if cos x = sin(20+x) degrees and 0 degrees < x < 90 degrees, the value of x is

If Cos X = Sin(20+x) Degrees And 0 Degrees &lt; X &lt; 90 Degrees, The Value Of X Is

Answers

Answer 1

Answer:

x = 35°

Step-by-step explanation:

From the question given above:

cos x = sin(20 + x)

The value of x can be obtained as follow:

cos x = sin(20 + x)

Recall:

sin(A + B) = sinAcosB + cosAsinB

Therefore,

sin(20 + x) = sin20cosx + cos20sinx

cos x = sin(20 + x)

cos x = sin20cosx + cos20sinx

Collect like terms

cos x – sin20cosx = cos20sinx

cos x(1 – sin20) = cos20sinx

Divide both side by cosx

(1 – sin20) = cos20sinx / cosx

Recall:

Tan x = sinx / cosx

(1 – sin20) = cos20tanx

Divide both side by cos20

(1 – sin20) / cos20 = tanx

(1 – 0.3420) / 0.9397 = tanx

0.658 / 0.9397 = tanx

0.7 = tanx

Take the inverse of tan

x = tan¯ 0.7

x = 35°


Related Questions

Haley worked 287 hours during the summer and earned $16 for each hour she worked.

Which is the closest estimate for the total amount she earned?

$4,500

$5,000

$5,500

$6,000

Answers

Answer: The closest estimate for the total amount she earned = $4,500

Step-by-step explanation:

Given: Total hours worked = 287 hours

Earning for each hour = $16

Total earning = (Total hours worked ) x (Earning for each hour)

= $ (287 x 16)

= $ 4592 ≈ $4500

The closest estimate for the total amount she earned = $4500

Which expression can be used to find the price of a 400$ telescope after a 32% markup?
A. 400 x 0.32
B. 400 x 3.2
C. 400 x 1.32
D 400 + 400 (0.32)
E. 400 x 400(1.32)

Answers

32% = 0.32

Usually = 400x32/10

Now do 32/100 = .32

Answer is A. 400x0.32

Answer:

A

Step-by-step explanation:

A because a markup means the price times the number given which was 32% and 32% is the same as 0.32.

an one hour mathematcis class ks divided up into the schedule shown jn the table below how many mintyee of class are allowed for independent pratice?

Answers

Answer:

i got 15

Step-by-step explanation:

which is the correct answer?

(Note): (If you give a silly or absurd answer I will report you)​

Answers

Answer:

lolooollollolololo-

jk

The answer is

J) 334.06

Step-by-step explanation:

We know the rate is 1.5 inch an hour

So 1.5*2.54 is 3.81

Now 3.81 cm every hour

24 hours a day

3.81*24=91.44

Now 91.44 cm A day

1 Year or 365 days

91.44*365= 33375.6cm a year

now we also need to add the extra 12 inches in the beginning

12*2.54=30.48cm

Now add those 2

33375.6+30.48= 33406.08

now the answer asked for meters so we divide 33406.09/100

you’ll get 334.06 or J

J) 334.06

This is your answer

Pls help with math ASAP pls

Answers

B: it stabilizes the distance between them

i do not think the order matters, so the answer should be the first two.

any help
please
thanks

Answers

Answer:

n=54

Step-by-step explanation:

Since this is a proportion problem, you have cross mulitply.

7n=9x42

7n=378

n=54

Answer:

cross multiply

9×42=378

7×n=7n

n=378/7

n=54

PLEASE HELP! A chemist is estimating the volume of a solution in a test tube. The actual volume of the solution is 33.4 ml. The chemist's estimate is 35 ml.
Find the absolute error and the percent error of the chemist's estimate. If necessary, round your answers to the nearest tenth.

Answers

Absolute error is actual- estimate=33.4-35=-1.6 that in percent can be found using a rule of three, we say that 33.4 is the 100% and we find the % for -1.6

33.4ml -------- 100%

-1.8ml-----------x

x=(-1.8)(100)/33.4

x=-5.4

the percentage error is -5.4%

Pls pls help it is due todayyy:)))

Answers

Answer:

a dilation is different from a translation because it enlarges an image or shrink them instead of moving them. it's also different from rotation since it doesn't rotate but enlarge or shrink. it's way far from reflection because it enlarges or shrinks.

Answer: A diliation is a non rigid transformation, whereas reflections, transitions and rotations are rigid transformations. This means that dilations do not preserve the size of the shape.

Somebody please help me :(

Answers

A, C, and E are the correct answers

What type of number is -296.2i

Answers

it is a negetive integer

HOPE THIS HELPS

PLEASE MARK ME AS BRAINLIEST.

HELLO! Negative integer

उपलब्धियों

Which fraction is equivalent to the decimal 0.68 with the line on top?HELP FAST

A. 31/45
B. 682/999
C. 62/99
D. 2/3

Answers

Answer:

A 31/45

Step-by-step explanation:

A 31/45=0.6888 (this is the awnser as the line on top means repeating)

B 682/999=0.682 (0.68 rounded)

C 62/99=0.62626 (repeating)

D 2/3=0.66666 (Or 0.67 rounded)


Find the length of side x in simplest radical form with a rational denominator

Answers

Answer:

rggsktvvg gggggggggggg yyyhhhhg

The price of shares of Nadir Explorations Ltd. fell by 76% in the past year, to the current price of $0.45 per share. In dollars and cents, how much did the price of each share drop in the past year?

Answers

Answer:

$0.342 ; 34.2 cents

Step-by-step explanation:

Given that:

Share price fell by 76% in past year :

current price per share = $0.45

Drop in price of share in past year :

76% of current price

0.76 * $0.45

= $0.342

Price dropped by $0.342 per share

In cent, 0.342 * 100 = 34.2 cents

1 3/8 minus 1/2 thanks

Answers

Answer:

0.833

Step-by-step explanation:

The kittens, Annie and Josie, are pushing a ball, Annie with a force magnitude of 80 N in a direction of 133 degrees, and Josie with a magnitude of 95 N in a direction of 290 degrees. If a third cat wants to prevent the ball from moving, with what magnitude and direction of force must she push?

Answers

Answer: Then the magnitude of the force is 37.86N, and the direction is 54.35°

Step-by-step explanation:

We can write the forces as vectors.

We know that Annie pushes with a magnitude of 80N in a direction of 133° (Remember that the angles are always measured from the x-axis)

The components of this force, (Ax, Ay), are then:

Ax = 80N*cos(133°)

Ay = 80N*sin(133°)

And we know that Josie pushes with a magnitude of 95N in direction of 290°

The components of this force, (Jx, Jy), are:

Jx = 95N*cos(290°)

Jy = 95N*sin(290°)

When we add these forces, the total force acting on the ball is:

F = (80N*cos(133°) ,  80N*sin(133°)) + (95N*cos(290°), 95N*sin(290°))

F = (80N*cos(133°) + 95N*cos(290°), 80N*sin(133°) + 95N*sin(290°))

Now, the third kitten wants to do a force K, in a direction θ, such that the net force acting on the ball is zero.

Then we must have that, each component of the force of the third cat (K*cos(θ)  on the x-axis and k*sin(θ) on the y-axis), is such that:

K*cos(θ) + 80N*cos(133°) + 95N*cos(290°) = 0

k*sin(θ)  + 80N*sin(133°) + 95N*sin(290°) = 0

Now we need to solve that system for k and θ

if we simplify the equations we get:

k*cos(θ) - 22.07N = 0

k*sin(θ)  -30.76N  = 0

Now we can rewrite them as:

k*cos(θ) = 22.07N

k*sin(θ)   = 30.76N  

Now we can take the quotiet between both equations to get:

(k*sin(θ))/(k*cos(θ)) = 30.76N/22.07N

Tan(θ) = 1.394

θ = Atan(1.394) = 54.35°

Now that we know the angle, we can find the value of the magnitude k, by using one of the two equations of the system:

k*cos(54.35°) = 22.07N

k = 22.07N/cos(54.35°) = 37.86N

Then the magnitude of this force is 37.86N, and the direction is 54.35°

Find the percent change from the first value to the second. 32; 56

Answers

Answer:

75%

Step-by-step explanation:

Percentage change = (change) ÷ (first value) × 100

Change = second value - first value = 56 - 32 = 24

∴ Percentage change = [tex]\frac{24}{32} * 100 =[/tex] 75%

6 is _______________ % of 30. fill in the blank

Answers

Answer:

6 is 20% of 30

Step-by-step explanation:

6 × 5 = 30

take one of the five parts and you get 20% of the full product

find the slope of the line

Answers

Answer:

y= 3 + 3/4x sooooooo 3/4 is the slope... I think

Answer:

3/4

Step-by-step explanation:

You can use the x- and y--intercepts since they are easy-to-read points.

x-intercept: (-4, 0)

y-intercept: (0, 3)

To go from (-4, 0) to (0, 3), go up 3 and right 4. That is a rise of 3 and a run of 4.

slope = rise/run = 3/4

Answer: slope = 3/4

Engineers are playing a new bridge to cross a small river. Surveyors created the diagram to show where the bridge across the river.

What is the distance across the river where the new bridge will be built?

A. 36 feet
B. 56.25 feet
C. 100 feet
D. 101.25 feet

Answers

A. You need to show the diagram.

Answer:

I believe it was B.

Step-by-step explanation:

How do the graphs of the functions differ from the graph of f(x)=3.5x^3?
For each function, select Steeper, Less steep, or Reflected over the x-axis to describe the differences between the graph of the function and the graph of f(x).
Select all answers that are correct.

Answers

Answer:

First, let's do some general definitions:

We start with:

f(x) = 3.5*x^3

A general equation of this form is:

g(x) = a*x^3

if:

IaI > 3.5 the function will be steeper.

IaI < 3.5 the function will be less steep.

a < 0, means that we have a reflection over the x-axis.

Then:

p(x) = 4.5*x^3

bassed on what we wrote above, this function is steeper than f(x)

q(x) = -x^3

This is less steep ( a = -1 in this case) and we also have a reflection over the x-axis.

r(x) = 3*x^3

In this case 3 < 3.5, this means that this will be lees steep than f(x)

Write the ratio of 3/5 miles to 1/2 miles as a fraction in simplest form

Answers

Answer:

Three over Ten

Question 7
1 pts
8. Tianna worked 45 hours last week. Her employer pays time and a half for hours over 40. Her gross pay was $451.25. What is her
hourly rate?

Answers

Answer:

$9.50

Step-by-step explanation:

40x + (5*1.5*x) = 451.25

40x + 7.5x = 451.25

47.5x = 451.25

x = 9.50

8. Simon is saving his money to buy an Xbox. He earn money by mowing lowns for his
neighbors. The situation can be represented using the equation 35x - 2y = -42 where x
represents the number of lawns mowed and y represents the amount of money Simon has in his
bank account.

( explainations are muc appreciated:) )

a. How much money does Simon earn for mowing each lawn?

b. How much money was in Simon's bank account before mowing any lawns?

Answers

Answer:

a. $35

b.$21

Step-by-step explanation:

a. It is what your are multiplying the number of lawns mowed by

b. -2y = -42

divide by -2 on each side

y=21

(you don't need the 35x because we are trying to find how much before he started mowing)

Given the function y=2x and the domain (-1, 0, 1, 2), the corresponding range is (-2,
0.2, 6).
True
False

Answers

the answer is False.

2x2≠6

Do all of them for cookie idek

Answers

Step-by-step explanation:

slope.

1.2x

2.-x

3.1/4x

4.6x

5.3/4x

y intercept:

1.4

2.-2

3.1

4.12

5.1/2

Write an equation to represent the number of pages Jesse has read. Using x, the number of days Amir has been reading, write an expression to represent the number of days Jesse has been reading. Remember that Jesse started reading one day before Amir. Use this expression to write an equation for the number of pages Jesse has read. Let y represent the number of pages read.

Answers

Question:

Jesse and Amir were assigned the same book to read. Jesse started reading on Saturday, and he is reading 30 pages a day. Amir didn't start until Sunday, but he is reading 35 pages a day.

How many days will it take Amir to catch up to Jesse, and how many pages will they each have read?

Write an equation to represent the number of pages Amir has read. Use x to represent the number of days Amir has been reading and y to represent the number of pages he has read.

Answer:

It will take 6 days

Step-by-step explanation:

For Jesse:

[tex]Rate = 30\ pages/day[/tex]

This implies that Jesse will cover 30y in y days

For Amir:

[tex]Rate = 35\ pages/day[/tex]

This implies that Amir will cover 35x in x days

Because Amir starts a day later,

[tex]y = x + 1[/tex]

So, we have the following equations:

[tex]Jesse = 30y[/tex]

[tex]Amir= 35x[/tex]

[tex]y = x + 1[/tex]

To get the number of days when they read the same number of pages, we have:

[tex]Jesse = Amir[/tex]

Substitute values for Jesse and Amir

[tex]30y = 35x[/tex]

Substitute x + 1 for y

[tex]30(x+1) = 35x[/tex]

Open bracket

[tex]30x+30 = 35x[/tex]

Collect Like Terms

[tex]30 = 35x-30x[/tex]

[tex]30 = 5x[/tex]

Solve for x

[tex]\frac{30}{5} = \frac{5x}{5}[/tex]

[tex]\frac{30}{5} = x[/tex]

[tex]6 = x[/tex]

[tex]x = 6[/tex]

simplifly the expression 2(x - 5)

Answers

Answer:

2x - 10

Step-by-step explanation:

2(x - 5)

distribute

2*x - 2*5

2x - 2*5

2x - 10

Answer:????? Math (O-O)

Answers

Answer: the first one is 30. The second is .294. The third is 2/3.

Step-by-step explanation:

How do percents show the relationship between quantities?

Answers

9514 1404 393

Explanation:

A percentage is a representation of a fraction. Just as any fraction relates a quantity to a whole, so does a percentage.

Example:

  3/5 represents 3 parts out of 5.

Its equivalent as a percentage is ...

  3/5 · 100% = 60%

which also represents 3 parts out of 5, or 6 parts out of 10, or 60 parts out of 100.

__

Note that the percent symbol (%) can be considered to be a shorthand way to write /100. Similarly, the "mils" symbol (‰) can be considered a shorthand way to write /1000. That is, 60% is fully equivalent to 60/100, and vice versa.

write a story to represent the equation 1/2÷3 solve the equation and complete the story​

Answers

Answer: ↓↓

Step-by-step explanation:

Fred, Ben, and George bought a pizza. George's sister and her friends ate some of the pizza, they left 1/2 of the whole pizza. Fred decided that they should share the remaining pizza equally. How much of the pizza will they each get?

1/2 ÷ 3 = 1/6

The three boys will each get 1/6 of the pizza.

Hope this is good! :3

Other Questions
What are two homeostatic functions of the liver? O blood sugar regulation and nitrogenous waste conversionO store and mix foodO secrete bicarbonate into the small intestine and neutralize stomach acidO absorbs nutrients and stores waste material what happens to an angles measure when the angle is rotated. i will brainlist Anglo settlers were encouraged to come to Texas by the _[blank]_.Which best completes the sentence?A.) general law of expulsionB.) secularization actC.) national colonization lawD.) dissolution of the missions What controls an organisms development and growth of body structures? If L II M, solve for x and yIll give Brainliest to best answer JUST DO ME A FAVOR AND GIVE ME RANDOM FACTS ABOUT SPERM WHALES PLZ fact about historian art Which of the following was NOT used by Darwin in his studies? What is thirty divided by ten Read this scene from The Miracle Worker Act 3.HELP IM TIMED(Now HELEN begins groping, sensing something, trembling herself; and KATE, falling one step in onto her knees, clasps her, kissing her. HELEN clutches her, tight as she can. KATE is inarticulate, choked, repeating HELENS name again and again. She wheels with her in her arms, to stumble away out the doorway. . . .)How do these stage directions add meaning to the play?The stage directions explain the characters facial expressions. HELP ME IM ON A TESTThe stage directions illustrate the appearance of the room.The stage directions reveal the historical time period.The stage directions describe the characters emotions. Which of the following could be the graph of the equation y= -2x + 5? How do you know??(plz answer!!) What is the slope of that line? Mr. Green paid $7.50 for a set of dry erase markers. He used a $2.00 coupon for his purchase. Write AND solve an equation that represents the difference between d, the original price of the markers and the coupon. Solve for d. A cooling tower is 120 meters tall. The sides of the tower are in the shape of a hyperbola defined by the equation x^2/500 - y^2/900 = 1 with units in meters. The center of the tower is at the origin. How wide is the tower at the top? 50 m 92 m 100 m 184 m 1956 BCE is in this century: A 20th Century CE B 19th Century BCE C 18th Century BCE D 20th Century BCE What is 10x30 thanks need help kinda being sped today lol Please help me with number 15. If you could provide work, that would be great. The difference between 16.03 and 7.385 is . reason that railway couldnot develop in nepal Pls help due in 7 mins,ill give brainliest and 5 stars and thank you