Mathematics High School

Write the expression as an algebraic expression of x that does not involve trigonometric functions:

[tex] csc({cos}^{ - 1} x)[/tex]
​

Answers

Answer 1

Answer:

[tex]\displaystyle \csc(\cos^{-1}(x))=\frac{1}{\sqrt{1-x^2}}[/tex]

Step-by-step explanation:

Please refer to the attachment.

We have:

[tex]\csc(\cos^{-1}(x))[/tex]

First, we will let:

[tex]\cos^{-1}(x)=\theta[/tex]

Then:

[tex]x=\cos(\theta)[/tex]

So, the adjacent side of our triangle is x and the hypotenuse is 1.

Then by the Pythagorean Theorem, the opposite side is given by:

[tex]x^2+o^2=1^2[/tex]

So:

[tex]o=\sqrt{1-x^2}[/tex]

Going back, we have:

[tex]\csc(\cos^{-1}(x))[/tex]

Since arccos(x) is θ:

[tex]=\csc(\theta)[/tex]

Cosecant is the ratio of the hypotenuse over the opposite side. Therefore:

[tex]\displaystyle \csc(\theta)=\frac{1}{\sqrt{1-x^2}}[/tex]

Hence:

[tex]\displaystyle \csc(\cos^{-1}(x))=\frac{1}{\sqrt{1-x^2}}[/tex]

Write The Expression As An Algebraic Expression Of X That Does Not Involve Trigonometric Functions:[tex]

Related Questions

During a five-year period 24% of snowstorms in a certain city caused power outages. 57 of the snow storms did not cause power outages how many snow storms were in the city in the five-year period

Answers

Answer:

divide it and do multiply and add it and subtract it

The number of snow storms were in the city in the five-year period is 75.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, during a five-year period 24% of snowstorms in a certain city caused power outages.

Let the number of snow storms were in the city in the five-year period be s.

57 of the snow storms did not cause power outages.

So, the equation is

s -24% of s =57

s-0.24s=57

0.76s=57

s=57/0.76

s=75

Therefore, the number of snow storms were in the city in the five-year period is 75.

To learn more about an equation visit:

https://brainly.com/question/14686792.

#SPJ5

Daniela has 214 basketball games left to play in a tournament, and she has 34 gallon of water left to drink. If she drinks the same amount of water each game, how much water can she drink each game?

Answers

Answer:3 gallons 0f water

Step-by-step explanation:

How many solutions does the system have?
You can use the interactive graph below to find the answer.
2x+3y=-6
3x-4y=-12
A: exactly one solution
B: no solutions
C: infinitely many solutions

Answers

Answer:

1 solution

Step-by-step explanation:

when you graph it, there is only one point in the line that you can see matches up

The graph shows the distance, y in miles, of a moving train froma station for a certain period of time, x, in hours:
Distanco vs. Time
$5
30C
256
from Station 20
Distance
(in mi )
10
2 nr)
5
Time
What is the speed (in miles per hour) of the train?

Answers

Answer:

  50 miles per hour

Step-by-step explanation:

The speed can be found from a graph of distance versus time by looking at the slope of the graph. Here, the graph is a straight line, so the slope is constant. This means the speed is constant.

__

It can be convenient to determine the speed by looking at distance for times that are 1 time unit apart. Here, that could be the distances at t=0 and at t=1. We see in that hour, the train traveled from 100 miles to 150 miles away from the station. Its speed was 150 -100 = 50 miles per hour.

Answer:

50 miles per hour

Step-by-step explanation:

Hope this helps sorry if it doesn't

5•11+5•(-4)=5(11-4) wich property?​

Answers

Answer:

Step-by-step explanation:

55

F∝a If F=48 when a=4 find, F when a=5

Answers

Step-by-step explanation:

48/4 = F/5

Therefore F is 60 when a is 5.

Clancy has 423 cups of yogurt to share with his friends at a party. Each guest will receive 1 serving of yogurt which is 34 of a cup. How many people can Clancy invite to his party if he needs a serving of yogurt as well?

Answers

Answer:

564 people

Step-by-step explanation:

Total cups of yogurt to share = 423 cups

Each guests get = 3/4 of a cup per serving

How many people can Clancy invite to his party if he needs a serving of yogurt as well?

Number of people Clancy can invite to his party = Total cups of yogurt to share / servings per guests

= 423 cups ÷ 3/4 cups

= 423 × 4/3

= 141 × 4

= 564

Number of people Clancy can invite to his party = 564 people

NUMBER 14 PLEASE
i need this soon

Answers

Answer:

a=22.478

Step-by-step explanation:

Answer:

Angle DE = 11

Step-by-step explanation:

DE = DF

8x + 3 = 6x + 5

8x = 6x + 5 - 3

8x - 6x = 2

2x = 2

2x/2 = 2/2

x = 1

DE = 8x + 3

DE = 8(1) + 3

DE = 8 + 3

DE = 11

Hope this helps

Luke has 9/10 yard of colored ribbon. He plans to cut the ribbon into pieces. Each piece will be 1/6 yard long. How many whole pieces can luke make from the ribbon?

Answers

Answer:

He can make 5 ribbons and 2/5 yards is left over.

Step-by-step explanation:

It is given that,

Length of the colored ribbon = 9/10 yards

Luke plans to cut the ribbon into pieces.

Each piece will be 1/6 yard long.

We need to find the number of pieces that Luke can made from the ribbon. Let he can make x pieces.

[tex]x=\dfrac{\dfrac{9}{10}}{\dfrac{1}{6}}\\\\=\dfrac{9}{10}\times 6\\\\=5.4\\\\=5\dfrac{2}{5}[/tex]

It means he can make 5 ribbons and 2/5 yards is left over.

Val measures the perimeter of her rectangular garden as 80 ft. Use the perimeter of the garden and the appropriate formula. Solve the formula for the width of the garden. Use the equation to help explain how the width changes in relation to changes in the length. A. w = 40 − l; the width increases as the length decreases B. w = l − 40; the width increases as the length increases C. w = 40 − l; the width increases as the length increases D. w = l − 40; the width increases as the length decreases

Answers

Answer:

D. w = l − 40; the width increases as the length decreases

Step-by-step explanation:

The formula for the perimeter of a rectangle =

P = 2l + 2w

Where to find the Width, we make w the subject of the formula.

Hence:

P - 2l = 2w

w = P - 2l/2

From the question, P = 80

Hence,

w = 80 - 2l/2

w = 80/2 - 2l/2

w = 40 - l

The width of a rectangle is always the longer side ,hence:

D. w = l − 40; the width increases as the length decreases

PLEASE HELP 20 points!!!6) Find the inverse function. Use f-1(x) to indicate the inverse function and 5 points
parenthesis for the numerator, if needed. Example: f-1(x)=(x+7)/5 *
f(x) = 4x - 2
Your answer

Answers

Answer:

Step-by-step explanation:

ANSWER: 16x+=92

HELP ASAP PLEASE & THANK U!!!!

Answers

Answer:

1. (1, -3.5)

2. (-9, 25) *note, there is a typo in the question, please ask your teacher about this

Step-by-step explanation:

Use the midpoint formula to calculate the midpoint.

Use the formula to find the end point, and double the distance between your endpoint and midpoint to find the other endpoint.

Since the distance between the x coordinate is 8 (from -1 to 7), then the other endpoint is 8 away from -1, or -9.  

please give thanks :)

What’s 2/3 divided by 5

Answers

Answer:

10/3

3.3reaping

3 1/3

Step-by-step explanation:

Which expression has the same value as 37.4 - 54.9?

Answers

Answer:

D

Step-by-step explanation:

In the original expression =  37.4 - 54.9 = -17.5

So, we have to solve all the equations but 1 of them has to equal to -17.5

A) -54.9 + (-37.4) = -92.3

   Remove parentheses

   = -54.9 - 37.4

Subtract the numbers

    -92.3

B) 54.9 - 37.4 = 17.5

Since 54.9 is greater than 37.4 just subtract normally

 4   14

  5  4.   9                < ------- Line up the decimal points like this

-  3  7.   4                <---------  Subtract the decimals

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

   1   7   .    5       <---------- This is the final answer to B.                    

 

C)  37.4 - (- 54.9) = 92.3

   Change the sign to addition

        =37.4 + 54.9

  Add the numbers normally

  54.9

+ 37. 4

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

  92.3

D)  37.4 + (-54.9) = -17.5

   Change the sign to subtraction

      =    37.4 - 54.9

Subtract them normally (but as you can see you are subtracting a smaller number from a larger number so heres a trick that you can use switch the equation by putting the larger number in first like this....)

54.9 - 37.4 = 17.5 (REMEMBER the answer is not 17.5 because the original equation of D is reversed  37.4 - 54.9 so in this case your answer should be

- 17.5)

37.4 - 54.9 = -17.5

Your final answer is D because it matches 37.4 - 54.9.

Hope this helps!

Answer: -54.9+(-37.4)

Step-by-step explanation:

Your final answer is D because it matches 37.4 - 54.9.

heights of adults women have a mean of 63.6 in and a standard deviation of 2.5 indies chebyshevs theorem say about the percentage of women with heights between 58.6 and 68.6in

Answers

Answer:

Chebyshev's Theorem (Tchebysheff's Theorem) suggests that this percentage would be greater than [tex]75\%[/tex].

Step-by-step explanation:

Let [tex]Y[/tex] be a random variable with a mean of [tex]\mu[/tex] and a (finite) variance of [tex]\sigma[/tex]. By Chebyshev's Theorem, for any constant [tex]k[/tex] where [tex]k > 0[/tex]:

[tex]\displaystyle P\left(\left|Y -\mu\right| \le k\, \sigma\right) \ge 1 - \frac{1}{k^2}[/tex].

In this question, let [tex]Y[/tex] denote height (in inches.) Accordingly, [tex]\mu = 63.6[/tex] whereas [tex]\sigma = 2.5[/tex].

Note, that the interval of interest [tex](58.6,\, 68.6)[/tex] is centered at [tex]\mu = 63.6[/tex]. Besides, the difference between [tex]\mu[/tex] and either endpoints of this interval is equal to [tex]5.0[/tex], which is the same as [tex]2\, \sigma[/tex].

Rewrite the interval [tex](58.6,\, 68.6)[/tex] as [tex](63.6 - 2\times 2.5,\, 63.6 + 2 \times 2.5)[/tex].

For the height [tex]Y[/tex] of one such individual, [tex]Y \in (58.6,\, 68.6)[/tex] is equivalent to [tex]\left|Y - 63.6\right| < 2 \times 2.5[/tex]. With [tex]\mu = 63.6[/tex] whereas [tex]\sigma = 2.5[/tex], that expression is equivalent to [tex]\left|Y - \mu \right| < 2\, \sigma[/tex].

The percentage of individuals with a height in the interval [tex](58.6,\, 68.6)[/tex] would be equal to the probability [tex]P(\left|Y - \mu \right| < 2\, \sigma)[/tex].

Compare this expression to Chebyshev's Theorem. Notice that [tex]k = 2[/tex]. Therefore:

[tex]\displaystyle P\left(\left|Y -\mu\right| \le 2\, \sigma\right) \ge 1 - \frac{1}{2^2} = 0.75[/tex].

In other words, at least [tex]75\%[/tex] of the heights would be between [tex]58.6[/tex] inches and [tex]68.6[/tex] inches.

What are exercises to strengthen the upper body?

Answers

Answer:

Banded Lat Stretch. The range of motion in the shoulders is directly connected to how well the muscles of the upper back allow them to move.

Banded Pull Aparts.

Banded Pass Through.

Pull Ups

Push Ups

Step-by-step explanation:

Some exercises to strengthen the upper body include:

1. Chest Press.

2. Bench Dip.

3. Bicep Curl.

4. Pull Ups.

5. Push Ups.

6. Arm Raise

**DUE SOON PLEASE PLEASE HELP!!!**

A 20-ounce box is filled with cans. Each can weighs 16 ounces. The total weight of the box with
cans is 212 ounces. Which equation can be used to find c, the number of cans in the box?
A. 16C + 20 = 212
C. 16(c + 16) = 212
B. 20c + 16 = 212
D. 20(c + 16) = 212

Answers

Letter d is the correct answer

PLEASE HELP! I HAVE A TIME LIMIT AND IM BEHIND
When a transversal intersects a
pair of parallel lines it will create
two pairs of alternate exterior
angles.
Ricky claims the angles within
each pair are congruent to each
other, but not congruent to
either angle in the other pair.

Answers

Answer:

Part A none

Part B drawn

Step-by-step explanation:

Suppose the transversal intersects a pair of parallel lines it creates two pairs of alternate exterior angles.

Now if we look at the first figure we find that the alternate exterior angle 1 and 4 are equal . Also 3 and 2 are equal.

But <1 and < 2 are not equal . They are supplementary angles. Their sum is equal to 180 degrees.

Similarly angles 3 and4 are supplementary angles.

This situation does not support Ricky's claim. So you will select none in part A.

Now in part B we see that angle 5 &8 are equal and 6 & 7 are congruent.

This refutes Ricky's claims and this can be proved mathematically.

Angles 5 & 6 are supplementary angles. Similarly 7 & 8 are supplementary therefore they cannot be equal as they are unequal and a transversal is drawn not a perpendicular.

The part A none and for part B drawn.

Suppose the transversal intersects a pair of parallel lines it creates two pairs of alternate exterior angles.

Now if we look at the first figure we find that the alternate exterior angle 1 and 4 are equal . Also 3 and 2 are equal.

What is the meaning of the supplementary angle?

Two angles are called supplementary when their measures add up to 180 degrees.

But <1 and < 2 are not equal because they are supplementary angles. and the sum is equal to 180 degrees.

Similarly angles 3 and 4 are supplementary angles.

This situation is not support Ricky's claim so select none in part A.

Now for  part B we see that angle 5 &8 are equal and 6 & 7 are congruent.

This refutes Ricky's claims and this can be proved mathematically.

Angles 5 & 6 are supplementary angles. Similarly 7 & 8 are supplementary

Therefore they cannot be equal as they are unequal and a transversal is drawn not a perpendicular.

Therefore for the part A none and for part B drawn.

To learn more about the transversal visit:

https://brainly.com/question/24607467

Which of these units would be best to measure the length of our classroom?

1. meters
2. centimeters
3. liters
4. kilometers
5. millimeters

Answers

Answer:

1. meters

Step-by-step explanation:

The smallest unit given in the choice is millimeters. Then comes the centimeters, then meters,  and the kilometers.

Liters is used to measure the volume of a liquid. For example we get 1 liters of milk but not 1 kilometers of milk.

The kilometers has a 1000 meters and

1m= 100 cm

1cm = 10mm

The kilometers is quite a large space and usually long distances such as length between 2 towns is measured in kilometers.

The area of the room or length is usually measured in feet but since feet is not given here.

1 feet = 0.3048 m

so the most suitable selection would be meters.

The millimeters is very small. 1 cm has 10 mm. A foot consists of 30.48 cm.

So meters is used.

Josh kept 75% of the ride tickets he bought at a carnival and gave the rest to his friend Sam. Sam gave 50% of these tickets to Rob. If Rob was given 3 tickets, how many tickets did Josh buy?​

Answers

Josh bought 24 tickets and kept 75% or 18 tickets; he gave the rest to Sam which is 6 and Sam gave rob 3 tickets

PLEASEEEE HELPPP !!!!!!!! Will mark Brianliest !!!!!!!!!!!!!

Answers

Answer:

If HF = 6 units, then BF = 12 units.

Step-by-step explanation:

In ΔBCD, H is the centroid.

Given

HF = 6

We know that the centroid is the point of intersection of the medians of a triangle.

Centroid divides a median in a 2:1 ratio.

In other words, the location of the centroid lies at 2/3 of the distance from the vertex along the segment BF that connects the vertex to the midpoint of the opposite side.

so

HF = 1/2 BF

substituting HF = 6

6 = 1/2BF

BF = 12 units

Therefore, if HF = 6 units, then BF = 12 units.

Answer:

HF = 6 units and BF = 12 units

Step-by-step explanation:

Hope this helps!

Consider a geometric sequence who third term is 9 and whose sixth term is -8/3. What is the first term? QUICKLY PLEASE!

Answers

Answer:

81/4

Step-by-step explanation:

Given

Geometric sequence with:

a₃ = 9a₆ = -8/3To findThe first term a₁Solution

Formula for nth term is:

aₙ = a₁rⁿ⁻¹

For the given terms we have:

a₃ = a₁r² anda₆ = a₁r⁵

Comparing the terms:

a₆/a₃ = r³

Substituting values to find the value of r:

-8/3 : 9 = -8/27 = (-2/3)³ r³ = (-2/3)³r = -2/3

Then finding a₁:

a₁(-2/3)² = 9a₁(4/9) = 9a₁ = 81/4

Please answer am really failing my math and i need this answer asap​

Answers

Answer:

[tex]9) \: y = - 1x - 6[/tex]

[tex]10) \: y = \frac{1}{6}x + 4[/tex]

Which value of w is the solution to the question? 2w-5=w+10

Answers

Answer:

w = 15

Step-by-step explanation:

2w - w = 10+5

w = 15

simple!

|9+x|>19 absolute value

Answers

Answer:

           x ∈ (-∞ , -19) ∪ (10 , ∞)

Step-by-step explanation:

|9 + x| > 19

9 + x > 19       ∨       9 + x < -19

   x  > 10        ∨          x < -19

         x ∈ (-∞ , -19) ∪ (10 , ∞)

solve for x please!!​

Answers

Answer:

x would be = to 13

Step-by-step explanation:

(IM GIVING 15 POINTS )A water cooler holds 15 liters of sports drink. Approximately how many gallons is this? (1 gallon = 3.785 liters)

3 gallons
4 gallons
11 gallons
18 gallons

Answers

Answer:

4 gallons

Step-by-step explanation:

divide 15 by 3.785

Answer:

4 gallons

Step-by-step explanation:

15 divided by 3.785 liters)

Select all expressions that are equivalent to 6x+1−1(3x−1) . a. 6x+1−3x−1a. 6 x plus 1 minus 3 x minus 1 b. 6x+(−3x)+1+1b. 6 x plus open paren negative 3 x close paren plus 1 plus 1 c. 3x+2c. 3 x plus 2 d. 6x−3x+1−1d. 6 x minus 3 x plus 1 minus 1 e. 6x+1+(−3x)−(−1)

Answers

Answer:

c. 3x + 2( 3 x plus 2 )

d. 6x − 3x+ 1 −1(6 x minus 3 x plus 1 minus 1)

Step-by-step explanation:

We are given the expression:

6x+1−1(3x−1) .

Solving this expression:

6x + 1 - 3x +1

Collect like terms

6x - 3x +1 +1

3x + 2

Hence, the expression that are equivalent to 3x + 2 are:

c. 3x+2( 3 x plus 2 )

d. 6x−3x+1−1(6 x minus 3 x plus 1 minus 1)

Selec*t the shape bel*ow that has exactl*y two lines of symmetry as well as 180 rotation symmetry.
-None of these
-Parallelogram
-Rectangle
-Square
-Regular Hexagon

Answers

2 and 3 are the correct ones

find the hcf of the following numbers
22,18​

Answers

Answer:

the required hcf is 2

okay

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