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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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(-6time + 3) + (5time -4)
Fynjy0 [20]

Answer:

-2

Step-by-step explanation:

18+-20

-2

3 0
3 years ago
Which problem will have the greater quotient, 376.0 divided by 92 OR 376 divided by 93.01? Explain how you know logically
xxTIMURxx [149]
1. 376.0 / 92 = ?

2. 376 / 93.01 = ? 

So the question asks us which quotient will be greater. In plain English it is asking which of the two, ?, will be greater. Seeing how the question is asking for a logical answer we are not going to actually solve the problem. Instead we will use logic. 

First let's do some examples, and explain more in-depth how division works.

A. 6/3 = 2
B. 6/2 = 3

In this case, B is greater than A.

Greater than being any number that is larger than another on a scale reading from left to right, so if you were to count out all the way to the number the one that comes first is lower in value than the one that comes second.

Division works like this: Say we have a full delicious pie. We want to divide it up into 12 pieces so all our friends can have some. What we're doing is simply finding a value that if multiplied by 12 would equal our 1 pie. If you instead divided it by 24 you would have even SMALLER pieces of pie. 

A. 5/2
B. 5/3

You might not be able to answer this one, but say our pie is equal to 5. For A. imagine we take a pie and cut it in half. Now for B. imagine a pie and cut it into 3 equal sized pieces. Which one will have the bigger individual pieces? A. will!

Keep in mind that the individual size of the piece would be the quotient (the quotient just means the answer to a division problem).
 
Now to quickly dismiss the 376.0, When you add 0's to the DECIMAL you do not change the value.
If you did then, 0.0 wouldn't still be 0. Or 1.0 wouldn't still be 1. The .0 is just a place holder and signifies nothing. Don't get this confused with adding a zero to the end of a number, because that does change the value (except in the case of 0). 1 with an extra zero becomes 10, and so on. 

So let's tackle this problem!
A. 376.0 / 92
B. 376 / 93.01

In the end the .0 is meaningless so it's the same as this: 
A. 376 / 92
B. 376 / 93.01

All we are looking for is the dividend that is smaller. (A dividend being what is dividing a number. In the case of 4/2 the dividend is 2. 5/2, the dividend is 2. 6/3, the dividend is 3. So in other words the dividend is the number after the division symbol, or in this case the slash (they are the same)).

So let's see, which is smaller? 92, or 93.01.
Whichever is smaller is going to have a bigger slice of pie than the other one. So, 92. Is our answer.

Note that this reasoning worked, because the numerator (376) is the same on both division problems. If they differed we wouldn't be able to use the same logic (at least as easily as we did in this problem!).  

 
3 0
3 years ago
The two triangles are similar.
Neko [114]

Given that the triangles are similar.

When triangles are similar, all three pairs of corresponding sides are in the same ratio.

Similarly in the given triangles, the ratio of the corresponding sides are equal.

\frac{8}{2x-2}= \frac{8+6}{3x}

\frac{8}{2x-2}= \frac{14}{3x}

Cross multiplying, we get

8 \times 3x = 14 \times (2x-2)

24x = 28x-28

-4x = -28

Dividing both sides of the equation by -4.

So, we get

x = 7.

7 0
3 years ago
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Hshehebeirjiejeueb why
Aleksandr [31]

Answer:

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Step-by-step explanation:

7 0
3 years ago
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Kerry is planning to plant a rectangular garden that is 16 feet longer than it wide. Kerry wants to find its width if its area i
trapecia [35]
I think it is A. I hope Im correct.
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3 years ago
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