What’s the combined like tens for x + 40 3x -17+2x -5

Use trigonometric identities to solve each equation within the given domain.

katrin [286]

Recall that the tangent function is defined by

tan(x) = sin(x)/cos(x)

Also recall the double angle identity for sine,

sin(2x) = 2 sin(x) cos(x)

Then the equation is the same as

3 sin(x)/cos(x) = 4 sin(x) cos(x)

Move everything to one side to prepare to factorize:

3 sin(x)/cos(x) - 4 sin(x) cos(x) = 0

sin(x)/cos(x) (3 - 4 cos²(x)) = 0

As long as cos(x) ≠ 0, we can omit the term in the denominator, so we're left with

sin(x) (3 - 4 cos²(x)) = 0

and so

sin(x) = 0 or 3 - 4 cos²(x) = 0

sin(x) = 0 or cos²(x) = 3/4

sin(x) = 0 or cos(x) = ±√3/2

On the interval [0, 2π),

• sin(x) = 0 for x = 0 and x = π

• cos(x) = √3/2 for x = π/6 and x = 11π/6

• cos(x) = -√3/2 for x = 5π/6 and x = 7π/6

(None of these x make cos(x) = 0, so we don't have to omit any extraneous solutions.)

6 0

3 years ago

Consider the following used to find the volume of a cone

Marta_Voda [28]

You need to list the options/ “following” otherwise you most likely won’t get an answer or a right one at least

5 0

3 years ago

A waitress sold 12 ribeye steak dinners and 39 grilled salmon totaling $575.53 on a particular day. Another day she sold 25 ribe

DedPeter [7]

Answer:

The cost of a ribeye steak dinner is $18.60.

The cost of a grilled salmon dinner is $9.03.

Step-by-step explanation:

let r be the cost of a ribeye steak dinner

let g be the cost of a grilled salmon dinner

Represent the two situations using equations:

12r + 39g = 575.53 (equation 1)

25r + 13g = 582.43 (equation 2)

The best method to use for this case is elimination, which is when you get rid of one of the variables by subtracting or adding.

Since the coefficients for "g" are 39 and 13, they can be eliminated if equation 2 was triple itself.

(25r + 13g = 582.43) X 3

= 75r + 39g = 1747.29 (new equation 2)

Subtract "equation 1" from "new equation 2"

. 75r + 39g = 1747.29

- 12r + 39g = 575.53

. 63r + 0g = 1171.76 <=we only deal with "r" because 0g is nothing

. 63r = 1171.76 <=divide both sides by 63 to isolate r

. r = 18.60 <=rounded from 18.599...

The cost of a ribeye steak dinner is $18.60.

Use any one of the equations to solve for "g", the cost of grilled salmon dinners. I will use equation 1.

12r + 39g = 575.53

Substitute r = 18.6

12(18.6) + 39g = 575.53 <=only one variable now

223.2 + 39g = 575.53 <=subtract 223.2 from both sides

39g = 352.33 <=divide both sides by 39 to isolate g

g = 9.03 <=rounded from 9.0341...

The cost of a grilled salmon dinner is $9.03.

4 0

3 years ago

In a certain town, the wind speed, x, in km/h on a certain day is described by two statements: If 2 times the wind speed is incr

hodyreva [135]

1) if 2 times the wind speed is increased by 2, the wind speed is still less than 46 km/h.

=> 2x + 2 < 46

2) Twice the wind speed minus 27 is greater than 11 km/h.

=> 2x - 27 > 11

Part A: Create a compound inequality to represent the wind speed range. (3 points)

from 2x + 2 < 46

=> 2x < 44

=> x < 22

from 2x - 27 > 11

=> 2x > 11 + 27

=> 2x > 38

=> x > 19

The set of inequalities is

2x + 2 <46
2x - 27 > 11

The solution is x < 22 and x > 19, which is:

19 < x < 22 <----- answer

Part B: Can the wind speed in this town be 20 km/h? Justify your answer by solving the inequalities in Part A. (3 points)

Yes, the wind speed can be 20 km/h, because the solution of the inequality is the range (19,22).

Part C: The average wind speed in another town is 23 km/h, but the actual wind speed is within 4 km/h of the average. Write and solve an inequality to find the range of wind speed in this town.

x ≥ 23 - 4 => x ≥ 19

x ≤ 23 + 4=> x ≤ 27

=> 19 ≤ x ≤ 27

=> [19,27]

4 0

3 years ago

20. The table shows the numberof days you keep a rented movie before returning it and the total cost of renting the

Harlamova29_29 [7]

Step-by-step explanation:

According to given table we have pairs of points:

(4, 6.00), (5, 8.25), (6, 10.50)

The rate of change is:

(8.25 - 6.00)/(5 - 4) = 2.25

or

(10.50 - 8.25)/(6 - 5) = 2.25

It is 2.25 and the meaning is:

Rental per day is $2.25

5 0

2 years ago