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poizon [28]
3 years ago
7

Find all solutions to the equation. (1 point) sin x = square root of three divided by two.

Mathematics
2 answers:
viva [34]3 years ago
7 0

sin x = \frac{\sqrt{3}}{2}

x = 60° = pi/3 radians

pi/3 is one solution

then

pi - pi/3 = 2 pi/3 is another one

pi/3 + 2.k.pi

2.pi/3 + 2.k.pi

k e Z

Are the solutions

Serggg [28]3 years ago
4 0

Answer:

x=pi/3 + 2pi*k

x=2pi/3+2pi*k

Step-by-step explanation:

sin(x)=sqrt(3)/2

This happens twice in the first rotation on our unit circle.

It happens in the first quadrant and in the second quadrant. Third and fourth quadrants are negative for sine.

So we are looking for when the y-coordinate on the unit circle is sqrt(3)/2.

This is at pi/3 and 2pi/3.

So we can get all the solutions by adding +2pi*k to both of those.  This gives us a full rotation about the circle any number of k times. k is an integer.

So the solutions are

x=pi/3 + 2pi*k

x=2pi/3+2pi*k

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Compare the functions.
marshall27 [118]

Function h has the largest y-intercept which is 44

Step-by-step explanation:

Any linear function is represented in the form

f(x) = mx+b

Here b is the y-intercept of the linear function i.e. the constant term in the function.

We will compare all the functions with the general form we get

y-intercept of f(x) = 1

y-intercept of g(x) = 8

y-intercept of h(x) = 44

y-intercept of j(x) = 0

Hence,

Function h has the largest y-intercept which is 44

Keywords: intercepts, linear functions

Learn more about intercepts at:

  • brainly.com/question/9532142
  • brainly.com/question/9590016

#LearnwithBrainly

5 0
3 years ago
Find the limit, if it exists, or type dne if it does not exist.
Phantasy [73]
\displaystyle\lim_{(x,y)\to(0,0)}\frac{\left(x+23y)^2}{x^2+529y^2}

Suppose we choose a path along the x-axis, so that y=0:

\displaystyle\lim_{x\to0}\frac{x^2}{x^2}=\lim_{x\to0}1=1

On the other hand, let's consider an arbitrary line through the origin, y=kx:

\displaystyle\lim_{x\to0}\frac{(x+23kx)^2}{x^2+529(kx)^2}=\lim_{x\to0}\frac{(23k+1)^2x^2}{(529k^2+1)x^2}=\lim_{x\to0}\frac{(23k+1)^2}{529k^2+1}=\dfrac{(23k+1)^2}{529k^2+1}

The value of the limit then depends on k, which means the limit is not the same across all possible paths toward the origin, and so the limit does not exist.
8 0
3 years ago
Find the radius of the circle. please.
labwork [276]

Answer:

12in

Step-by-step explanation:

2r = 24

r = 12

8 0
3 years ago
Read 2 more answers
Are the fractions 1/5 , 5/5 , and 5/1 equivalent?Explain.
Debora [2.8K]
No, these equations are not equivalent. 

1/5, or one fifth, is part of a whole. Imagine you have a pie, cut into five pieces, and your friend comes over and eats four pieces, so now you have one of the five original pieces. That's what you have here. 

5/5, or five fifths, is a whole. any number divided by itself is automatically one, so it is like making another pie and cutting it into five pieces, only this time no one eats any of it because it's burned or something. At the end, you have five pieces of pie

5/1 is actually just another way of writing plain old 5. To keep the pie example rolling, you have five pies, and no one eats any of these either, so they are all yours. You have 5 pies divided between one person, so at the end of the day you have 5 whole pies. 

Hope that helped!
7 0
3 years ago
Read 2 more answers
Tomas wants to buy a new baseball bat. The one he likes costs $130, but it's one sale for $104. What is the percent of the disco
OLga [1]
130 x .20% = 26
130-26 = 104
So 20%
3 0
3 years ago
Read 2 more answers
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