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Marianna [84]
2 years ago
8

−10sin(x)=−4csc(x)+3

Mathematics
1 answer:
tatiyna2 years ago
7 0

-10 sin(x) = -4 csc(x) + 3

Recall that csc(x) = 1/sin(x) :

-10 sin(x) = -4/sin(x) + 3

Multiply both sides by sin(x) :

-10 sin²(x) = -4 + 3 sin(x)

Move everything to one side:

10 sin²(x) + 3 sin(x) - 4 = 0

Factorize the left side:

(2 sin(x) - 1) (5 sin(x) + 4) = 0

Then we have two cases,

2 sin(x) - 1 = 0   or   5 sin(x) + 4 = 0

Solve for sin(x) :

sin(x) = 1/2   or   sin(x) = -4/5

Solve for x :

• if sin(x) = 1/2, then

x = arcsin(1/2) + 2nπ   or   x = π - arcsin(1/2) + 2nπ

x = π/6 + 2nπ   or   x = 5π/6 + 2nπ

• if sin(x) = -4/5, then

x = arcsin(-4/5) + 2nπ   or   x = π - arcsin(-4/5) + 2nπ

x = -arcsin(4/5) + 2nπ   or   x = π + arcsin(4/5) + 2nπ

(where n is any integer)

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pantera1 [17]

Answer:

p=0.063

Step-by-step explanation:

Let X be number of the certain brand of jelly beans that are made so that each package contains about the same number of beans.

X is N(375, 8)

YOu are collecting a sample size of

n = 8

Findings from the sample

\bar x =370\\

H_0: \bar x =375\\H_a: \bar x

(Left tailed test at 5% level)

Since sample size is small though sigma is known we use Z test, since norm

Mean difference = -5

Std error = \frac{8}{\sqrt{8} } =2.828

Test statistic t = mean diference / std error = \frac{-5}{2.828} \\=-1.768

df = n-1 =5

p value = 0.063

7 0
3 years ago
Patty is inviting her friends to a party.She has 30 snack bars and 45 juice boxes and she wants to give the same number to each
Alexeev081 [22]

Answer

15 friends

Step-by-step explanation:

The largest common factor ( meaning the biggest number that goes into both 30 and 45) is 15. Each friend could get 2 snack bars and 3 juice boxes and there would be none left over

8 0
3 years ago
Arnoldo needs to write this system in slope-intercept form. Which shows how he could do that? 3 x minus 2 y = 6. 0.4 (20 y + 15)
kotegsom [21]

Answer:

  y = three-halves x minus 3

Step-by-step explanation:

Subtract 3x from both sides of the original equation.

  -2y = -3x +6

Divide by -2

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4 0
3 years ago
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In the diagram of circle M shown, the measure of major arc PRQ=268 . Which of the following
padilas [110]

Step-by-step explanation:

The Answer is 46

The measure of Arc PRQ is 268. Another part of the arc is PQ. PRQ+PQ forms a full circle In which a circle has 360 degrees. Using that

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x = 92

Since we are asked to the measure of PRQ and it is inscribed in arc PQ. It is half of PQ so the answer is

92 \div 2

which is 46.

8 0
3 years ago
I’ll give you brainliest!
weeeeeb [17]

Answer:

2139m (total area)

Step-by-step explanation:

I am like 98% sure this is right

23* 31= 713 (1 side area)

713+713=1426 (2 sides area)

31-12=19 (middle height)

19*23= 437 (middle area)

437+1426=2139m (total area)

7 0
2 years ago
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