What is the value of sin {3sin^-1 (2/5)} ?​

Answers

Answer 1

Answer:

[tex]\displaystyle \frac{118}{125}[/tex]

Step-by-step explanation:

Trigonometry

Calculate

[tex]\sin (3\sin^{-1}(2/5))[/tex]

We use the formula for the sine of triple angle:

[tex]\sin 3x=3\sin x-4\sin^3 x[/tex]

And recall:

[tex]\sin \sin^{-1}x=x[/tex]

For this problem, we set:

[tex]x=\sin^{-1}(2/5)[/tex]

Thus:

[tex]\sin 3x=3\sin (\sin^{-1}(2/5))-4\sin^3 (\sin^{-1}(2/5))[/tex]

[tex]\displaystyle \sin 3x=3*\frac{2}{5}-4\left(\frac{2}{5}\right)^3[/tex]

[tex]\displaystyle \sin 3x=\frac{6}{5}-4*\frac{8}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{6}{5}-\frac{32}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{6*25}{125}-\frac{32}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{150-32}{125}[/tex]

[tex]\mathbf{\displaystyle \sin 3x=\frac{118}{125}}[/tex]


Related Questions

LOOK AT PICTURE, THEN ANWSER, WHOEVER IS CORRECT I WILL MARK BRAINIEST:)

Answers

Answer:

C

Step-by-step explanation:

It has to be either A or C because the function is decreasing as you move left to right, this only occurs when the number inside parenthesis is less than 1.

It isn't A because if you plug in x=0, the value is 2, but on the graph it is greater than 2.

pleae give thanks by hitting heart button :)

lol the answer is C .

What is the elevation of the deck where Winston ate dinner?

plz helppp

Answers

Question:

What is the elevation of the deck where Winston ate dinner?

Answer:

The surf shop was higher and the distance would be 12.8 feet above the oceans surface.

12.8

Step-by-step explanation:

ostulate
Point D is on segment BC. Segment BC measures 8x units in length.

A line has points C, D, B. The length of line C D is 3 x + 8. The length of line D B is 4 x + 10.
What is the length of segment BC?

Answers

Answer:

144

Step-by-step explanation:

If point D is on BC, then BD + DC = BC

Given

BC = 8x

CD = 3x + 8

BD = 4x + 10

Substitute and get x

8x = 3x+8 + 4x + 10

9X - 7X = 18

x = 18

Get BCBC = 8x

BC = 8(18)

BC = 144

Hence the  length of segment BC is 144

Answer:

144

Step-by-step explanation:

I just had this assignment on edge 2021. Hope this helped :)

To help consumers assess the risks they are​ taking, the Food and Drug Administration​ (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette yielded mean nicotine content of milligrams and standard deviation of milligrams for a sample of cigarettes. Construct a ​% confidence interval for the mean nicotine content of this brand of cigarette.

Answers

Answer:.

Step-by-step explanation:.


A salesperson works 40 hours per week at a job where she has two options for being paid. Option
A is an hourly wage of $22. Option B is a commission rate of 10% on weekly sales. How much
does she need to sell this week to earn the same amount with the two options?

Answers

Answer:

the weekly sales are $8,800 to earn the similar amount with the two options

Step-by-step explanation:

The computation is shown below:

The earnings in option A is

= 40 hours × $22

= $880

Now let us assume the weekly sales be x

So the equation would be

10%x = $880

0.10x = $880

x = $8,800

Hence, the weekly sales are $8,800 to earn a similar amount with the two options

Solve: 2x + 3x? - 11x-6=0​

Answers

Answer:

To solve the following equation we must first combine like terms Recognize the easiest way to manipulate the equation Lastly rearrange to isolate for x: usually done with division

2x+3x-11x-6=0

Combine like x variables

-6x-6=0

Add 6 to the right side

-6x = 6

Divide by -6

x=-1

Rate positively and give brainlist

Answer:

x = - 1

Step-by-step explanation:

2x + 3x - 11x - 6 = 0

-6x = 6

x = - 1

Find the prime factorization of 100. Show all of your work and write your answer using exponents.

Answers

this is the ans ..............................

Given the drawing as shown below and that p || a, which of the following cannot be supported by the evidence shown?

A - B - C - D -

Answers

Answer:

D. <b ≅ <g

Step-by-step explanation:

Given that lines p and q are parallel to each other, therefore the following can be concluded:

✔️<f ≅ <h, this is because they are both Vertical angles.

✔️<d and <h are supplematry, this is because they are same side consecutive interior angles. Consecutive angles are supplematry.

✔️<a and <b are supplematry, this is because they are linear pair angles.

✔️<b cannot be congruent to <g. They are not corresponding angles, nor are they alternate interior angles.

BRAINLIST ASAP
When marcus started school at 5 years old, his parents put $9,050 into a college fund account that earned 7.5% interest. What is the total amount in the account when he starts college at 18 years old? ____

Answers

Answer: 17873.75 dollars

Step-by-step explanation:

We can use the equation: l = p x r x t (Total Interest = principal x interest rate x years/time)

9050 will be the principal; it's the amount you deposit in the first place.

7.5% is the interest rate. You can convert it to 0.075 as a decimal.

13 is the years/time. If Marcus's parents put the college fund in when he was 5 and now he's 18, there has been 13 years in between.

9050 x 0.075 x 13 = 8823.75

8823.75 + 9050 = $17873.75

So in Conclusion, the total amount in the account when Marcus is 18 is 17873.75 dollars.

Hope this helps!

In triangle ABC shown below, point A is at (0,0)
point B is at (x subscript2, 0)
point C is ([x sub1]/ 2, [y sub1]/2
point D is [x sub1 + xsub2]/2, ysub1/2)

Prove that segment DE is parallel to segment AB.

Answers

Answer:

Proof below

Step-by-step explanation:

To prove DE and AB are parallel, we compare the slopes of both segments

Suppose we know a line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Segment AB goes through the points (0,0) and (x2,0), thus:

[tex]\displaystyle m_{AB}=\frac{0-0}{x_2-0}=0[/tex]

The slope is 0 because the line is horizontal.

Now for the segment DE, the endpoints are

[tex]\displaystyle (\frac{x_1}{2},\frac{y_1}{2}),\ (\frac{x_1+x_2}{2},\frac{y_1}{2})[/tex]

The slope is:

[tex]\displaystyle m_{DE}=\frac{\frac{y_1}{2}-\frac{y_1}{2}}{\frac{x_1+x_2}{2}-\frac{x_1}{2}}[/tex]

[tex]\displaystyle m_{DE}=\frac{0}{\frac{x_2}{2}}=0[/tex]

Segment DE is also horizontal, thus is parallel to segment AB.

I need help plssssss.....

Answers

No the answer is C
y=3x+3

Which of the following letters have perpendicular line segments.
A E F H MNV X Z

Answers

Answer:

I think it's E, F, H

Step-by-step explanation:

Hope you got it.

Merry Christmas...

Y=log base(rootx) x find dy/dx

Answers

Given:

[tex]y=\log_{\sqrt{x}}x[/tex]

To find:

The value of [tex]\dfrac{dy}{dx}[/tex].

Solution:

We have,

[tex]y=\log_{\sqrt{x}}x[/tex]

It can be written as

[tex]y=\log_{\sqrt{x}}(\sqrt{x})^2[/tex]

Using property of log, we get

[tex]y=2[/tex]          [tex][\because \log_aa^x=x][/tex]

Now, differentiate both sides with respect to x.

[tex]\dfrac{dy}{dx}=\dfrac{d}{dx}(2)[/tex]

[tex]\dfrac{dy}{dx}=0[/tex]          [tex][\because \dfrac{d}{dx}(Constant)=0][/tex]

Therefore, the value of [tex]\dfrac{dy}{dx}[/tex] is 0.

A pound of sweet potatoes costs $1.81 at Walmart. Shelly buys 14.6 pounds to make a sweet potato pie. How much money
will she spend at Walmart?

Answers

Answer:

$26.43

Step-by-step explanation:

A pound = $1.81. Multiply the price per pound by however many pounds Shelly is buying.

Answer:

26.426

Step-by-step explanation:

1.81x14.6=26.426

-4(x+6)-2(-3x-9) simplify

Answers

Answer:

-4x-24+6x+18

Step-by-step explanation:

-4x+3y=-2
y=x-1

x=
y=

Answers

Answer:

Easy thankyou for coming to me your answer is x= -1 and y=-2

Step-by-step explanation:

Hope that help.

Answer:

Step-by-step explanation:

here you go mate'

step 1

-4x+3y=-2,y=x-1  equation

step 2

y=x-1;-4x+3y=-2  rewrite the equation

step 3

y=x-1  1st equation

step 4

-4x+3y=-2  saubstitute

-4x+3(x-1)=-2

-x-3=-2

step 5

-x-3=-2  simplify by adding 3 to both sides

-x=1

step 6

-x/-1=1/-1  divide

x=-1

second equation

step 1

y=x-1  substitute

y=-1-1

step 2

y=-1-1 simplify

y=-2

answer

x=-1 and y=-2

Which operation is NOT closed for polynomials?
es )
A)
add a trinomial to a trinomial
B)
divide a binomial by a trinomial
multiply a binomial by a binomial
D)
subtract a binomial from a trinomial

Answers

Answer:

B)

divide a binomial by a trinomial

Step-by-step explanation:

As we know that the polynomials are very closed to the addition, subtraction and the multiplication but the same cannot be happen under the division as the division of two polynomials could not become a polynomial it is not necessary

Now if we divide the binomial from a trinomial so it would give a rational expression and contain a negative exponent and negative exponent is not allowed under the same

Therefore the option B is correct

can u pls help me with this question asap ​

Answers

Answer:

$13.50

Step-by-step explanation:

5 bags is 22.50 so 22.50/5 = 4.50 for 1 bag. Multiply that by 3 for 3 bags and get $13.50

in eleven years ted will be 22 years old how old is he now?

Answers

Answer:

11

Step-by-step explanation:

22-11=11

Please Help thank you I appreciate it

Answers

Answer:

48in sq

Step-by-step explanation:

8*12/2=8*6=48

Answer:

48in

Step-by-step explanation:

A triangle like this is like half of a rectangle. The rest fits in the upper left and right. So to find the area of the triangle, we're going to start be pretending it's a recrangle.

Our rectangle is 12 by 8.

12 x 8 = 96

If this were a rectangle, the area would be 96in.

Since it's a triangle and that's only half of a rectangle, the area is half of that.

96 / 2 = 48

The area of this triangle is 48in.

Picture below
mathematics

Answers

Answer:

false

Step-by-step explanation:

5/9 is .5 repeating

Macy wants to sell her old Playstation 4 games on decluttr.com. The wtbsite charges sellers a comission of 20%
for items sold on their website. If Macy sells a Playstation 4 game on the website for $35.00. How much willshe
actually receive?

Answers

Answer:

$28

Step-by-step explanation:

The website charges 20%, so Macy receives 80%.

Then:

80% x 35=.8 x 35=28 ....................

slove for x
(6x+4)+81+41

Answers

Answer: 6x + 126

Hope this helped.

Sarah read 64 1/2 pages of her book in 6 hours. What is the average number of pages that Sarah reads per hour?

Answers

Answer:

We conclude that the average number of pages that Sarah reads per hour will be: 10.75 page per hour

Step-by-step explanation:

Given

Number of pages Sarah read [tex]=64\frac{1}{2}=\frac{129}{2} = 64.5[/tex]Number of hours Sarah spent = 6 hours

The average number of pages per hour can be calculated by simply dividing the total number of pages i.e. 64.5 pages by the number of hours spent on reading i.e. 6 hours.

Thus,

Average number of pages per hour = 64.5 pages / 6 hours

                                                            = 10.75 page per hour

Therefore, we conclude that the average number of pages that Sarah reads per hour will be: 10.75 page per hour

For the triangles shown, which detail would have to be given to prove them congruent by the Angle Angle Side congruence criteria?

Answers

Answer:

The measure of the angle labeled d

Step-by-step explanation:

I took the quick check for "angle angle side postulate"

Anyone know this answer?

Answers

the answer is =10

10

10

10


HELPP PLEASE ILL NAME YOU BRAINLIEST!!!

Answers

Look this up on Socratic & it’ll help you and show you step by step

Complete the statement with the appropriate symbol.

1.42 _____ 1.420

=
>

Answers

Answer:

=

Step-by-step explanation:

After the decimal point if the zeros are on the right side they do not have any value.

Answer: = because 0 has no value

Complete the statement with the appropriate symbol.

1.42 ___=__ 1.420

>

<

=

Step-by-step explanation: = because the 0 has no value.

VWXY is a parallelogram. Find the measure of XY and WY

Answers

Answer:

WY = 30

XZ = 10.5

Step-by-step explanation:

Paralellogram's diagonal's bisect eachother

Therefore,

[tex]n + 7 = 3 n[/tex]

Move the n over,

2n = 7

Divide both sides by 2,

n = 3.5

WY = 2(ZY) because definition of bisector

Simplify...

WY = 2(4n+1)

WY = 2(4(3.5)+1)

WY = 2(15)

WY = 30

You asked for XY, but the question asks for XZ, so I'm going to give XZ.

With n = 3.5 from above,

XZ = 3n

XZ = 3(3.5)

XZ = 10.5

The measure of XY and WY are; WY = 30 and XZ = 10.5

What is a parallelogram?

That quadrilateral in which opposite sides are parallel is called a parallelogram.

Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.

Since Paralellogram's diagonal's bisect each other

Therefore,

2n = 7

Divide both sides by 2;

n = 3.5

WY = 2(ZY)

because definition of bisector

Simplify;

WY = 2(4n+1)

WY = 2(4(3.5)+1)

WY = 2(15)

WY = 30

we asked for XY,

With n = 3.5 from above,

XZ = 3n

XZ = 3(3.5)

XZ = 10.5

The measure of XY and WY are; WY = 30 and XZ = 10.5

Learn more about parallelogram;

https://brainly.com/question/28854514

#SPJ2

Leicester City Fanstore (LCF) will be selling the "new season jersey" for the 2018-2019 season. The regular price of the jersey is $80. Each jersey costs $40. Leftover jerseys will be sold at the end of the season (or later) at $30. Since jerseys are produced in China and lead time is long, Puma wants LCF to decide the quantity right now (December 2017).

a. After some analysis using historic data, LCF expects that the demand will follow a Normal distribution with a mean 40,000 and a standard deviation of 8,000 due to uncertainty in team performance. How many jerseys should LCF order?
b. If a customer cannot buy the jersey from LCF (in the case of a stock-out), they may leave the store disappointed and use other channels (such as Puma stores or puma.com) in future. LCF thinks that the lost customer goodwill is around $10. Should LCF change their decision in part (a)? If yes, please state the number of jerseys LCF should order.
c. Please state whether the following statement is always true, and give a brief explanation. If c=c, the newsvendor solution is the mean.

Answers

Complete Question

Leicester City Fanstore (LCF) will be selling the "new season jersey" for the 2018-2019 season. The regular price of the jersey is $80. Each jersey costs $40. Leftover jerseys will be sold at the end of the season (or later) at $30. Since jerseys are produced in China and lead time is long, Puma wants LCF to decide the quantity right now (December 2017).

a. After some analysis using historic data, LCF expects that the demand will follow a Normal distribution with a mean 40,000 and a standard deviation of 8,000 due to uncertainty in team performance. How many jerseys should LCF order?

b. If a customer cannot buy the jersey from LCF (in the case of a stock-out), they may leave the store disappointed and use other channels (such as Puma stores or puma.com) in future. LCF thinks that the lost customer goodwill is around $10. Should LCF change their decision in part (a)? If yes, please state the number of jerseys LCF should order.

c. Please state whether the following statement is always true, and give a brief explanation. If [tex]C_o =C_i[/tex], the news vendor solution is the mean.

Answer:

a

   [tex]N = 46728[/tex]

b

  [tex]n = 47728[/tex]

c

  Yes it is always true  

Step-by-step explanation:

From the question we are told that

   The regular price of the jersey is  [tex]P_r = \$ 80[/tex]

    The cost of producing a jersey is [tex]C= \$ 40[/tex]

  The left-over price of the jersey is [tex]P_o = $ 30[/tex]

   The mean is  [tex]\mu = 40000[/tex]

   The standard deviation is [tex]\sigma = 8000[/tex]

   The cost of lost customer goodwill is [tex]C_g = \$ 10[/tex]

Generally the fund that LCF will loss for one jersey if they order for too many  jersey (i.e more than they need )is mathematically represented  

           [tex]C_o = P_o - C[/tex]

=>        [tex]C_o = 40 - 30[/tex]

=>        [tex]C_o = \$ 10[/tex]

Generally the fund that LCF will loss for one jersey if they order lesser amount  jersey (i.e less than they need )is mathematically represented  

           [tex]C_i = P_r - C[/tex]

=>        [tex]C_i = 80 - 40[/tex]

=>        [tex]C_i = \$ 40[/tex]

Generally the critical ratio is mathematically represented as

             [tex]Z = \frac{C_i }{ C_i + C_o}[/tex]

=>           [tex]Z = \frac{40}{ 40 + 10}[/tex]

=>           [tex]Z = 0.8[/tex]

Generally the critical value of  [tex]Z = 0.8[/tex] to the right of the normal curve is

         [tex]z = 0.841[/tex]

Generally the optimal quantity of jersey to order is mathematically represented as

             [tex]N = \mu * [z * \sigma][/tex]

=>          [tex]N = 40000 * [0.841 * 8000][/tex]

=>          [tex]N = 46728[/tex]

Considering question b

  Generally considering the factor of customer goodwill  the fund that LCF will loss for one jersey if they order lesser amount  jersey (i.e less than they need )is mathematically represented  as

           [tex]C_k = C_i + C_g[/tex]

=>        [tex]C_k = 40 + 10[/tex]

=>        [tex]C_k = \$ 50[/tex]

Now   the critical ratio is mathematically represented as

             [tex]Z = \frac{C_k }{ C_k + C_o}[/tex]

=>           [tex]Z = \frac{50}{ 50 + 10}[/tex]

=>           [tex]Z = 0.833[/tex]

Generally the critical value of  [tex]Z = 0.833[/tex] to the right of the normal curve is

         [tex]z = 0.966[/tex]

Generally the optimal quantity of jersey to order is mathematically represented as

             [tex]n = \mu * [z * \sigma][/tex]

=>          [tex]n = 40000 * [0.966 * 8000][/tex]

=>          [tex]n = 47728[/tex]

Considering question c

    When [tex]C_o =C_i[/tex] then

The critical ratio is mathematically represented as

             [tex]Z = \frac{C_k }{ C_k + C_k}[/tex]

=>           [tex]Z = \frac{1}{ 2}[/tex]

=>           [tex]Z = 0.5[/tex]          

Generally the critical value of  [tex]Z = 0.5[/tex] to the right of the normal curve is

         [tex]z = 0[/tex]

So

The optimal quantity of jersey to order is mathematically represented as

             [tex]n = \mu * [z * \sigma][/tex]

=>          [tex]n = 40000 * [0* 8000][/tex]

=>          [tex]n = 40000 = \mu[/tex]

Hence the statement in c is true        

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