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3 years ago

Solve 2cos^2x + cosx − 1 = 0 for x over the interval [0, 2 π ).

1 answer:

6 0

Let cos x = a, then
2a^2 + a - 1 = 0,
solving the quadratic equation, we have:
a = 0.5 or -1.

i.e. cos x = 0.5 or cos x = -1
for cos x = 0.5,
x = pi/3, 2pi - pi/3 = pi/3, 5pi/3

for cos x = -1,
x = pi

therefore, x = pi, pi/3, 5pi/3
Answer: B

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Pls answer quickly. Thanks!

Gwar [14]

Answer:

the answer is D

Step-by-step explanation:

4 0

3 years ago

What is the next term in the arithmetic sequence? 9,17,25,33,...

lions [1.4K]

Answer:

41

Explanation:

To solve this problem we must first understand what the pattern is in the arithmetic sequence. Once we understand the pattern, we can then apply it to the final known term to find the next term.

Take a look at the arithmetic sequence given:

9, 17, 25, 33,...

Let's start by figuring out how they got the second term in the sequence. To do that, subtract the second term by the first term. This will reveal the pattern.

9 - first term

17 - second term

17 - 9 = 8

So, this means they added eight to get the next term. Therefore, the pattern should be 'add eight' to get the next term. Just to be sure the pattern we found is correct, apply it to the given arithmetic sequence.

9, 17, 25, 33,...

9 + 8 = 17

17 + 8 = 25

25 + 8 = 33

So, since 'adding eight' every time gives us the next term, the pattern is correct.

Finally, let's continue the pattern to find the next term.

9, 17, 25, 33,...

33 + 8 = 41

9, 17, 25, 33, 41,...

Therefore, the next term in the arithmetic sequence is 41.

3 0

2 years ago

HURRY PLEASE!! find the lcm of 3x^2-6x-24 and 9x^2-36

Mrac [35]

Answer:

yeeeeeeeeeeee

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

In triangle ABC, the size of angle B is 5 times the size of angle A, and the size of angle C is 7 less than 4 times the size of

kipiarov [429]

It sounds like everything is being described in reference to angle A, so a good starting point is to pick a variable to represent the measure of angle A. I'm going to use "a" for that.

Next, I'm going to take the verbal descriptions in the problem and "translate" them into "math language". They say angle B is 5 times angle A, so that means the measure of angle B is actually 5a. The size of angle C is 5 degrees less than 4 times the size of A, so that translates to 4a-5.

We now know the following:

Angle A: a
Angle B: 5a
Angle C: 4a-5

Now, to find the value of a, we need to remember that all the angles in a triangle add up to 180 degrees.

So we have: a+5a+4a-5 = 180

We can solve that equation by combining like terms to get: 10a-5=180

We can add 5 to both sides: 10a =185

And divide by 10: a = 18.5

That tells us the measure of angle A! (It's 18.5 degrees). Now we can go back and find B by multiplying A by 5. We get 92.5 degrees for that.

Finally, we can find C by taking 4*18.5-5. We get 69 degrees for that.

One last thing-- let's check that they really do add up to 180! 69+92.5+18.5 = 180. Yep!

Hope that helps you!!

5 0

3 years ago

PLEASE ANSWER + BRAINLIEST!!!

quester [9]

Use the Cosine Rule

q^2 = 20^2 + 30^2 - 2^20*30 cos 15

= 140.89

so q = sqrt 140.89 = 11.9 (answer)

6 0

3 years ago