Solve 2 cot x = csc^2 x symbolically on the interval (0,2pi).

Answers

Answer 1

Answer:

x=pi/4, 5pi/4

Step-by-step explanation:

cot x = cos x / sin x, csc x = 1/sin x, so we have 2 cos x / sin x = 1/ sin^2 x. multiply both sides by sin^2 x to get 2 cos x * sin x = 1, divide both sides by 2 to get cos x sin x = 1/2, this would work for angles pi/4 and 5pi/4 (3pi/4 and 7pi/4 would make cos x sin x = -1/2) since cos x = sin x = sqrt(2)/2


Related Questions

Mr. Haynes wants to expand his rectangular living room to make room for an indoor theater system. He asks the contractor to make the width of the room 5 feet longer and he wants the length of the room to be 5 feet longer than twice the width. When finished the new room will have a perimeter of 140ft around. The new dimensions of the room will be

Answers

Step-by-step explanation:

check the image for detailed solution

A local hamburger shop sold a combined total of 637 hamburgers and cheeseburgers on Wednesday. There were 63 fewer cheeseburger sold than burgers. How many hamburgers were sold on Wednesday?

Answers

X + x-63=637
2x=700
X=350
Burgers=350
Cheeseburgers=350-63
Cheeseburger=287

brainiest to whoever correct

Answers

Answer:

y = 138

Step-by-step explanation:

90 + 4x + 3x + 6 = 180

96 + 7x = 180

7x = 84

x = 12

———

3(12) + 6

36 + 6

42

———

180 - 42 = 138

Rick’s Rentals is a car rental company that uses the function f(x)=22+0.10x to determine the to
tal cost of a rental as a function of how many miles a person drives. Penny’s Pencils is another company that uses a similar function g(x)=22+0.10x to determine the total cost of an order of personalized pencils as a function of the number of pencils ordered. Determine the domain and range of the company whose function is continuous and justify your answer.

Answers

Answer:

Step-by-step explanation:

The number of miles driven is sometimes written as a mixed number, and thus is a continuous variable (whereas the number of pencils purchased is not continuous (it's a whole number).

The domain of the continuous function are [0, n), where n represents the number of miles driven and is rarely over about 500 miles per day; the range is [$22, r), where r is ($0.10/mile)(number of miles driven), or approximately $50.  If the renter drove 600 miles the upper end of the range would be $60.  And so on.

If each rabbit consumes 10 pounds of rabbit food each year, then how much rabbit food is consumed in 10 years

Answers

Answer:

100 pounds in 10 years

Step-by-step explanation:

10 pounds per year for 10 years

We simply multiply 10 pounds to 10 years to get 100 pounds

-Chetan K

Simple Arcs and Sectors question attached. First person to answer correctly gets 50 points. ONLY ANSWER 1ST QUESTION Good Luck!! Spam comments will be blocked and accounts reported.

Answers

Answer:

θ = 60º

Step-by-step explanation:

s = (θ/180)πr

Solving for θ yields

θ = (180s) / (πr)

--------------------------------

For the 1st one

θ = (180 * 12.56) / (π * 12)

θ = 60º

5. The coordinate increments from (4, 3) to (9, 7) are :

6. The coordinate increments from (- 6, - 4) to (12, - 9) are:

7. The coordinate increments from (10, - 7) to (14, - 9) are: are:

8. The coordinate increments from (- 47, - 10) to ( 17 , 8) are:

Answers

Answer:

the correct answer is 8

Step-by-step explanation:

Answer:

5. Is "+"      6. is "-"        7. is "+"               8. is "-"

Step-by-step explanation:

¿Cuál es la pendiente perpendicular a la pendiente m = 3 ?

Answers

Answer:

The slope of a line perpendicular to a vertical line is zero.

Step-by-step explanation:

help plz
find the size of unknown angle in the flowing figures ​

Answers

Answer:

it is 95 degrees because it is a vertically opposite angle

Please help me out with this Math sheet. Thanks

Answers

Answer:

1. acute

2. obtuse

3. right

4. acute

5. straight

6. obtuse

7. acute

8. obtuse

9. straight

10. ∠ EAD , ∠ CED , ∠ BCE , ∠ BEA  , EBC

11. ∠CDA  , BCD

12. ∠AED ,∠BEC

13. ∠ AEC, ∠ BED

14. ∠ EAU , ∠EUI , ∠IUO , OAE

15. ∠ EUO , ∠IUA

16. ∠AUO , ∠EIO

How many solutions does this equation have

-4(5-3x)=12x+20
A) no solution
B) one solution
C) two solutions
D) infinitely many solutions

Answers

Answer:

A) no solution

Step-by-step explanation:

It’s A Contradiction

Answer:

its one solution

Step-by-step explanation:

-20+12

What is the base of 4×4×4×4×4?

Answers

Answer:

Step-by-step explanation:

Your base would be the 4

Answer:

4

Step-by-step explanation:

When you have a something raise up to a number this can be represented as:

[tex]b^a = b_1 \cdot b_2 \cdot \cdot \cdot b_a[/tex]

Where [tex]b[/tex] is the base and [tex]a[/tex] the exponent. In this case you have five times four, then you can re-write the expression as:

[tex]4 \times 4 \times 4 \times 4 \times 4 = 4^5[/tex]

Where the [tex]b[/tex] is equal to 4 and [tex]a[/tex] equal to 5

¿Qué fuerza media se requiere para que un objeto de 2 Kg aumente su velocidad de 5 m/s a 12 m/s en una distancia de 8 m?

Answers

Answer:

14.87

Step-by-step explanation:

Para conocer cual es la fuerza que necesita el cuerpo para aumentar su velocidad de 5 m/s a 12 m/s en 8 m

Necesitamos conocer la aceleración y para conocer la aceleración debemos saber cuanto tiempo tarda en recorrer los 8m

Vf = Vo +a(t)

12 = 5 +a(t) -------> Vamos a despejar el tiempo.

t = 7/a

X= Vo(t) +1/2a(t²)

X= 5(7/a)+1/2a( 7/a )²

8 = 35/a+49/2a

a = 7.43 m/s²  

Ahora que conocemos la aceleración podemos calcular la fuerza como:

F = m*a

F = 7.43 * 2 kg.

F = 14.87

Two functions f and g are defined on the set R, of real numbers by f : x  2x  3 and
x g : x 1 3x . Find the inverse of the function f and the domain of gof.

Answers

Answer:8

Step-by-step explanation:

The cost of producing higlighter​s with the company logo printed on them consists of a onetime setup fee of $160.00 plus $0.65 for each higlighter produced. This cost can be calculated using the formula C=160.00+0.65p, where p represents the number of higlighters produced and C is the cost. Use the formula to calculate the cost of producing 2400 higlighters. (Do not inlcude a comma in your answer)

Answers

Answer:

7839 ...........

I need help as soon as possible please!!!!

Answers

Answer:

Which grade math is this? I haven't learned it

A square field has a side length of 6x10 meters. Which of the following is its area in square meters?

Answers

Answer:

60 square meters

Step-by-step explanation:

area is just its length times its width and both numbers are provided here

6 * 10 is 60

Match the equation to the type of solution.


3=3 A. One solution


x=0. B. No solution


4=-2. C. Infinite many solutions

Answers

3=3 - C. Infinite many solution
X=0 - B. No solution
4=-2 - A. One solution
hope this helps .

Use properties to evaluate 1/3 (-5 ÷ 1/2 ) 1/4?

A. - 5/2
B. 5/8
C. - 5/8
D. 5/2

Answers

I believe the correct answer is C

Please help me :/!!!!

Answers

Answer:

(3, 9)

Step-by-step explanation:

Set 3x and 2x+3 equal to each other forming an equation in x.

3x=2x+3

Solve for x.

x=3

Substitute the given value of x into the equation y=3x.

y=3x3

Solve for y.

y=9

(x, y) = (3, 9)

Hope this helps :)


The mean of 11 numbers is 49. Removing one of the numbers causes the mean to decrease to 45. What number was removed?

Answers

Answer:

89

Step-by-step explanation:

The mean:

[tex]\overline{x}=\dfrac{a_1+a_2+a_3+...+a_n}{n}[/tex]

We have:

[tex]\overline{x}=49;\ n=11[/tex]

Then we have

[tex]\dfrac{11\cdot49}{11}=49[/tex]

[tex]n[/tex] - the number

new mean is equal 45.

Therefore we have the equation:

[tex]\dfrac{11\cdot49-n}{11-1}=45\\\\\dfrac{539-n}{10}=45\qquad|\text{multiply both sides by 10}\\\\539-n=450\qquad|\text{subtact 539 from both sides}\\\\-n=-89\qquad|\text{change the signs}\\\\n=89[/tex]

Step-by-step explanation:

(x1 + x2 + ... + x11)/11 = 49

x1 + x2 + ... + x11= 49×11 = 539

(x1 + x2 + ... + x10)/10 = 45

x1 + x2 + ... + x10 = 45×10 = 450

so, the difference in both sums is

539 - 450 = 89

89 was the removed number.

0.7619047619 as a fraction?
which one
1. 1/16
2. 16/21
3. 2
4. 4

Answers

Answer:

16/21

Step-by-step explanation:

A family buys a studio apartment for $180,000. They pay a down payment of $27,000.
a. Their down payment is what percent of the purchase​ price?
b. What percent of the purchase price would a ​$9,000 down payment​ be

Answers

Answer:

down is $153000 while purchase price is $144000

is 0.667 elastic or inelastic?​

Answers

Answer:

inelastic is the answer

keep safe

What is 20% of $1575.00

Answers

step:

20% = 20/100

of = ×

20/100 × $1575.00

answer : $315

Step:

20% = 20/100

of = ×

20/100 × $1575.00

Answer : $315

Dependent Task:

Directions: Write the place value and the value of the underlined digit.

Number PLACE OF VALUE VALUE
1. 0.345 _____________ _____
2. 0.3469 _____________ _____
3. 0.6ó54 _____________ ______


(UNDERLINED DIGIT)
1. 5
2.3
3.4


please​

Answers

Answer

Use your mind  

Nobody wants to help you, especially since you are no help to others.

a scale diagram, 0.125 inch represe
5 feet. How many inches represent
pot?
0.001
0.01
0.1
0.12
Math

Answers

Answer:

the scale diagram is 9.12

A shirt cost $24.92 with 10% discount if the sales tax is 6.35% how much will the shirt cost?

Answers

Cost 24.92*10/100
= 2.492
Sale tax 6.35+2.492
The total Cost of shirt is = 8.732

The hypotenuse of a 30°-60°-90º triangle is 8 units and one leg is 4 units. What is the length of the other leg?

Answers

Answer:

The length of the other leg is [tex]4\sqrt{3}[/tex]

Step-by-step explanation:

There are 2 ways to solve this.

1) Pythagorean theorem (the harder way)

A 30-60-90 triangle is a right triangle, and therefore you can use the pythagorean theorem to calculate the measure of 1 side given the 2 others.

[tex]a^2+b^2=c^2\\a^2+4^2=8^2\\a^2+16=64\\a^2=48\\a=\sqrt{48}\\a=6.9282...[/tex]

That's one solution, but its not a very nice number or the exact answer you probably want. Instead, you can simplify the root.

First, you need to factor 48:

[tex]2*24=48\\2*12=24\\2*6=12\\2*3=6[/tex]

The prime factors of 48 are:

[tex]2*2*2*2*3=48[/tex]

Then, you need to find perfect squares:

[tex](2*2)*(2*2)*3=48\\2^2*2^2*3=48[/tex]

And finally, you can remove those like this:

[tex]\sqrt{48} =\sqrt{2^2*2^2*3} \\\sqrt{48} =2\sqrt{2^2*3} \\\sqrt{48} =2*2\sqrt{3} \\\sqrt{48} =4\sqrt{3}[/tex]

The length of the other leg is [tex]4\sqrt{3}[/tex]

2) 30-60-90 triangle relationships (the easier way)

There are 4 simple rules here:

Short leg × 2 = hypotenuseShort leg × √3 = long legLong leg ÷ √3 = short legHypotenuse ÷ 2 = short leg

They're actually pretty easy to remember. You can multiply the short leg by 2 or √3, and 2 is greater than √3 (check a calculator). The hypotenuse of course is also longer than the long leg, so you have to multiply by 2 to get it. Then for the long leg, the only option is to multiply by √3. The same works in reverse for both of those.

Here, we have the short leg. You can check that with the pythagorean theorem again to be sure:

[tex]a^2+4^2=8^2\\a^2+16=64[/tex]

Because 16 is less than half of 64, a has to be the longer leg. Using the rules above, multiply the short leg by √3 to get the answer:

[tex]4 * \sqrt{3} \\4\sqrt{3}[/tex]

Same answer as the previous method.

Food A 150 calories in 3/4 of a serving. Food B 250 calories in 2/3 of a serving. Find each unit rate. Which food has fewer calories per serving?

Answers

Food A 112.50
Food B 166.50
Food A has less calories
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