What is the exact value of tan ( 5 pi/8 )

What Is The Exact Value Of Tan ( 5 Pi/8 )

Answers

Answer 1
Answer: Choice D) [tex]\tan\left(\frac{5\pi}{8}\right) = - \sqrt{\frac{2+\sqrt{2}}{2-\sqrt{2}}}\\\\\\[/tex]

===================================================

Explanation:

Make sure your calculator is in radian mode. Use your calculator to find that tan(5pi/8) = -2.41421 which is approximate.

Since the value is negative, this means the answer is between choices C and D. You can use your calculator to compute those expressions given and you should find it matches with choice D.

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

Further explanation:

We can apply the half angle identity for tangent like so

[tex]\tan\left(\frac{x}{2}\right) = \pm \sqrt{\frac{1-\cos(x)}{1+\cos(x)}}\\\\\\\tan\left(\frac{5\pi/4}{2}\right) = -\sqrt{\frac{1-\cos(5\pi/4)}{1+\cos(5\pi/4)}}\\\\\\\tan\left(\frac{5\pi}{8}\right) = -\sqrt{\frac{1-\left(-\frac{\sqrt{2}}{2}\right)}{1+\left(-\frac{\sqrt{2}}{2}\right)}}\\\\\\[/tex]

Simplifying further, we get

[tex]\tan\left(\frac{5\pi}{8}\right) = -\sqrt{\frac{1+\frac{\sqrt{2}}{2}}{1-\frac{\sqrt{2}}{2}}}\\\\\\\tan\left(\frac{5\pi}{8}\right) = -\sqrt{\frac{2+\sqrt{2}}{2-\sqrt{2}}}\\\\\\[/tex]

In the last step, I multiplied top and bottom of the outer fraction by 2 to clear out the denominators of the inner fractions.

Answer 2

Answer:

Answer D

Step-by-step explanation:

on edge 2023

What Is The Exact Value Of Tan ( 5 Pi/8 )

Related Questions

Please help me asap
Select the correct answer from each drop-down menu.
A system of linear equations is given by the tables. x y -1 1 0 3 1 5 2 7 x y -2 -7 0 -1 2 5 4 11

Answers

Answer:

1) The first equation of the system is y = 2·x + 3

2) The second equation of the system is y = 3·x - 1

3) The solution of the system is (4, 11)

Step-by-step explanation:

1) From the coordinates of the first table, we have;

The points of the y-coordinate have a common difference of two

The rate of change of the function using the first and the last point is given as follows;

Rate of change = Slope, m = (7 - 1)/(2 - (-1)) = 2

The, equation of the line in point and slope form is, y - 7 = 2 × (x - 2)

∴ The equation of the line in slope and intercept form is y = 2·x + 3

Therefore, the first equation of the system is y = 2·x + 3

2) Similarly from the coordinates of the second table, we have;

The points of the y-coordinate have a common difference of six

The rate of change of the function using the first and the last point is given as follows;

Rate of change = Slope, m = (11 - (-7))/(4 - (-2)) = 3

The, equation of the line in point and slope form is, y - 11 = 3 × (x - 4)

∴ The equation of the line in slope and intercept form is y = 3·x - 1

Therefore, the second equation of the system is y = 3·x - 1

3) Equating both equations in the system of equations to find a common solution gives;

2·x + 3 = 3·x - 1

∴ x = 4

From y = 3·x - 1  or y = 2·x + 3, we have the value of y at the solution point as  y = 3 × 4 - 1 = 11 or 2 × 4 + 3 = 11

∴ y = 11 at point of the common solution of the system of equations

Therefore, the coordinates of the common point which is the solution of the system is (4, 11).

Answer:

Select the correct answer from each drop-down menu.

A system of linear equations is given by the tables.

x y

-1 1

0 3

1 5

2 7

x y

-2 -7

0 -1

2 5

4 11

The first equation of this system is y =

2

x + 3.

The second equation of this system is y = 3x −

1

.

The solution of the system is (

4

,

11

).

Step-by-step explanation:

SOS HELP PLEASE!!!!!!!

Answers

Answer:

a for 2 b for 3 c for 1 and d is 4

Step-by-step explanation:

If 5p - 2r = 19 and 2p + r = 4, find (p+r)​

Answers

Answer:

5p-2r =19 in this one 5*5-2*3 so in this one p is =5 and r =3 and in the next one 2p+r=4 the answer is for p =1 and r =2 this means 2*1=2 and 2+2=4 and the first one is 5*5=25 and 2*3= 6 and 25-6=19 so that's it I guess

Explain how to estimate the quotient using compatible numbers. 27 and two-thirds divided by 3 and nine-tenths

Answers

Answer:

the estimation of the quotient is  7

Step-by-step explanation:

The computation of estimating the quotient is shown below:

It is given that the number is 27

After that the two-third would be divided by 3

And, then the nine-tenth

Based on the above information, the estimation of the quotient is  

= 27 + 2 ÷ 3 ÷ 3 + 9 ÷ 10

= 27 + 0.67 ÷ 3 + 0.9

= 27.67 ÷ 3.9

= 28 ÷ 4

= 7

hence, the estimation of the quotient is  7

What is the value of x In this equation?
75 + 10x = 225

150

15

25

10

Answers

Answer:

15

225-75=150

150÷10=15

The answer is 15
75-75 is 0 , 225-7 is 150

10x/10 = 150/10

X=15

Giving brainleest for brainly.

Answers

Can anyone help me with my questions

Which graph represents the solution set of and ?

graph I
graph II

graph III
graph IV

A.
graph I
B.
graph II
C.
graph III
D.
graph IV

Answers

Answer:

GRAPH III

Step-by-step explanation:

Look at the picture.

We have

y = x² - 4 → move the graph of x² 4 units down (the vertex is (0, -4))

x + y + 2 = 0   subtracy x and 2 from both sides

y = -x - 2 → move the graph of -x 2 units down (the y-intercept os -2)

Only graph III and IV meets these conditions.

The solution is the points of intersection of the graphs.

Therefore your answer is GRAPH III

Answer:

[tex]\fbox {C. graph lll}[/tex]

Step-by-step explanation:

The solution of the system of equations can be found at their intersections.

The graph which is correct is graph III as it has the correct representations of the equations and correctly indicates the points of intersection.

which is the better value 36 pictures for $8 or 24 pictures for $5

Answers

Answer:

24 pictures for $5

Step-by-step explanation:

To find out the better value, we have to find the price of a singular picture. To do this, we will divide each number by the amount of pictures.

For the first deal, 36 pictures cost $8, so 1 picture costs about $0.22.

For the second deal, 24 pictures cost $5, so 1 picture costs about $0.21.

Since the second deal costs less, it is a better deal.

Answer:

The best deal is 24 pictures for $5.

Step-by-step explanation:

In order to find out which price is better, we need to find the amount of pictures per dollar. This is also known as the unit rate.

36 ÷ 8 = 4.5 or 5 when rounded to the nearest whole number.

24 ÷ 5 = 4.8 or 5 when rounded to the nearest whole number.

However, since 4.8 is in fact higher than 4.5, the best deal is 24 pictures for $5.

Hope this helps! :D

Marisol is making a rectangular wooden frame. She wants the length of the frame to be no more than 12 inches. She has less than 30 inches of wood to use. Which system of inequalities represents the possible length, l, and the possible width, w, that her frame could have?

l ≤ 12
2l + 2w 12
2l + 2w 12
l + w < 30

Answers

Answer:

a i the answer

Step-by-step explanation:

l ≤ 12

2l + 2w < 30

Answer: a

Step-by-step explanation:

Using the Arc length formula s = r θ, find the missing variable.
Find s when r = 18.4 and θ 3π/4
13.8π
15.2π
24.5π

Answers

Step-by-step explanation:

13.8pie is correct answer of your question

Which is equivalent to 6x-8y

Answers

Answer:

24 i guess. im not sure

-2(-3x + 4). -2 multiply -3 you get a positive 6, and -2 multiply +4 you get a negative 8

Question 4
Write an algebraic expression for the following.
Joe spent three dollars less than twice as much as Fernando did.
Use x for the variable.
Question 5
Ayliah is 7 years more than 1/2 of Deb's age
use x for the variable

Answers

Question 4:
2x-3
Because we don’t know how much Fernando has that would be where we fill in the variable giving you 2x then 3 dollars less will give you the -3 therefore 2x-3
Question 5:
1/2x+7
Because we don’t know Deb’s age that would be the variable and we are looking for half of Deb’s age giving you 1/2x then the 7 years more giving you the +7 hence 1/2x+7

Help please thank you !!!

Answers

It’s c, the other 3 is so off from the answer

This year, a small business had a total revenue of $89,700. If this is 38% more than their total revenue the previous year, what was their total revenue the previous year?

Answers

Answer:

The business' total revenue last year was $65,000.

Step-by-step explanation:

So, if you need to find the previous year's total revenue, you would set up an equation like this:

    x + 0.38x = 89,700

I think it would work out something like this:

    x + 0.38x = 89,700

    1.38x = 89,700

    x = 65,000

To check, we would substitute 65,000 into the equation x + 0.38x = 89,700.

    x + 0.38x = 89,700

    (65,000) + 0.38(65,000) = 89,700

    65,000 + 24,700 = 89,700

    89,700 = 89,700

Find the missing angle measure Angle STU?

Answers

The answer is 60 degrees because the red thingy indicated that it is a 90 degree angle then you subtract that from 150 to get your answer= 60

The cost of 5 cans of dog food is 4.35. At this price how much do 11 cans of dog food cost? Explain!

Answers

Answer:

Ok so it would be 9.57

Step-by-step explanation:

4.35÷5 = 0.87

so 1 can is 0.87

$0.87*11=$ 9.57

it’s 9.57

each can is 87 cents

Write P(x) = x^3 + x^2 − 17x + 15 as a product of two factors, using x − 3 as one factor.
A. (x − 3)(x^2 + x − 17)
B.(x − 3)(x^2 + 4x − 17)
C.(x − 3)(x^2 – 4x − 5)
D.(x − 3)(x^2 + 4x − 5)

Answers

Answer:

D. (x-3)(x^2 + 4x - 5)

Step-by-step explanation:

P(x) = x³ + x² - 17x + 15 can be written as (x - 3) (x² + 4x - 5) as a product of two factors.

What is Polynomials?

Polynomials are expressions in algebra which consist of variables, constants and exponents combined using the basic operations in mathematics like addition, subtraction, multiplication and division.

Polynomials can be classified as monomials, binomials and trinomials depending on the degree of the variables as 1, 2 and 3 respectively.

The given polynomial is P(x) = x³ + x² - 17x + 15.

We already have x - 3 is the factor of this polynomial.

To get the other factor which is a binomial, we have to divide the given polynomial with x - 3.

On dividing, we get x² + 4x - 5 as the quotient and remainder equals zero.

So x² + 4x - 5 is the other factor of the given polynomial.

Hence, the polynomial P(x) = x³ + x² - 17x + 15 can be written as (x - 3) (x² + 4x - 5) as a product of two factors.

To learn more about Polynomials, click on the link given below:

https://brainly.com/question/11536910

#SPJ2

Review the graph. On a coordinate plane, a vector has origin (6, 2) and terminal point (0, 4). What is the component form and magnitude of the vector shown? LeftAngleBracket negative 2, 7 RightAngleBracket and StartRoot 53 EndRoot LeftAngleBracket negative 2, 7 RightAngleBracket and 53 LeftAngleBracket negative 7, 2 RightAngleBracket and StartRoot 53 EndRoot LeftAngleBracket negative 7, 2 RightAngleBracket and 53

Answers

Answer:

I think C

Step-by-step explanation:

The component form and magnitude of the vector is  < -6, -2>, √ 40, the correct option is A.

What is a Vector?

A vector is a quantity that needs both magnitude and direction for its representation.

A vector has origin (6, 2) and terminal point (0, 4).

The component of vectors is determined by the formula

<x,y> = < (x₂- x₁ ) , (y₂-y₁)>

<x,y> = < (0-6), (4-2)>

<x,y> = < -6, -2>

The magnitude of the vector is determined by

[tex]\rm |v| = \sqrt{x^2 +y^2[/tex]

|v| = √ 40

The correct options are  

LeftAngleBracket negative 6, 2 RightAngleBracket and StartRoot 40 EndRoot LeftAngleBracket negative 6, 7 RightAngleBracket and 40 LeftAngleBracket negative 2,6 RightAngleBracket and StartRoot 47 EndRoot LeftAngleBracket negative 2, 6 RightAngleBracket and StartRoot 40

To know more about Vectors

brainly.com/question/25705666

#SPJ5

Find the length of the missing side. Round to the nearest tenth (one decimal place).

Answers

Answer: pretty sure it is 56.5

Step-by-step explanation:

how to use standard form

Answers

Answer: Standard form is another way to write slope-intercept form (as opposed to y=mx+b). It is written as Ax+By=C. You can also change slope-intercept form to standard form like this: Y=-3/2x+3. Next, you isolate the y-intercept(in this case it is 3) like this: Add 3/2x to each side of the equation to get this: 3/2x+y=3.

Step-by-step explanation: hope this helps

Square ABCD was translated using the rule (x. y) «-4,y + 15) to form A'B'CD. What are the coordinates of point
D in the pre-image if the coordinates of point D' in the image are (9, -8)?
TE
O (13, -23)
(5, 7)
O (18, 1)
O (6,4)

Answers

Answer:

[tex](13,-23)[/tex]

Step-by-step explanation:

Given

Translation: [tex](x,y) -> (x-4,y+15)[/tex]

Required

Determine the pre-image of (9,-8)

In (9,8)

[tex]x = 9[/tex] and [tex]y = -8[/tex]

So:

[tex](x,y) -> (x-4,y+15)[/tex]

Becomes

[tex](9,8) ->(x-4,y+15)[/tex]

By comparison:

[tex]x - 4 = 9[/tex]

[tex]y + 15 = 8[/tex]

Solving for (x):

[tex]x - 4 = 9[/tex]

[tex]x = 9 + 4[/tex]

[tex]x = 13[/tex]

Solving for (y):

[tex]y + 15 = -8[/tex]

[tex]y = -8 - 15[/tex]

[tex]y = -23[/tex]

Hence, the pre -image has a coordinate of [tex](13,-23)[/tex]

These two triangles are similar. If the base of △ A B C is 3 cm and the base of △ D E F is 7 cm, and the area of △ A B C is 7 cm², calculate the area of △ D E F. Round your answer to two decimal places.

Answers

Answer:

38.11 cm^2

Step-by-step explanation:

DEF is larger than ABC

therefore find the height of ABC

7 = 1/2 * 3 * h

h = 7 * 2/3

h = 14/3

So, lets find height for DEF, 7/3 = H/ 14/3

H = 98/9

A = 1/2 * 7 * 98/9

A = 38.11 cm^2

what is the answer to 3c-7c+a+b

Answers

The answer is -4c+a+b

Mel works as a delivery person for Amazon. The graph shows a linear model for his delivery times on
different days.
(a) What is the equation of the line, first written in point-slope form and then written in slope-intercept
form? Show how you determined the equation.
(b) Based on the linear model, predict how long it initially took Phillip to deliver his packages.
Approximately how much did his delivery time decrease per day?

Answers

Answer:

Point slope form: -9 = m(3)

Slope intercept form: y = -3x + 30

At x = 0, his delivery time was 30 minutes. It decreased by 3 minutes per day.

Step-by-step explanation:

We have 2 points to calculate the line.

(3, 21) x1 y1

(6, 12) x2 y2

First, we need to calculate the slope.

m =

m =

m = -3

Point slope form is:

y - y1 = m(x - x1)

So for our case:

-9 = m(3)

And slope intercept form is:

y = mx + b

We need to solve for the y intercept (b)

y = -3x + b --- enter the slope

21 = -3(3) + b --- enter in any point on the line for x and y

21 = -9 + b

b = 30 --- solve for b

Now our slope intercept form of the line is:

y = -3x + 30

At x = 0, his delivery time was 30 minutes. It decreased by 3 minutes per day.

Mrs. Brim made a chart to see how long it took her students to finish a test. How many students took more than thirty minutes to finish the test?

Answers

Answer:

As, this question is incomplete and without data we can not answer this question. But we can make it complete by adding our own values. Let's do it and calculate.

Average Time = 23.4 minutes is the time that Mrs Brim wanted to see.

Step-by-step explanation:

As, this question is incomplete and without data we can not answer this question. But we can make it complete by adding our own values. Let's do it and calculate.

Let's suppose, there are 10 students in the class of Mrs. Brim and she took 5 tests on subsequent days and made chart to know the average time her students took to solve the test.

Total time of test = 30 minutes

Average time taken by the students to solve the test on Day 1 = 25 minutes.

Average time taken by the students to solve the test on Day 2 = 27 minutes.

Average time taken by the students to solve the test on Day 3 = 22 minutes.

Average time taken by the students to solve the test on Day 4  = 23 minutes.

Average time taken by the students to solve the test on Day 5 = 20 minutes.

Average Time in all Tests = Sum of all times / total number of days

Average Time = (25 + 27 + 22 + 23 + 20) / 5 days

Average Time = 117/5

Average Time = 23.4 minutes is the time that Mrs Brim wanted to see.

Order the following from biggest to smallest = 10 g = 10 kg = 10 mg​

Answers

Answer:

10 kg = 10g = 10 mg

Hope this helped ;)

grams of fish
number of calories
1000
2001
Enter the missing values in the boxes below.
b=0

Answers

Answer:

‍♂️ but if you know please answer

Answer:

12344567891011121314151617181920

Step-by-step explanation:

12344567891011121314151617181920

convert to standard form y=-4x-8

Answers

Answer:

[tex]4x + y = - 8[/tex]

Step-by-step explanation:

write in standard form :

[tex]ax + by = c[/tex]

A submarine is 105 feet below the surface of the water, and it begins to ascend at a rate of 3 feet per minute. After how many minutes will the submarine be 81 feet below the surface?

Answers

Answer:

8 minutes

Step-by-step explanation:

Step one:

given

A submarine is 105 feet below the surface of the water

depth of submarine= 105 feet

let the time of ascending be x

Required

The time taken to ascend up to 81 ft

Step two:

the expression for the situation is

81=105-3x

solve for x

3x=105-81

3x=24

divide both sides by 3

x= 24/3

x=8 minutes

I don't understand this question. I was hoping someone could help.​

Answers

Answer:

A

Step-by-step explanation:

The constant rate of change in this question simply means the slope

To get the slope, we simply get two points and apply the slope equation;

The points are;

(3,60) and (6,30)

The slope equation is;

m = (y2-y1)/(x2-x1) = (30-60)/(6-3) = -30/3 = -10 ft/s

So our answer is the first option as it represents a decent of -10 ft/s

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