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ahrayia [7]
4 years ago
6

Please help me with this question.

Mathematics
1 answer:
Elanso [62]4 years ago
7 0

Answer:

\frac{ \sin( x)}{ \cos(x) }  and \:  \frac{1}{ \cot(x) }

Step-by-step explanation:

x represents symbol 'theta';

In trigonometry, it is important to know that:

\frac{ \sin(x) }{cos(x) }  =  \tan(x)

and also:

\cot(x)  =  \frac{1}{ \tan(x) }

which gives:

\tan(x)  =  \frac{1}{ \cot(x) }

Thus,

\tan(x)  =  \frac{ \sin(x) }{ \cos(x) }  =  \frac{1}{ \cot(x) }

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The sum of the measures of the interior angles of a convex polygon is 3960°.
scZoUnD [109]

Step-by-step explanation:

The sum of the interior angles of a convex regular polygon is 180 times (n-2), where n is the number of sides. Since we already know the sum, we can write 3,960 = 180(n-2). If you solve for n in this equation, you will have the number of sides.

5 0
3 years ago
the length of a rectangle garden is 8 feet longer than its width. if the gardens perimeter is 196 feet what is the area of the g
Mumz [18]
1) width = x
length = x + 8
perimeter = 2 (length + width)
196 = 2 * (x+8+x)
196 = 2* (2x+8)
196 = 4x + 16
180 = 4x
x = 45 (thats width)

2) length would be 45+8=53

3) area = length times width = 45 * 53 = 2385 square feet


3 0
3 years ago
eu (european union) countries report that 46% of their labor force is female. The United Nations wnats to determine if the perce
Brrunno [24]

Answer:

Step-by-step explanation:

The question is incomplete. The complete question is:

EU (European Union) countries report that 46% of their labor force is female. The United Nations wants to determine if the percentage of females in the U.S. labor force is the same. Based on a sample of 500 employment records, representatives from the United States Department of Labor found that the 95% confidence interval for the proportion of females in the U.S. labor force is 0.357 to 0.443. If the Department of Labor wishes to tighten its interval, they should:

A. increase the confidence level

B. decrease the sample size

C. increase the sample size

D. Both A and B

E. Both A and C

Solution:

Confidence interval for population proportion is written as

Sample proportion ± margin of error

Where sample proportion is the point estimate for the population proportion.

Margin of error = z × √pq/n

The z score for 95% confidence level is 1.96

p = 46/100 = 0.46

q = 1 - p = 1 - 0.46

q = 0.54

n = 500

Margin of error = 1.96√0.46 × 0.54/500 = 0.044

To tighten it's interval, the margin of error needs to be reduced.

If we increase the confidence level, say to 99%, z = 2.58

Then

Margin of error = 2.58√0.46 × 0.54/500 = 0.058

It increased

Also, If we increase the sample size, say to 700, then

Margin of error = 1.96√0.46 × 0.54/700 = 0.037

It has reduced

Therefore, the correct options is

C. increase the sample size

8 0
3 years ago
Find the general solution of the following equation: y'(t) = 3y -5
Anton [14]

Answer:

The general solution of the equation is y = \frac{A}{3}e^{3t} + 5

Step-by-step explanation:

Since the differential equation is given as y'(t) = 3y -5

The differential equation is re-written as

dy/dt = 3y - 5

separating the variables, we have

dy/(3y - 5) = dt

dy/(3y - 5) = dt

integrating both sides, we have

∫dy/(3y - 5) = ∫dt

∫3dy/[3(3y - 5)] = ∫dt

(1/3)∫3dy/(3y - 5) = ∫dt

(1/3)㏑(3y - 5) = t + C

㏑(3y - 5) = 3t + 3C

taking exponents of both sides, we have

exp[㏑(3y - 5)] = exp(3t + 3C)

3y - 5 = e^{3t}e^{3C}        

3y - 5 = Ae^{3t}                A = e^{3C}

3y = Ae^{3t} + 5    

dividing through by 3, we have

y = \frac{A}{3}e^{3t} + 5

So, the general solution of the equation is y = \frac{A}{3}e^{3t} + 5

3 0
4 years ago
HELP PLEASE I NEED IT NOW.
icang [17]

Answer:

Below :)

Step-by-step explanation:

1) 5^2 = 25

2) 12^2 = 144

3) 9^2 = 81

4) 15^2 = 225

5) 8^2 = 64

6) 7^2 = 49

7) 20^2 = 400

8) 13^2 = 169

9) 30^2 = 900

10) 25^2 = 625

3 0
2 years ago
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