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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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Ria can paint a room in 4 hours. Destiny can paint the same room in 6 hours. How long would it take Ria and Destiny to paint the
Lerok [7]

Time taken by Ria to paint a room = 4 hours

Time taken by Destiny to paint a room = 6 hours

If they work together, they complete 1 job. So,

\frac{1x}{4}+\frac{1x}{6}=1

The LCD of 4 and 6 is 12

\frac{3x+2x}{12}=1

\frac{5x}{12}=1

5x=12

x=\frac{12}{5}

Hence, both of them can paint the room in \frac{12}{5} hours or 2.4 hours.


4 0
2 years ago
Read 2 more answers
Michelle is trying to buy a car that costs $35,550, and she has saved up $20,700. She borrowed the remaining amount that she nee
Dimas [21]

Answer: $ 4,515

Step-by-step explanation:

\\The cost of the car she wanted to buy = $35,550

\\Her savings = $20,700

\\That means she needs( $35,550 - $20,700) more in order for her to buy the car.

\\Amount borrowed from the finance company  = $35,550 - $20,700

\\= $ 14,850

\\Since she now owes the financial company a total of $19,365, then the interest accrued by the loan she borrowed is given by:

\\$19,365 - $ 14,850

\\= $4,515

7 0
2 years ago
Rona mixes 2 pounds of meat with some chopped vegetables to make a mixture. She divides the mixture into 4 equal portions. Each
AVprozaik [17]

Answer:

First choice: (1/4)(2 + v) = 3; v = 10 pounds of chopped vegetables

Step-by-step explanation:

"2 pounds of meat with some chopped vegetables"

2 + v

"She divides the mixture into 4 equal portions."

(1/4)(2 + v)

"Each portion weighs 3 pounds."

(1/4)(2 + v) = 3

2 + v = 12

v = 10

Answer: (1/4)(2 + v) = 3; v = 10 pounds of chopped vegetables

7 0
2 years ago
The ratio of length to width in a rectangle is 3 to 1. If the perimeter of the rectangle is 128 feet, what is the length of the
Serga [27]

Answer: B

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
A parcel has a mass of 500g. Calculate its weight. (Assume the gravitational field strength is 10N/kg).
Elan Coil [88]

Answer:

The weight of the parcel is 5 N

Step-by-step explanation:

we know that

Weight can be calculated using the equation:

 W=mg

where

W ----> weight (W) is measured in newtons (N)

m ----> mass (m) is measured in kilograms (kg)

g ----> gravitational field strength (g) is measured in newtons per kilogram (N/kg)

In this problem we have

g=10\ N/kg

m=500\ g

Remember that

1\ kg=1,000\ g

To convert g to kg

Divide by 1,000

so

m=500\ g=500/1,000=0.5\ kg

substitute the values in the equation

W=(0.5)(10)=5\ N

therefore

The weight of the parcel is 5 N

5 0
2 years ago
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