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Roman55 [17]
3 years ago
5

ASAPFind all solutions to the equation.7 sin^2 x - 14 sin x + 2 = -5

Mathematics
1 answer:
matrenka [14]3 years ago
3 0

Answer:

{-π/2, π/2}

Step-by-step explanation:

Rewrite this as:

7sin^2 x - 14sin x + 7 = 0.  Reduce this result by dividing all terms by 7:

sin^2 x - 2sin x + 1

Temporarily replace "sin x" with y:

y^2 - 2y + 1 = 0

Solve this through factoring:  (y - 1)^2 = 0, or y - 1 = ± 0, or y = ±1

Recalling that y = sin x, we write

sin x = ±1, whose solutions are sin x = 1 and sin x = -1

The solution of sin x = 1 is π/2 and that of sin x = -1 is -π/2

and so the solution set is {-π/2, π/2}

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Total profit P is the difference between total revenue R and total cost C. Given the following​ total-revenue and​ total-cost fu
gavmur [86]

Answer:

The profit function is:

P(x)=-x^2+1280x-3300

The maximum value is 406, 300 occurring when x = 640.

Step-by-step explanation:

The revenue function is:

R(x)=1300x-x^2

And the cost function is:

C(x)=3300+20x

Then the total profit function will be:

P(x)=R(x)-C(x)=(1300x-x^2)-(3300+20x)=-x^2+1280x-3300

This is a quadratic function.

Therefore, the maximum value of the total profit will occur at its vertex point.

The vertex of a quadratic is given by:

\displaystyle \Big(-\frac{b}{2a}, f\Big(-\frac{b}{2a}\Big)\Big)

In this case, a = -1, b = 1280, and c = -3300.

Then the point at which the maximum profit occurs is at:

\displaystyle x=-\frac{1280}{2(-1)}=640

And the maximum profit will be:

P(640)=-(640)^2+1280(640)-3300=406300

5 0
3 years ago
Read 2 more answers
Find the value of x if 7,x and 11 are in A.p.​
krok68 [10]

Answer:

x = 9

Step-by-step explanation:

since the terms are in AP then there is a common difference between consecutive terms, that is

a₂ - a₁ = a₃ - a₂ ( substitute values )

x - 7 = 11 - x ( add x to both sides )

2x - 7 = 11 ( add 7 to both sides )

2x = 18 ( divide both sides by 2 )

x = 9

7 0
2 years ago
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What is the equation of the line that passes through the point (8,4) and has a slope of 3/2
iren [92.7K]

Answer: Y= 3/2x-8=

Step-by-step explanation:Y=4 M= 3/2. X=-8

Y=mx+b

4 = 3/2(8)+b

4= 24/2+b

4= 12+b

-12=-12

-8=b

3 0
3 years ago
Find the circumference
tia_tia [17]

Answer:

6.25\pi

Step-by-step explanation:

A circumference of a circle can be determined by this: 2*pi*r

We're given the diameter. Divide that by 2 to get the radius.

6.45/2 = 3.225

Now multiply that by 2*pi. That gives us 2 * 3.14 * 3.225 = 20.253.

This could've also been done easier by doing pi*d where d is the diameter and you give the answer by multiplying them both. Also works, but the above formula is just key to many things and can also be used to derive the simpler one. Hope it helps! :)

7 0
2 years ago
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Whats the answers to this question
marin [14]

Answer:

B and D

Step-by-step explanation:

7 0
4 years ago
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