arccos 2x + arccos x = TT/2
How to solve ​find x ?

Answers

Answer 1

arccos(2x) + arccos(x) = π/2

Apply cos to both sides, then expand the right side using the identity I mentioned in a comment:

cos(arccos(2x) + arccos(x)) = cos(π/2)

cos(arccos(2x)) cos(arccos(x)) - sin(arccos(2x)) sin(arccos(x)) = 0

Now think of arccos(2x) and arccos(x) as angles in two right triangles. Let θ = arccos(2x) and φ = arccos(x) (and let's also assume that both have measure between 0 and π/2). These are angles such that

cos(θ) = 2x

cos(φ) = x

In these triangles, you then have

sin(θ) = sin(arccos(2x)) = √(1 - 4x ²)

sin(φ) = sin(arccos(x)) = √(1 - x ²)

while

cos(θ) = cos(arccos(2x)) = 2x

cos(φ) = cos(arccos(x)) = x

So the original equation is transformed to

2x ² - √(1 - 4x ²) √(1 - x ²) = 0

Solve for x :

2x ² = √(1 - 4x ²) √(1 - x ²)

(2x ²)² = (√(1 - 4x ²) √(1 - x ²))²

4x ⁴ = (1 - 4x ²) (1 - x ²)

4x ⁴ = 1 - 5x ² + 4x

0 = 1 - 5x ²

x ² = 1/5

x = ± 1/√5

Now bearing in mind that we assume 0 < φ < π/2, we should have cos(φ) = x > 0, so we take the positive solution,

x = 1/√5


Related Questions

What is the value of the expression below when w=2 and x=2
9w - x

Answers

Here, all we need to do is subtitute w = 2 and x = 2 into the expression, by multiplying and adding. First, we will muliply 9w:

9w

9 · w =

9 · 2 =

18

Now, all we have to do is use our answer for 9w, and subtract x from it:

9w - x

18 - (2) =

18 - 2 =

16

So, our answer is 16.

Let me know if you have any other questions! :)

This two-way frequency table shows the results of a survey of users of the mass-transit system in a city. People were asked their age and whether they used the system regularly (three or more times per week).

Answers

Answer:

if Q={1,3,5,7,9}Express it in description methods

Answer: With the condition that age is 30 or under, the sample space is restricted to the first column. This simplifies the problem to:

P(uses mass transit |age is 30 or under) = 125/575=0.217

Step-by-step explanation:

edmentum

Find the approximate side length of a square game board with an area of 128 in2. HELP PLZ

Answers

Answer:

The side length is approximately 11.3 inches

Step-by-step explanation:

The area of a square is given by

A = s^2 where s is the side length

128 = s^2

Take the square root of each side

sqrt(128) = sqrt(s^2)

11.3137085= s

The side length is approximately 11.3 inches

Answer:

11.3

Step-by-step explanation:

Formula for square: x^2 = A

Plug in:

x^2 = 128

√x^2 = √128

  x = 11.3

Hope this helped.

PLS HELP ME ON THIS QUESTION!!!

Answers

Answer:

210 in³

Step-by-step explanation:

length = 10 in

Width = 7 in

Height = 3 in

Volume of rectangular prism = length * width * height

                                               = 10 * 7 * 3

                                                = 210 in³

Answer: Option D

210 in³

Volume of Rectangular prism = lwh

Height = 3in

Width = 7in

Length = 10in

Volume = 10(7)(3)

Volume = 210 in³

Must click thanks and mark brainliest

Write the polynomial in standard form 8-5x+x^3-2x^4

Answers

Answer:

-2x^4+x^3-5x+8

Step-by-step explanation:

8-5x+x^3-2x^4

Write the polynomial from highest powers of x to lowest

-2x^4+x^3-5x+8

This equation shows how the total number of necklaces Denise owns is related to the amount of money she spends on additional necklaces.

n = d + 74

The variable d represents the amount of money she spends on additional necklaces, and the variable n represents the total number of necklaces she owns. With $16 to spend on new necklaces, how many total necklaces can Denise own?

Answers

answer: n=90

please mark brainliest

Solve for x: -5 < 8x + 11 < 19

Answers

Answer:

-2<x<1

Step-by-step explanation:

-5 < 8x + 11 < 19

Subtract 11 from all sides

-5-11 < 8x + 11-11 < 19-11

-16 < 8x<8

Divide by 8

-16/8 < 8x/8 <8/8

-2<x<1

Match all the part of the circle to their correct name.

1. YW
2. Q
3. WX
4. W
5. ST
6. VQ
7. TW

a. Center
b. Secant Line
c. Chord
d. Radius
e. Point of Tangency
f. Diameter
g. Tangent Line

Answers

Answer:

halo

1. YW - chord

2. Q - center

3. WX - tangent line

4. W - point of tangency

5. ST - secant line

6. VQ - radius

7. TW - diameter

please mark brainliest???

The correct matches are,

1. YW - chord

2. Q - center

3. WX - tangent line

4. W - point of tangency

5. ST - secant line

6. VQ - radius

7. TW - diameter

What is diameter?

In geometry, a diameter of a circle exists as any straight line segment that passes via the center of the circle and whose endpoints lie on the circle. It can also be described as the longest chord of the circle. Both descriptions exist also valid for the diameter of a sphere.

The correct matches are,

1. YW - chord

2. Q - center

3. WX - tangent line

4. W - point of tangency

5. ST - secant line

6. VQ - radius

7. TW - diameter

To learn more about diameter refer to:

https://brainly.com/question/23220731

#SPJ2

Question 2 Evaluate the expression 2(x - 3) + 3y when x = 5 and y = 3. Mark the correct answer.
A. 13
B. 15
C. 16
D. 25​

Answers

Answer:

A. 13

Step-by-step explanation:

2(x - 3) + 3y

2(5 - 3) + 3×3

2× 2 + 3×3

4 + 9

13

Answer:

The correct answer is A

Step-by-step explanation:

2(x-3) + 3y so you replace them and get 2( 5 - 3) +3(3)

next,

you would solve it

2 x 5 and 2 x 3 you get 10-6 + 9, the 9 is from multiplying 3 by 3

finally you solve it

10-6 = 4 +9

= 13!

I need help make sure to round it to the nearest 10th

Answers

Answer:

10.52

Step-by-step explanation

Answer: x= 10.5

Step by step explanation: in order to find the missing side you need to use sin=opposite/hypotenuse, which gets you sin26*=x/24, multiply both sides by 24 which will get you 24(sin26*)=x once rounded to the nearest tenth will give you the result of 10.5

find the ratio in lowest term b 750m and 1km​

Answers

Hope it helps !!!!!!!

Answer:

4m/3m

Step-by-step explanation:

1km = 1000m

750m : 1km

750m : 1000m

Reduce ratio in simplest form.

HCF of 1000 and 750 is 250

750  ÷ 250 / 1000  ÷ 250

= 4/3

Hence, the simplest form of the ratio 750m : 1km is 4m/3m

what is the electrical work done in a circuit​

Answers

the electrons must move by some distance through a wire or conductor, the work done is stored in the flow of electrons as energy. therefore “Work” is the name we give to the process of energy.

Answer:

a open and close switch and a condentation out put.

Mr.Swanson drove 150 miles in 4 hours how many miles will he drive in 1 hour

Answers

Answer:

37.5 miles

Step-by-step explanation:

Distance covered in 4 hours = 150 miles

Distance covered in 1 hour = 150/4 = 37.5 miles

Trong mặt phẳng tọa độ cho tam giác ABC biết các đỉnh A(-1,2), B(4,7) và trọng tâm tam giác G(3,2). Viết phương trinh đường thẳng d chứa đường cao đi qua A của tam giác ABC

Answers

can you translate so i can help you out .

find the area of the following composite figure​

Answers

Answer: 28.6 square inches

Explanation:
square: 4x4=16
Two half circles = one whole circle
Area of a circle is (pie x r^2)
R=radius; the radius is 4/2=2
Pie x 2^2=4pie
4pie=12.6
12.6 + 16= 28.6 square inches

plz help me to slove this ​

Answers

Answer:

50

Step-by-step explanation:

= 3^3 + (2 x 2 x 3) + 2^2 + ( 3 + 2)^5

= 3^3 + (12) + 2^2 + (3 + 2)^5

= 3^3 + 12 + 2^2 + (5)^5

= 9 + 12 + 2^2 + 5^5

= 9 + 12 + 4 + 5^5

= 9 + 12 + 4 + 25

= 50

The Boeing777-300ER flies between Auckland and Los Angeles. It has 246 Economy
class seats, 50 Premium Economy seats and 44 Business Premier seats. Out of the 340
seats in total, what percentage are Economy seats?

Answers

Answer:

72.35%

Step-by-step explanation:

246/340 = .723529

Just multiply it by 100 to get the percentage

.723529 x 100 = 72.3529

find x. A. 21√2 B. 7 C. 21√3 over 2 D. 21√2 over 2

Answers

Answer:

D

Step-by-step explanation:

for you to find x you first have to find the adjacent of the 45° angle you can do that by using the other triangle.using the sin ratio

sin60=opposite/hypotenuse

sin60=a/73

a=10.5

then after you have found the adjacent you can use the cos ratio

cos45=adjacent/hypotenuse

cos45=10.5/x

cos45x/cos45=10.5/cos45

x=14.849

which is the same as 212 over 2

I hope this helps

Answer:

D

Step-by-step explanation:

Using sine ratio in left right angled triangle to find the altitude a of the large triangle which is common to both right triangles and the exact value

sin60° = [tex]\frac{\sqrt{3} }{2}[/tex] , then

sin60° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{a}{7\sqrt{3} }[/tex] = [tex]\frac{\sqrt{3} }{2}[/tex] ( cross- multiply )

2a = 21 ( divide both sides by 2 )

a = [tex]\frac{21}{2}[/tex]

Using the cosine ratio in the right side triangle and the exact value

cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then

cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{a}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

x = [tex]\sqrt{2}[/tex] a = [tex]\sqrt{2}[/tex] × [tex]\frac{21}{2}[/tex] = [tex]\frac{21\sqrt{2} }{2}[/tex] → D

Factorize no g, h, j, k, m, n​

Answers

answer =

=3a²-16ab+13b²

=3a²-(13+3)ab+13b²

=3a²-13ab-3ab+13b²

=a(3a-13b)-b(3a-b)

=(3a-13b)(a-b)

Answer:

even I got confused in question no. j

no worry rest all are solved .

all the questions are solved by middle term splitting method .

Not looking for answer but does anyone know this specific topic in math

Answers

Answer:

This is called system of equations.

Step-by-step explanation:

This combines two equations and then lines them up to a system.

Answer:

Step-by-step explanation:

 

  matrix

     or

vector geometry

1/5 of a certain number is added to 5½ the same as when ⅙ of the number that is subtracted from 30⅖find the number​

Answers

Step-by-step explanation:

1%2F5n + 51%2F5 = 302%2F5 - 1%2F6n

make the 3rd term an improper fraction

1%2F5n + 51%2F5 = 152%2F5 - 1%2F6n

multiply equation by 30, cancel the denominators, resulting in:

6n + 6(51) = 6(152) - 5n

6n + 306 = 912 - 5n

6n + 5n = 912 - 306

11n = 606 is the number

n = 606/11

n = 55 1/11

Answer:

68

Step-by-step explanation:

let unknown number be x

⅕x + 5½= 30⅖ - ⅙x

⅕x + 11/2= 152/5 - ⅙x

collect like terms

⅕x+⅙x= 152/5 - 11/2

[tex] \frac{11}{30}x = \frac{249}{10} [/tex]

cross multiply

30 * 249=(11 * 10)x

7470=110x

x=7470/110

x= 68

Hello! I have an algebra 1 dba tomorrow (flvs). I am just a little nervous and want to be a little more prepared. Does anybody know what questions I will be asked? Btw this is for algebra 1 module 4. Thank you :)

Answers

Answer:

Im not sure what is in the algebra 1 module 4 but for algebra 1 you should study how to graph equations, solve system of equations with substitution and elimination. those topics, at least for e, have been a little tricky

Step-by-step explanation:

. Waipio Rd in Honokaa, Hawaii, is one of the steepest roads in the world. It rises 450 ft over a horizontal distance of 1,000 ft. a. What is the percentage grade of this hill? Round to the nearest tenth of a percent.

Answers

Answer: 50%

Step-by-step explanation:

From the question, we're given the information that Waipio Rd in Honokaa, Hawaii, is one of the steepest roads in the world and that it rises 450 ft over a horizontal distance of 1,000 ft.

Therefore, the percentage grade of this hill will be calculated as the height over the length and this will be:

= 450/1000 × 100

= 45%

= 0.45

= 0.5 to nearest tenth

= 50% to nearest tenth.

Best answer gets brainliest and 5 stars

Answers

Answer:

No, because 6² + 8² ≠ 12²

Step-by-step explanation:

In a right angled triangle,

Perpendicular² + Base² = Hypotenuse² (pythagoras theorem)

But in the given triangle; 6² + 8² ≠ 12²

36 + 64 ≠ 144

100 ≠ 144

Perpendicular² + base² ≠ hypotenuse²

Thus the given triangle is not right angled.

which is the graph of g(x) = sqrt x-16

Answers

Answer:

Step-by-step explanation:

I am not sure if you are asking for the graph of

√(x-16) that has a x intercept at (16,0)

or

√ x -16 that has a y intercept at (0, -16)

Use the parabola tool to graph the quadratic function f(x)=(x−5)2+1 . Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Answers

Answer:

Vertex (5, 1)

Example of second point (4, 2)

Step-by-step explanation:

THe equation given is in vertex form so it will be easy to find the vertex

(x-5)^2+1

Vertex is at h,k and vertex form is y = a(x−h)^2 + k

x coordinate will be 5

y coordinate will be 1

vertex - (5, 1)

You can plot a second point by plugging in any number into the x or y

For example, if you set x to be 4,

(4-5)^2+1

1^2+1

1+1=2

If g(x) = 2(x − 4), find the value of x if g(x) = 20

Answers

Answer:

x=14

Step-by-step explanation:

g(x) = 2(x − 4)

Let g(x) = 20

20 = 2(x − 4)

Divide each side by 2

20/2 = 2(x-4)/2

10 = x-4

Add 4 to each side

10+4 = x-4+4

14 =x

which inequality is represented on the number line shown?

Answers

Answer:

A

Step-by-step explanation:

b/ of shaded region can make to closed inequality & it's not closed to make open inequality.

our of 1000 new born
babies, there are 514
boys, what will be the
empirical probability
the newly born baby is
(i) a boy (ii) a girl​

Answers

Look a view at this picture

Someone help me on this, thats my illustration for it its a lil long

Answers

The uppercase letters are the angles, while the lowercase letters are the sides. We have side 'a' opposite angle A, side b opposite angle B, side c opposite angle C.

We have this given info:

A = 25a = 13.2b = 25.5

Let's use the law of sines to find angle B

sin(B)/b = sin(A)/a

sin(B)/25.5 = sin(25)/13.2

sin(B) = 25.5*sin(25)/13.2

sin(B) = 0.81642164

B = arcsin(0.81642164) or B = 180 - arcsin(0.81642164)

B = 54.72817392 or B = 180 - 54.72817392

B = 54.72817392 or B = 125.27182608

When rounded to the nearest whole degree, we get B = 55 or B = 125.

However, I'll use the slightly more accurate values of B for the next two sections.

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

Let's consider the case that B = 54.72817392

This would have to mean

A+B+C = 180

C = 180-A-B

C = 180-25-54.72817392

C = 100.27182608  which rounds to C = 100

Through the law of sines we can say

c/sin(C) = a/sin(A)

c = sin(C)*a/sin(A)

c = sin(100.2718 2608)*13.2/sin(25)

c = 30.73327084 which rounds to c = 30.7

One solution is

A = 25, B = 55, C = 100

a = 13.2, b = 25.5, c = 30.7

As you can probably guess, the phrasing "solve the triangle" means find all sides and angle measures.

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

Now we'll consider the case that B = 125.27182608

We follow the same steps as the previous section

A+B+C = 180

C = 180-A-B

C = 180-25-125.27182608

C = 29.72817392 which rounds to C = 30

and

c/sin(C) = a/sin(A)

c = sin(C)*a/sin(A)

c = sin(29.72817392)*13.2/sin(25)

c = 15.48842618 which rounds to c = 15.5

The other solution is

A = 25, B = 125, C = 30

a = 13.2, b = 25.5, c = 15.5

Check out the diagrams below.

Other Questions
QUESTION 2 Write the slope-intercept form of the equation of the line through the gran point micia the grea slope through: (5,-2), siope--1 Oay=-2=6 Oby=-2-3 O cy=-x=3 Ody=-z-6 You were asked to read U.S. Statistics in 1912 and in your writing journal, you reflected upon how different your life would be had you lived 100 years ago. The learning objective of this assignment was:__________ Conducting a postaudit ______. Multiple select question. provides an opportunity to reinforce and possibly expand successful projects flags any manager's attempts to inflate benefits or downplay costs in a project proposal determines which capital project should be selected for investment provides an opportunity to cut losses on floundering projects Johnson bought a wrist watch for $y and sold it at a loss of 15% Write an expression for the selling price.A. 0.85 yB. 0.85C. 85 yD. 1.159HELPPPPP ILL GIVE BRAINLIEST D.2 please help Ill mark brainliest What is 51809 rounded to 1,2 and 3 significant figures?PLSS HELP 40 pointsAfter being destroyed in World War II, what did Japan have that helped it recover from the devastation?a.a sound economyc.a great education systemb.tremendous wealthd.unlimited natural resourcesPlease select the best answer from the choices providedABCD According to the growth accounting studies, if you lived in a country where illiteracy was high and 40% of the children left school early and did not complete their education what would probably be the results for that country Seven and one-half foot-pounds of work is required to compress a spring 2 inches from its natural length. Find the work required to compress the spring an additional 3 inch. Find the area of the regular polygon. Round your answer to the nearest hundredth. can someone answer this? I'll mark u the brialintest! ANSWER QUICK !!Yuri is participating in a tund-raiser at school. She will receive donations from 2 people. A cousin will donate $0.40 for every 1/8 mile that Yuri walks.A friend will give Yuri a one-time donation of $30What is the minimum number of miles Yuri needs to walk to raise at least $507 Enter the answer in the box, A line contains the piont (4,5) and is perpendicular to a line with a slope of -2/3. Write an equarion of the line satisfying the given conditions. Write the answer in slope-intercept form Round 573.073 to the greatest place is noise energy a kind of energy or not An unlevered firm has a cost of capital of 12.46 percent and a tax rate of 35 percent. The firm is considering a new capital structure with 35 percent debt. The interest rate on the debt would be 6.68 percent. What would be the firm's levered cost of A small cruise ship struck a whale swimming underwater, causing the ship to suddenly lurch sideways. A passenger on the ship who was walking down a corridor lost his balance and bumped his head on the edge of a doorway. Because of a previously existing medical condition that made him susceptible to bleeding on the brain, he suffered a cerebral hemorrhage and permanent mental impairment, despite prompt medical attention on the ship. The passenger brought suit against the cruise ship owner for his damages. At trial, the passenger presented evidence of how he was injured as he walked down the hallway, his previous medical condition, and his medical expenses and other damages. The cruise ship owner presented evidence that the cruise ship was following its approved route and that the whale could not have been detected before impact, and that the bump would not have injured someone in ordinary health. At the close of the evidence, the cruise ship owner moved for a directed verdict. How should the court rule 1. How can stories reveal the fears and worries of a particular culture? Define guidance and counseling in the perspective of five authors clearly stating the differences and similarities between the two terms? Daisy (5,9,2,6,14,3)Milkweed (10,8,22,12,12,9)Coneflower (3,7,2,10,16,7)A biology class took a field trip. The students counted the number of daisy, milkweed, and coneflower plants in six different locations. The data sets are shown above. What is the overall range in the number of plants for all three types of plants?