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3 years ago

Find the solutions of each equation on the interval [0, 2π).

Mathematics

1 answer:

inysia [295]3 years ago

7 0

Answer:

x = 0

Step-by-step explanation:

Given sin(3π/2+x) + sin(3π/2+x) = -2

2sin(3π/2+x) = -2

sin(3π/2+x) = -1

clearly x = 0 on satisfies the above equation

We know that sin(3π/2+x) = - cosx

-cosx = -1

cosx = 1 Has only one solution at x=0 in x∈ [0,2π)

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You can jog around your block twice and the park once in 10 minutes. You can jog around your block twice and the park 3 times in

exis [7]

2x + y = 10
2x + 3y = 22

Please consider marking this answer as Brainliest to help me advance, and let me know if you need any clarifications.

4 0

3 years ago

If you help I will give you brainliest

hammer [34]

9514 1404 393

Answer:

5 miles

Step-by-step explanation:

Time/speed/distance problems can be worked a number of ways. Here, we want to know the distance walked. We know the total time and the total distance and the two different speeds. So, we can use a variable to represent the value we want to know: w = distance walked (in miles).

The total time is 9:00 -6:50 = 2:10 = 2 1/6 hours = 13/6 hours.

The total time is the sum of times for the two parts of the trip: walking and riding.

walking time = walking distance/walking speed

= w/3

riding time = riding distance/riding speed

= (20-w)/30

The total time is that given above:

w/3 +(20-w)/30 = 13/6

10w +(20 -w) = 65 . . . . . . . . multiply by 30

9w = 45 . . . . . . . . . . . . subtract 20, collect terms

w = 5 . . . . . . . . . . . divide by 9

The girl walked 5 miles.

8 0

3 years ago

Which value of x satisfies both -9x+4y=8 and -3x-y=4 given the same value of y?

Deffense [45]

The value of x satisfies both -9x + 4y = 8 and -3x - y = 4 given the same value of y is $-\frac{8}{7}$

Step-by-step explanation:

The system of equations has two equations:

-9x + 4y = 8
-3x - y = 4

Let us solve the system of equations to find the value of x and substitute it in the two equations to check if it gives the same value of y in the two equations

∵ -9x + 4y = 8 ⇒ (1)

∵ -3x - y = 4 ⇒ (2)

- Multiply equation (2) by 4 to make the coefficients of y in the

two equations have same value and different signs

∴ -12x - 4y = 16 ⇒ (3)

- Add equations (1) and (3) to eliminate y

∴ -21x = 24

- Divide both sides by -21

∴ x = $-\frac{8}{7}$

Let us substitute this value of x in equations (1) and (2) to find y

∵ -9( $-\frac{8}{7}$ ) + 4y = 8

∴ $\frac{72}{7}$ + 4y = 8