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Prove sin^2 theta-sin^2 theta is sin tetha sin 3 theta<br><br>how to prove..pls help!! thanksss

Artemon [7]

Simply you can substitute theta=45 degrees (or any angle,not zero) in left hand side and right hand side.

or

using a^2 - b^2 =(a+b)(a-b)

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

3 0

3 years ago

your car stereo can be programmed to hold six radio stations of your choice. There are 9 stations you really like. How may diffe

Ira Lisetskai [31]

Combinations

nCr
you have n items and how many ways are there to chose r of them

nCr= $\frac{n!}{r!(n-r)!}$
remember than n! means n times all numbers before like
3!=3*2*1, 5!=5*4*3*2*1
9 stations, how many ways are there to chose 6 of them
9C6= $\frac{9!}{6!(9-6)!}$ =
$\frac{9!}{6!(3)!}$ =
$\frac{9*8*7}{3!}$ =
$\frac{9*8*7}{3*2*1}$ =
$\frac{3*4*7}{1}$ =
84

84 ways

6 0

3 years ago

At a cross-country track meet, Alicia ran 8 mph for the first part of the race, then increased her speed to 12 mph for the secon

Murrr4er [49]

She ran 15 miles at a quicker speed based on the information supplied. See explanation below. This is a distance time problem.

<h3>What is the justification for the above result?</h3>

The distances between the two "half" of the race are our unknowns here. We must assign them to variables - Alicia ran x miles in the first half of the race and y miles in the second.

Since the race is 21 miles in total, x and y together must add up to 21.

Hence,

x + y = 21

The speeds at which she raced and the total time involved are then given; we can link this to the distances using the speed and distance equation

d = st, or t = d/s.

Because she completed in two hours, the hours spent running the first and second parts must sum up to two hours, or:

x/8 + y/12 = 2

Two equations are sufficient to solve for two unknowns. We can approach this by multiplying the second equation by the LCM, 24

3x + 2y = 48

And rearrange the first to get y = 21 - x, which we can plug into the above. This gives us:

3x + 2(21 - x) = 48

3x + 42 - 2x = 48

x = 6

Use y = 21 - x again:

y = 21 - (6) = 15.

Recall that the question asks how long she ran at the faster speed - this would be the second half of the race, which we've labeled y, so 15 miles. But first, let's make sure our solution works.

Obviously, 15 + 6 = 21, thus the overall distance is correct.

In terms of time, 6 miles at 8 mph takes

6/8 =.75 hours = 45 minutes, whereas

15 miles at 12 mph takes 15/12 = 1.25 hours = 75 minutes.

As stated in the question, the total time to complete would be.

75 + 1.25 = 2 hours.

As a result, this solution is correct, as Alicia ran 15 miles at a quicker rate.

Learn more about distance time:
brainly.com/question/4931057
#SPJ1

4 0

2 years ago

Two parallel lines are cut by a transversal. Angle 1 measures (4x + 28)°, and the angle adjacent to the alternate exterior angle

DENIUS [597]

Answer:

The value of x = 8

Step-by-step explanation:

For better understanding of the solution, see the attached figure of the diagram :

∠1 and ∠2 are alternate exterior angle and ∠3 is adjacent to ∠2

⇒ ∠1 = (4x + 28)°

⇒ ∠3 = (14x + 8)°

Now, ∠2 + ∠3 = 180° (Linear Pair)

⇒ ∠2 = 180 - 14x -8

⇒ ∠2 = 172 - 14x

Since the alternate exterior angles formed by the transversal between two parallel lines are equal in measure.

⇒ ∠1 = ∠2

⇒ (4x + 28)° = (172 - 14x)°

⇒ 18x = 144

⇒ x = 8

Therefore, ∠1 = ∠2 = 60° and ∠3 = 120°

Hence, The value of x = 8

8 0

3 years ago

Read 2 more answers

Credo collects state quarters. He has 42 out of 50 available quarters. What 42 out of 50. What is 42 out of 50 as a percent

Aleks04 [339]

Answer:

The answer is 84%

Step-by-step explanation:

What's easy about dealing with a denoninator of 50 is that it goes in to 100 only twice.

By multiplying the numerator and denominator by 2, you get 84/100

That is the same as saying 84%

3 0

3 years ago