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Scorpion4ik [409]
3 years ago
15

Prove that:sin3A/sinA - cos3A/cosA=2​

Mathematics
1 answer:
LekaFEV [45]3 years ago
6 0

The result essentially follows directly from the triple-angle identities,

sin(3A) = 3 sin(A) cos²(A) - sin³(A)

cos(3A) = cos³(A) - 3 sin²(A) cos(A)

Then

sin(3A)/sin(A) = 3 cos²(A) - sin²(A)

cos(3A)/cos(A) = cos²(A) - 3 sin²(A)

and

sin(3A)/sin(A) - cos(3A)/cos(A)

= 3(cos²(A) + sin²(A)) - (sin²(A) + cos²(A))

= 3 - 1

= 2

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Jeremy has a weekend job as a soccer referee. One weekend, he earns $140 by working 4 games. Another weekend, he earns $210 by w
Ilya [14]

Answer:

$140 divided by 4 games = 35$ per games next $210 divided by 6 games = 35 also so the slope is 35 answer c

Step-by-step explanation:

i am good at this type of math

6 0
2 years ago
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Which of the following circumstances would likely make completing the square th
svet-max [94.6K]

Answer:

The leading coefficient is 1 and the linear term coefficient is an even number

Step-by-step explanation:

Leading coefficient must be one for the application of completing square method. If the completing square is not one than we must apply other methods like Ac method, quadratic formula to solve the equation. To solve the equation with completing square the numerical value must be on other side of the equation. In this method we multiply linear term’s coefficient with one-half and square it therefore, completing square is suitable method for the equation having leading coefficient is 1 and linear coefficient is even.

3 0
3 years ago
A triangle has an area of 36 cm². The base and height are scaled by a factor of 5.
ahrayia [7]
Triangle Area = .5 * (base * height)
36 = (base * height) / 2
So let's say base = 9 height 8
If base and height are scaled by a factor if 5 than
base = 45 height 40 and
area = .5 * (45 * 40)
area = 900

Basically, the area increases by a factor of 25.
The base increases by 5 and the height increases by 5 so the area increases by 5*5 = 25

4 0
3 years ago
A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. A previous study indicates that the propo
never [62]

Answer:

A sample of 997 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

The margin of error is of:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

A previous study indicates that the proportion of left-handed golfers is 8%.

This means that \pi = 0.08

98% confidence level

So \alpha = 0.02, z is the value of Z that has a p-value of 1 - \frac{0.02}{2} = 0.99, so Z = 2.327.  

How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 2%?

This is n for which M = 0.02. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.02 = 2.327\sqrt{\frac{0.08*0.92}{n}}

0.02\sqrt{n} = 2.327\sqrt{0.08*0.92}

\sqrt{n} = \frac{2.327\sqrt{0.08*0.92}}{0.02}

(\sqrt{n})^2 = (\frac{2.327\sqrt{0.08*0.92}}{0.02})^2

n = 996.3

Rounding up:

A sample of 997 is needed.

3 0
3 years ago
Suri solved the equation x squared = 49 and found that x=7. What error did Suri make?
Anastaziya [24]

Answer:

x = \frac{+}{-} 7

Step-by-step explanation:

x^{2} = 49

\sqrt{49} can equal 7 or -7

7 x 7 = 49.  -7 x -7 = 49

7 0
3 years ago
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