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cricket20 [7]
2 years ago
12

How do I solve this?

Mathematics
1 answer:
Sonbull [250]2 years ago
5 0

The question is somewhat poorly posed because the equation doesn't involve <em>θ</em> at all. I assume the author meant to use <em>x</em>.

sec(<em>x</em>) = csc(<em>x</em>)

By definition of secant and cosecant,

1/cos(<em>x</em>) = 1/sin(<em>x</em>)

Multiply both sides by sin(<em>x</em>) :

sin(<em>x</em>)/cos(<em>x</em>) = sin(<em>x</em>)/sin(<em>x</em>)

As long as sin(<em>x</em>) ≠ 0, this reduces to

sin(<em>x</em>)/cos(<em>x</em>) = 1

By definition of tangent,

tan(<em>x</em>) = 1

Solve for <em>x</em> :

<em>x</em> = arctan(1) + <em>nπ</em>

<em>x</em> = <em>π</em>/4 + <em>nπ</em>

(where <em>n</em> is any integer)

In the interval 0 ≤ <em>x</em> ≤ 2<em>π</em>, you get 2 solutions when <em>n</em> = 0 and <em>n</em> = 1 of

<em>x</em> = <em>π</em>/4   <u>or</u>   <em>x</em> = 5<em>π</em>/4

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There are 96 girls and 72 boys who want to participate in 6th grade intramurals.
Gekata [30.6K]

Answer:

i) 24

ii) 4 girls, 3 boys

Step-by-step explanation:

The GCF is 24

96= 24*<u>4</u>

72= 24*<u>3</u>

<u />

<u />

<u>I hope this helps!</u>

5 0
3 years ago
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If
pav-90 [236]

Answer:

Second option: One solution. Independent.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

y=mx+b

Where "m" is the slope and "b" is the y-intercept.

Since the equations of the system have this form, we know that they are lines.

We can identify that the y-intercept of the first equation y=-5x+1 is:

b=1

Now we need to find the x-intercept. Substitute y=0 and solve for "x":

0=-5x+1\\\\5x=1\\\\x=\frac{1}{5}=0.2

Then, we can graph the first line which passess through the points (0,1) and (0.2,0). Observe the graph attached.

The y-intercept of the second equation y=-2x-2 is:

b=-2

Now we need to find the x-intercept. Substitute y=0 and solve for "x":

0=-2x-2\\\\2x=-2\\\\x=\frac{-2}{2}=-1

Then, we can graph the second line, which passess through the points (0,-2) and (-1,0).

You can observe in the graph that the lines intersect at the point (1,-4). Therefore, that point is the solution of the system of equations.

Since the lines intersect, then there is one solution that is true for both equations. It is independent

4 0
2 years ago
What is 100:25 in lowest terms
Ray Of Light [21]

4: 1 because you could divide both sides of the ratio by 25

5 0
3 years ago
How many terms are there in 37,38,39,40...,437
aivan3 [116]

Answer:

There are 401 terms.

Step-by-step explanation:

The first term is 37 (subtract 36 to get 1st).  The last term is 437 (subtract 36 to get 401st).

8 0
2 years ago
Read 2 more answers
Suppose triangle ABC is reflected over the x-axis. If the distance between point A and A’ is 14, what is the distance between th
andreyandreev [35.5K]

Given:

The triangle ABC is reflected over the x-axis.

The distance between point A and A’ is 14.

To find:

The distance between the x-axis and A’.

Solution:

If a figure is reflected across the x-axis then the corresponding parts are mirror image of each other about the x-axis.

It means the distance between A and x-axis is same as the distance between x-axis and A'.

The distance between point A and A’ is 14.

Let d be the distance between the x-axis and A’. Then,

d+d=14

2d=14

d=\dfrac{14}{2}

d=7

Therefore, the correct option is 1.

7 0
2 years ago
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