All categories

3 years ago

Let cos(2x)/cos(x)+sin(x) = 0 where 0° ≤ x ≤ 180°. What are the possible values for x?

Mathematics

1 answer:

Harrizon [31]3 years ago

5 0

Answer:

Step-by-step explanation:

$\frac{cos2x}{cos x+sin x} =\frac{cos^2x-sin^2x}{cos x+sin x} =\frac{(cos~x+sin~x)(cos~x-sin~x)}{(cos~x+sin~x)} =cos~x-sin~x\\so~cos~x-sin~x=0\\divide ~by~cos~x\\1-tan~ x=0\\\\tan~x=1=tan ~45,tan (180+45)\\x=45^\circ,225^\circ$

You might be interested in

The heights of the men age 18 and over in HANES5 averaged 69 inches; the SD was 3 inches. Suppose the histogram of their heights

emmasim [6.3K]

Answer:

a) 84th percentile.

b) The 25th percentile is of 67 inches.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The heights of the men age 18 and over in HANES5 averaged 69 inches; the SD was 3 inches.

This means that $\mu = 69, \sigma = 3$

Such a man that is 6 feet tall is at the percentile of this height distribution.

6 feet = 6*12 inches = 72 inches. So this percentile is the p-value of Z when X = 72. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{72 - 69}{3}$

$Z = 1$

$Z = 1$ has a p-value of 0.84, so 84th percentile.

What is the 25th percentile, to the nearest inch

X when Z has a p-value of 0.25, so X when Z = -0.675.

$Z = \frac{X - \mu}{\sigma}$

$-0.675 = \frac{X - 69}{3}$

$X - 69 = -0.675*3$

$X = 67$

The 25th percentile is of 67 inches.

7 0

3 years ago

How many solutions does this equation -2(x+3)= 1/4x- (5-x) have?

pogonyaev

Answer:

the equation only has 1 solution

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

4. The range of a relation is given -3, 2, 0, 13, 17 Which domain makes the relation not a function? A. 0, 1, 2, 3, 4 B. 1,1, 2,

faust18 [17]

The domain that makes the relation not a function is c

6 0

3 years ago

The function C(x) = 25.50x + 50 models the total cost for a cleaning company to clean a house, where x is the number of hours it

vodomira [7]

Answer:

<em>The average rate of change is $25.5 per hour, option B.</em>

Step-by-step explanation:

<u>Average Rate of Change </u>

When we are explicitly given some function C(x), we sometimes need to know the rate of change of C when x goes from $x=x_1$ to $x=x_2$ . It can be computed as the slope of a line .

$\displaystyle m=\frac{C(x_2)-C(x_1)}{x_2-x_1}$

The provided function is

$C(x)=25.50x + 50$

We are required to compute the average rate of change between the points

$x_1=3\ ,\ x_2=9$

Let's compute

$C(3)=25.50(3) + 50=126.5$

$C(9)=25.50(9) + 50=279.5$

$\displaystyle m=\frac{279.5-126.5}{9-3}$

$\displaystyle m=\frac{153}{6}=25.5$

The average rate of change is $25.5 per hour, option B.

7 0

4 years ago

A house number is displayed on a plaque in the shape of a regular 7-sided polygon. The area of the plaque is 70 squared inches.

Svetllana [295]

Answer:

The perimeter of the plaque is 28 inches.

Step-by-step explanation:

Given : A house number is displayed on a plaque in the shape of a regular 7-sided polygon. The area of the plaque is 70 squared inches. The perpendicular distance from a side to the center is 5 inches to the nearest inch.

To find : What is the perimeter of the plaque?

Solution :

The 7-sided polygon can be divided into seven triangles whose height, h is equal to the perpendicular distance from each side to the center.

The base of each triangle is equal to the length of a side, s.

The area of each triangle is $A=\frac{1}{2}\times s\times h$