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Ainat [17]
3 years ago
5

Find the coordinates of the point (a, b).

Mathematics
1 answer:
Leviafan [203]3 years ago
5 0

Answer:

a = \frac{1}{\sqrt{2} } and b = \frac{\sqrt{2} }{2}

Step-by-step explanation:

As we know, the radius of the unit circle is 1 unit (it is the hypotenuse in the right triangle, the blue line)

We use trigonometric formulas to find out a and b

  • Sin(45) = opposite side / hypotenuse

<=> Sin(45) = b / 1

<=> b= Sin(45)*1 = \frac{\sqrt{2} }{2}

  • Cos(45) = adjacent side / hypotenuse

<=> Cos(45) = a / 1

<=> a =  Cos(45)*1 = \frac{1}{\sqrt{2} }

So: a = \frac{1}{\sqrt{2} } and b = \frac{\sqrt{2} }{2}

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gavmur [86]

we know that

In a right triangle we have

two legs and one hypotenuse

Let

a,b -----> the legs of the right triangle

c-----> the hypotenuse of the right triangle (the greater side)

Applying the Pythagoras Theorem

c^{2}=a^{2}+b^{2}

therefore

<u>the answer is</u>

The length of the hypotenuse squared is the length of one leg squared plus the length of another leg squared

6 0
3 years ago
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Step-by-step explanation:

4 ft (12 in/ft) / 15 = 48/15 = 3.2 inches

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2 years ago
Triangle X Y Z is shown. The length of side X Y is (9 n + 12) feet and the length of side X Z is (15 n minus 6) feet. Angles X Y
zmey [24]

Answer:

n = 3

XY = 39

XZ = 39

Step-by-step explanation:

Given

XY = 9n + 12

XZ = 15n - 6

Solving (a): n

To solve for n;

We make use of

XY = XZ

Substitute values for XY and XZ

9n + 12 = 15n - 6

9n - 15n = -12 - 6

-6n = -18

Divide through by -6

n = 3

Solving (b) XY

XY = 9n + 12

Substitute 3 for n

XY = 9 * 3 + 12

XY = 27 + 12

XY = 39

Solving (c): XZ

XZ = XY

XZ = 39

7 0
2 years ago
A political scientist wants to know how college students feel about the Social Security system. She obtains a list of the 3456 u
Marina CMI [18]

Answer:

For this case the population is described as:

All the college students

And the political have a list of 3456 undergraduates at her college for the sampling frame.

The sample would be the 104 students who return the survey.

Is important to notice that since he know the information about her college she can apply inference about the parameter of interest just at her college and not about all the possible students of college.

Step-by-step explanation:

For this case the population is described as:

All the college students

And the political have a list of 3456 undergraduates at her college for the sampling frame.

The sample would be the 104 students who return the survey.

Is important to notice that since he know the information about her college she can apply inference about the parameter of interest just at her college and not about all the possible students of college.

For this case we can also find the non reponse rate since we know that the total of questionnaires are 250 and she got back just 104 answered

Non-resp. = \frac{250-104}{250} = \frac{146}{250}= 0.584

So we have a non response rate of 58.4 %

4 0
3 years ago
At age 25, you decide to start your retirement account, and put $700 at the end of each quarter into an account paying 7.25% com
katrin [286]

Answer:

A

Step-by-step explanation:

3 0
2 years ago
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