

The roots of the tree go 6 and 5 over 12 meters below the ground level.

Now, 6 and 5 over 12 meters is equivalent to 6.4167 meters.

Again the top of the tree is 18.28 meters high from the ground level.

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A bulletin board can be covered completely by 30 square pieces of paper without any gaps or overlaps if each piece of paper has
34kurt

Answer:

The area of the bulletin board is 30 square foot.

Step-by-step explanation:

A bulletin board can be covered completely by 30 square pieces of paper without any gaps or overlaps.

If each piece of paper has side length of 1 foot so the area of each paper is 1 ft x 1 ft = 1 square foot.

There are 30 pieces of paper needed to completely cover the bulletin board, so 30 pcs of paper with an area of 1 square foot is equal to 30 square feet. The area of the bulletin board is 30 square foot.

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the area of each trapezoid is (v(t1)+v(t2))/2 times width

for the first interval
the average between 0 and 0.4 is 0.2
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2nd
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4th
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5.49
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