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Bingel [31]
3 years ago
12

How to express cos 3x in terms of cosx

Mathematics
1 answer:
Elena-2011 [213]3 years ago
5 0
\cos3x=\cos(x+2x)=\cos x\cos2x-\sin x\sin2x
=\cos x(\cos^2x-\sin^2x)-2\sin^2x\cos x
=\cos^3x-\cos x\sin^2x-2\sin^2x\cos x
=\cos^3x-3\cos x\sin^2x
=\cos^3x-3\cos x(1-\cos^2x)
=\cos^3x+3\cos^3x-3\cos x
=4\cos^3x-3\cos x
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Which of these equations have no solution? Check all that apply.
dlinn [17]
First one simplifies to 2x + 6 = 2x + 7  which can't be true   so this one has No Solution.
Same applies to the second equation  ( 5x + 15 = 5x - 15) No solution

also the last one has no solution because it simplifies to  4x + 20 = 4x + 19
6 0
3 years ago
Kevin hiked up lambs Canyon and two hours and then ran back down in one hour has been running downhill was 2.8 mph greater than
coldgirl [10]

Answer: he hiked 5.6 miles up the canyon.

Step-by-step explanation:

Let x represent his speed hiking uphill.

His speed running downhill was 2.8 mph greater than his speed hiking uphill. This means that his speed running downhill would be x + 2.8

Distance = speed × time

Kevin hiked up Lamb’s Canyon in 2 hours. This means that the distance covered by hiking uphill is 2 × x = 2x

He ran back downhill in 1 hour. This means that the distance covered by running downhill is 1 × (x + 2.8) =

x + 2.8

Since the distance uphill is the same as the distance downhill, then

2x = x + 2.8

2x - x = 2.8

x = 2.8

Therefore, the distance hiked up the canyon is

2x = 2 × 2.8 = 5.6 miles

8 0
3 years ago
use the slope formula to find the slope of the line that goes through the points (5, 0) and (-5, 2). 0. -5. −15. undefined.
dsp73

Answer: The slope is 5.

Step-by-step explanation:

3 0
3 years ago
Slove the equation of 6n-12=n+3
Makovka662 [10]
¤ 6n-12=n+3
¤ 6n-n=12+3
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8 0
3 years ago
Asa received scores of 72, 97, and 82 on her last three math tests. She needs a mean test score of 82 to qualify for the math te
Flauer [41]

Scores are {72, 97, 82, x} where x is the unknown fourth score

They add up to 72+97+82+x = x+251

Divide this sum over four because there are four scores we want to average out. We end up with (x+251)/4 = M where M is the mean. Asa wants the mean to be 82, so make M = 82.

We can replace M with 82 and solve for x like so

(x+251)/4 = M

(x+251)/4 = 82

x+251 = 4*82

x+251 = 328

x = 328-251

x = 77

Asa needs a score of 77 on the fourth test so that the mean of the four tests is 82. If she scores higher than 77 on the fourth test, then the mean will be larger than 82.

-----------------------------------

Depending on what your teacher is looking for, the first step is to establish your variable. So you would say "let x = fourth score". However, that seems too easy. So perhaps your teacher is looking for the equation (x+251)/4 = 82 or some variant of it.

5 0
3 years ago
Read 2 more answers
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