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Marianna [84]
3 years ago
8

−10sin(x)=−4csc(x)+3

Mathematics
1 answer:
tatiyna3 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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A line passes through the points (0, 9) and (9, 19). What is its equation in slope-intercept form?
STatiana [176]

Answer:

y = 10/9x + 9

Step-by-step explanation:

To write the equation in its slope-intercept form, y = mx + b, we need to find the slope (m) of the line and its y-intercept (b).

Given the points (0, 9) and (9, 19), we can solve for the slope of the line using the following formula:

m = \frac{y2 - y1}{x2 - x1}

Let (x1, y1) = (0, 9)

and (x2, y2) = (9, 19)

Substitute these values on the formula:

m = \frac{y2 - y1}{x2 - x1} = \frac{19 - 9}{9 - 0} = \frac{10}{9}

Therefore, the slope (<em>m </em>) = 10/9.

Next, the <u>y-intercept</u> is the point on the graph where it crosses the y-axis, and has the coordinates, (0, <em>b </em>). It is also the value of the y when x = 0.

One of the given points is the y-intercept of the line, given by (0, 9). The y-coordinate, 9, is the value of b.

Therefore, the linear equation in slope-intercept form is: y = 10/9x + 9

3 0
2 years ago
Choose one of the factors of x^3 + 343.
Debora [2.8K]

First, note that 343=7^3. Then use the formula for the sum of perfect cubes:

a^3+b^3=(a+b)(a^2-ab+b^2).

Therefore,

x^3 + 343=x^3+7^3=(x+7)(x^2-7x+49).

The quadratic trinomial x^2-7x+49 couldn't be factored anymore, so the expression x^3 + 343 has two factors x+7 and x^2-7x+49.

Answer: correct choice is A.

3 0
3 years ago
A gym membership is $100 sign-up fee and charges $20 a month thereafter. How much is the membership fee in a month?
trapecia [35]

Answer:

$120

Step-by-step explanation:

y = mx + b

The $100 sign up fee is a set amount, or the b value.

The $20 would be the m value since it the constant change, or the slope.

Thus, the equation would be y=20x + 100

The membership fee for 1 month would be --->

y= 20(1) +100

y= 20 + 100

y= $120

                                     

4 0
3 years ago
1/6d + 2/3 = 1/4(d-2)
xxMikexx [17]
D = 14

1/6d + 2/3 = 1/4d - 1/2
2d + 4*2 = 3d - 6
2d - 3d = -6-8
-d = -14
d = 14
4 0
3 years ago
Jan and Wayne went to the store to buy some groceries. Jan bought 2 cans of corn beef hash and 3 cans of creamed chipped beef fo
olasank [31]
You can solve this by using the system of equations.
Jan - 4.95 = 2H + 3C
Wayne - 5.45 = 3H + 2C

Use elimination.
-3(2H + 3C = 4.95)
2(3H + 2C = 5.45)

Solve. And you'll get:
-6H + (-9C) = -14.85
6H + 4C = 10.9

Cross out -6H and 6H because they cancel out. And you're left with:
-9C = -14.85
4C = 10.9

Add -9C with 4C, and -14.85 with 10.9.
-5C = -3.95

Divide each side with -5.
C = $0.79

Now to figure out what H is, just substitute the C in one of the equations with 0.79.
5.45 = 3H + 2(0.79)
5.45 = 3H + 1.58
-1.58            -1.58
3.87 = 3H
3.87/3 = 3/3(H)
1.29 = H

Finished!
7 0
3 years ago
Read 2 more answers
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