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3 years ago

Show that cos2x=cosx

Mathematics

1 answer:

PSYCHO15rus [73]3 years ago

3 0

cos (2x) = cos x

2 cos^2 x -1 = cos x using the double angle formula

2 cos ^2 x -cos x -1 =0

factor

(2 cos x+1) ( cos x -1) = 0

using the zero product property

2 cos x+1 =0 cos x -1 =0

2 cos x = -1 cos x =1

cos x = -1/2 cos x=1

taking the arccos of each side

arccos cos x = arccos (-1/2) arccos cos x = arccos 1

x = 120 degrees x=-120 degrees x=0

remember you get 2 values ( 2nd and 3rd quadrant)

these are the principal values

now we need to add 360

x = 120+ 360n x=-120+ 360n x = 0 + 360n where n is an integer

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Avaluate 2^3x-1 for x=1

DENIUS [597]

Answer:

4 or 7 (Check the explanation to see which one your equation actually is.

Step-by-step explanation:

One thing I want to clarify for you, It's Evaluate, not Avaluate.

Okay so, we want to find the value of 2^3x-1 and we know x = 1.

You didn't really clarify if the expression was $2^{3x-1}$ or $2^{3x}-1$ , so I'll be doing both:

For $2^{3x-1}$ , we should plug in x to get $2^{3(1)-1}$ and then simplify to get $2^{2}$ .

2 to the power of 2 or $2^{2}$ is equal to 2 * 2 or 4.

The second one, $2^{3x}-1$ , we should plug in x to get $2^{3(1)}-1$ and then to become $2^{3}-1$ . 2 to the power of 3 or $2^{3}$ is 8 and then minus 1 is 7.

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3 years ago

Read 2 more answers

What to know for geometry flvs module 3 DBA?

pishuonlain [190]

Essentially look at your formula sheets, Take notes on your assessment questions and you should be fine.

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2 years ago

What are the areas of each smaller rectangle and the large rectangle?

zhannawk [14.2K]

Answer:

Area of part 1: 3 * $5\sqrt{2}$ = $15\sqrt{2}$

Area of part 2: $3\sqrt{2} * 5\sqrt{2}$ $=30$

Area of entire rectangle: $30 + 15\sqrt{2}$

Step-by-step explanation:

The area of a rectangle can be found by using formula : length * width.

The area of part 1 can be simplified to this:

3 * $5\sqrt{2}$ = $15\sqrt{2}$

Area of part 2:

$3\sqrt{2} * 5\sqrt{2}$ $=30$

The area of the entire rectangle can simply be added from part 1 and part 2.

For area 2, remember multiplying the square root of 2 twice nullifies the square root. So it becomes 15 * 2, which is equal to 30.

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3 years ago

Without solving, explain how you can tell whether the solution to 0.5x = 10 is less than 1 or greater than 1

NemiM [27]

Greater than 1 because left side is a fraction less than 1 and right side is a number greater than 1.

The left side being a fraction less than 1 could only mean that you have to multiply a number greater than 1 to the other side. And since the other side is a number greater already than 1 then multiplying the left side to the right side must result in a number greater than 1.

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3 years ago

How do u round 33 and 89 to estimate their sum

Zolol [24]

33 would round down. (30)

This is because the second 3 is smaller than 5 and when your rounding, if number your rounding is smaller then 5 you will round down

89 would round up. (90)

This is because the 9 is larger than 5 which means you would round up.

Please mark brainlies

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2 years ago