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2 years ago

Solve the equation cos (x/2) = cos x + 1. what are the solutions on the interval 0° ≤ x < 360°?

Mathematics

1 answer:

Sedbober [7]2 years ago

7 0

Answer:

Step-by-step explanation:

cos (x/2)=cos x+1

cos (x/2)=2cos ²(x/2)

2 cos²(x/2)-cos (x/2)=0

cos (x/2)[2 cos (x/2)-1]=0

cos (x/2)=0=cos π/2,cos (3π/2)=cos (2nπ+π/2),cos(2nπ+3π/2)

x/2=2nπ+π/2,2nπ+3π/2

x=4nπ+π,4nπ+3π

n=0,1,2,...

x=π,3π

or x=180°,540°,...

180°∈[0,360]

so x=180°

2cos(x/2)-1=0

cos (x/2)=1/2=cos60,cos (360-60)=cos 60,cos 300=cos (360n+60),cos (360n+300)

x/2=360n+60,360n+300

x=720n+120,720n+300

n=0,1,2,...

x=120,300,840,1020,...

only 120° and 300° ∈[0,360°]

Hence x=120°,180°,300°

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Write an inequality to represent the phrase: the difference of a number and 9 is no more than 95

Sliva [168]

Answer:

$x-9\leq 95$

Step-by-step explanation:

Let

x ----> the number

we know that

The phrase " the phrase: the difference of a number and 9" is equal to

subtract the number 9 from the number x

(x-9)

The phrase" no more than 95" means "less than or equal to 95" (≤95)

The inequality that represent this situation is

$x-9\leq 95$

5 0

3 years ago

Granola costs $6.50 per pound. Assorted nuts cost $9 per pound. How many pounds of granola and nuts are needed to make 9 pounds

bezimeni [28]

Answer:

3.6 pounds of granola and 5.4 pounds of nuts

Step-by-step explanation:

Let the required granola be x pounds, then amount of nuts is 9 - x.

<u>The price of the mixture is as below equation:</u>

6.5x + 9(9 - x) = 8*9
6.5x + 81 - 9x = 72
81 - 2.5x = 72
2.5x = 81 - 72
2.5x = 9
x = 9/2.5
x = 3.6

<u>Find the amount of nuts:</u>

9 - 3.6 = 5.4

7 0

1 year ago

Angie and Becky each completed a separate proof to show that the measures of vertical angles AKG and HKB are equal. Who complete

Helga [31]

Answer:

Becky, because her justification for the second statement should be "definition of supplementary angles" rather than "angle addition postulate."

Step-by-step explanation:

Becky completed the proof incorrectly because her justification for the second statement is not totally correct.

Angle addition postulate does not really apply here, as the sum of 2 angles may not give you exactly 180°.

However, the second statement, m<AKG + m<GKB = 180° and m<GKB + m<HKB = 180°, can be justified by the "Definition of Supplementary Angles".

The sum of supplementary angles = 180°.

Therefore, Becky completed the proof incorrectly.

6 0

2 years ago

Which transformation represents a reflection over the y = x line?

dmitriy555 [2]

Answer:

see explanation

Step-by-step explanation:

Under a reflection in the line y = x

a point (x, y ) → (y, x )

4 0

3 years ago

Kara was making decorations for a school dance. She has a small figure to use for a pattern, but needs the actual

Sedbober [7]

Answer:

k = 5

Step-by-step explanation:

When a certain number $n$ is multiplied by a scale factor $k$ , the final number is given by

$n'=kn$

and the final number will be:

- Larger than the original number if $|n'|>|n|$

- Smaller than the original number if $|n'|$

In this problem, the number $n$ represents the size of the decoration.

If we apply the 4 scale factors given, we have:

- If $k=5$ , then $n'=5n$ : this means that the final decoration is larger than the original decoration --> this is the correct option

- If $k=1$ , then $n'=n$ : so the final decoration has same size as the original decoration

- If $k=1/5$ , then $n'=\frac{1}{5}n$ : so the final decoration is smaller than the original decoration

- If $k=-1/5$ , then $n'=-\frac{1}{5}n$ , so the final decoration is smaller and inverted

8 0

3 years ago

Read 2 more answers