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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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When solving -1/8 (x + 35) = −7, what is the correct sequence of operations?
mariarad [96]

<u>ANSWER: </u>

Division, multiplication, addition is the correct sequence of operations for solving -\frac{1}{8}(x+35)=-7

<u>SOLUTION: </u>

Given, equation is  -\frac{1}{8}(x+35)=-7

We need to solve the given equation in correct sequential order.

So, let us follow the BODMAS rule.

BODMAS means sequence of operations are brackets, orders, division, multiplication, addition, subtraction

Now,

-\frac{1}{8}(x+35)=-7

As the term in brackets cannot be processed further we can go for next term.

Now the division operation has to be done first according to BODMAS

- 0.125(x+35)= -7

Multiplication comes second in order.

-0.125x+4.375= -7

On rearranging the terms, we get

-0.125x+4.375+7=0

Now perform addition according to BODMAS

-0.125x+11.375=0

0.125x=11.375

x=\frac{11.375}{0.125}=91

Hence division, multiplication, addition is the correct sequence of operations for solving -\frac{1}{8}(x+35)=-7

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3 years ago
The width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches, then the area of t
Yuliya22 [10]

The original are would be 48.

Since we know that the length and width are two consecutive even integers, we can model them as follows:

Width = x

Length = x + 2

This works because no matter what even number is put in for x, the length will also be even.

Now we know if we subtract 3 from the width, we have a new rectangle that gives us an area of 24 inches. Therefore, our new triangle has the following:

Width: x - 3

Length: x + 2

Area: 24

And we can plug this into the equation.

Length* Width = Area

(x + 2)(x - 3) = 24

x^2 - x - 6 = 24

x^2 - x - 30 = 0

This is not a quadratic that we can factor to show the following:

(x - 6)(x + 5) = 0

This gives us the answers of x = 6 and x = -5. Since a side can't be negative, we throw out the x = -5 and the answer is x = 6.

So if we go back to the original rectangle, we know:

Width = x = 6

Length = x + 2 = 8

Area = 6*8 = 48

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WidthAnswer:

Step-by-step explanation:

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