if cosA=3√2/5,then show that cos2A=11/25

Answers

Answer 1

Answer:

Step-by-step explanation:

Cos 2A = 2Cos² A - 1

             [tex]= 2*(\frac{3\sqrt{2}}{5})^{2}-1\\\\=2*(\frac{3^{2}*(\sqrt{2})^{2}}{5^{2}})-1\\\\=2*\frac{9*2}{25} - 1\\\\=\frac{36}{25}-1\\\\=\frac{36}{25}-\frac{25}{25}\\\\=\frac{11}{25}[/tex]


Related Questions

(f⋅g) (x) = f(x) ⋅ g(x)
true
false**

Answers

Answer:

true

Step-by-step explanation:

(f×g)×x = f(x)×g(x)

What is the true solution to the equation below?

l n e Superscript l n x Baseline + l n e Superscript l n x squared Baseline = 2 l n 8
x = 2

Answers

Given:

The equation is:

[tex]\ln e^{\ln x}+\ln e^{\ln x^2}=2\ln 8[/tex]

To find:

The solution for the given equation.

Solution:

We have,

[tex]\ln e^{\ln x}+\ln e^{\ln x^2}=2\ln 8[/tex]

It can be written as:

[tex]\ln x+\ln x^2=2\ln 8[/tex]              [tex][\because \ln e^x=x][/tex]

[tex]\ln (x\cdot x^2)=2\ln 8[/tex]              [tex][\because \ln a+\ln b=\ln (ab)][/tex]

[tex]\ln (x^3)=\ln 8^2[/tex]         [tex][\because \ln x^n=n\ln x ][/tex]

On comparing both sides, we get

[tex]x^3=8^2[/tex]

[tex]x^3=64[/tex]

Taking cube root, we get

[tex]x=\sqrt[3]{64}[/tex]

[tex]x=4[/tex]

Therefore, the required solution is [tex]x=4[/tex].

Answer:

x=4

Step-by-step explanation:

What is the true solution to the equation below?

ln e Superscript ln x Baseline + ln e Superscript ln x squared Baseline = 2 ln 8

x = 2

x = 4

x = 8

one number is seven less than the second number. five times the first is 9 more than 6 times the second. find the numbers

Answers

Step-by-step explanation:

2nd number = x

1st number = x - 7

5 (x - 7) = 6x + 9

5x - 35 = 6x + 9

- x = 44

x = - 44

1st number = -51

2nd number = -44

Proof: 5 (-51) = 6(-44) + 9

-255 = -264 + 9

-255 = -255

hope it helps.

Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.

Mr. Clinton went to the lumber company. He bought 6 boards at a cost of $4.12 per board and 5 pounds of nails at $0.78 per pound. What was the total cost for these items (not including tax)?

Answers

Answer:

djjdjdjdjdjdjdjdjdidi

$28.62 not including tax.

emir is standing in a treehouse in looking down at a swing set in the yard next-door. The angle of depression from emir’s Highline to the swingset is 31.43°, and emir is 11 feet from the ground. How many feet is the base of the tree from the swing set

Answers

Answer:

18 feet

Step-by-step explanation:

The question is  illustrated using the attached image.

From the image, we have:

[tex]\theta = 31.43^o[/tex] --- angle of depression

[tex]h = 11ft[/tex] --- Emir's height

Required

The distance from the base of the tree (x)

From the attached triangle, we have:

[tex]\tan(90 - \theta) = \frac{Opposite}{Adjacent}[/tex]

This gives:

[tex]\tan(90 - 31.43) = \frac{x}{11}[/tex]

[tex]\tan(58.57) = \frac{x}{11}[/tex]

Make x the subject

[tex]x = 11 * \tan(58.57)[/tex]

[tex]x = 18.00[/tex]

Answer:

18

Step-by-step explanation:

took the test

how do we get 24 using 3,3,7 and7​

Answers

Answer:

2 Answers. #1. +11. [3+(3/7)] times 7 is 24. DarkBlaze347 May 1, 2015. +5. Good job, DB! civonamzuk May 1, 2015.

35 Online Users.

Step-by-step explanation:

brainliest please and follow:D

3+(3*7)
3*7=21
21+3=24

For P = {5, 12, 13, 14), Q = {2, 7, 11), and R = {4, 7, 8, 11}, find PU (Q n R).

Answers

Answer:

(5 7 11 12 13 14)

Step-by-step explanation:

Q inter R = 7 and 11

So the union between p and 7 and 11 is the answer above

the shorter side of a rectangle is 60% of the longer side and the perimeter of the rectangle is 96 inches. find the side lengths

Answers

Answer:

Length of the rectangle:

[tex]x = \frac{4800}{106} = \frac{2400}{53} [/tex]

Breadth of the rectangle:

[tex]60\%(x) = \frac{60}{100} \times \frac{4800}{106} \: \: \: \: \: \: \: \: \: \: \: \\ =60 \times \frac{48}{106} \\ = \frac{2880}{106} [/tex]

Step-by-step explanation:

Longer side of the rectangle(length) = x

Shorter side of the rectangle(breadth) = (60%)x

Perimeter of the rectangle = 2(l+b) = 96 inches

Hence,

[tex]96 = 2(x + 60\%(x))[/tex]

[tex]96 = 2(x + \frac{6}{100 } x)[/tex]

[tex]96 = 2( \frac{100}{1 00} x + \frac{6}{100} x)[/tex]

[tex]96 = 2( \frac{106}{100} x)[/tex]

[tex]96 = \frac{106}{50} x[/tex]

[tex]96 \div \frac{106}{50} = x[/tex]

[tex]96 \times \frac{50}{106} = x[/tex]

[tex] \frac{4800}{106} = x[/tex]

Round your answer to the nearest hundredth.
3
А
с
?
8
B
HELP!!!

Answers

Answer:

Step-by-step explanation:

This appears to be an SSA application of solving the triangle

We have 2 sides, so we will use the law of cosines

The law of cosines defines for a triangle ABC with side a/b/c with corresponding angles A/B/C

a^2 = b^2+c^2 - 2*b*c * (cos A)

this applies to the other 2 sides

first using the pythagorean theorem we find that BC = sqrt(55)

then we substitute all 3 sides into our equation to find angle A

55 = 64 + 9 - 2*8*3* (cos A)

18 = 2*8*3(cos A)

3/8 = (cos A)

and angle A is approximately 68 degrees

Please check if I'm correct

Answer:

67.98°

Step-by-step explanation:

Given 2 sides, you can find the missing angle of a right triangle using basic trig functions.

Since Cos∅=adjacent/ hypotenuse, we can use the adjacent side to the angle, 3 and they hypotenuse, 8 in the ratio by doing 3/8. This is 0.375. Then we use the inverse cosine function to find the angle. This gives 67.98°

Or

Cos∅=0.375

Cos^-1= 67.98

Which answers describe the shape below? Check all that apply.
A. Rectangle
B. Rhombus
C. Quadrilateral
D. Square
E. Parallelogram
F. Trapezoid

Answers

Answer:

E and C

Step-by-step explanation:

HELP ASAP! I don’t know how to solve this problem nor where to start. Can someone please help me out here?

Answers

Answer:   344

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

Explanation:

It might help to draw out the picture as shown below. The pool itself (just the water only) is the inner rectangle. The outer rectangle is the pool plus the border of those 1 by 1 tiles.

The pool is a rectangle 90 feet by 80 feet. If we add on the tiles, then we get a larger rectangle that is 90+2 = 92 feet by 80+2 = 82 feet.

We add on 2 since we're adding two copies of "1" on either side of each dimension.

The larger rectangle's area is 92*82 = 7544 square feet

The smaller rectangle's area is 90*80 = 7200 square feet

The difference in areas is 7544-7200 = 344 square feet.

Each 1 by 1 tile is of area 1*1 = 1 sq foot, meaning that 344 tiles will get us the 344 square foot border around the pool.

Helppp and explain!!!!!!!!!!!!!

Answers

Answer:

6x -15

Step-by-step explanation:

plug in gx for x in fx. So you have 2(3x-9) + 3

Question:

which is a y-intercept of the graphed function?

Answers:

A. (-9,0)
B. (-3,0)
C. (0,-9)
D. (0,-3)

Answers

Answer:

(0, -9)

Step-by-step explanation:

The y intercept is the y value when x =0

(0, -9)

Assume the population is bell-shaped. Between what two values will approximately 95% of the population be

Answers

Answer:The 95% Rule states that approximately 95% of observations fall within two ... about 95% will be within two standard deviations of the mean, and about 99.7% will be ... Suppose the pulse rates of 200 college men are bell-shaped with a mean of 72 ... 1.2 - Samples & Populations ... 3.5 - Relations between Multiple Variables.

Step-by-step explanation:

Suppose 49% of American singers are Grammy award winners. If a random sample of size 502 is selected, what is the probability that the proportion of Grammy award winners will differ from the singers proportion by greater than 4%

Answers

Answer:

0.0726 = 7.26% probability that the proportion of Grammy award winners will differ from the singers proportion by greater than 4%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Suppose 49% of American singers are Grammy award winners.

This means that [tex]p = 0.49[/tex]

Sample of size 502

This means that [tex]n = 502[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.49[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.49*0.51}{502}} = 0.0223[/tex]

What is the probability that the proportion of Grammy award winners will differ from the singers proportion by greater than 4%?

Proportion below 49% - 4% = 45% or above 49% + 4% = 53%. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Probability the proportion is below 45%

p-value of Z when X = 0.45. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.45 - 0.49}{0.0223}[/tex]

[tex]Z = -1.79[/tex]

[tex]Z = -1.79[/tex] has a p-value of 0.0363.

2*0.0363 = 0.0726

0.0726 = 7.26% probability that the proportion of Grammy award winners will differ from the singers proportion by greater than 4%

Please answer of question num 20 and 21 only please

Answers

Answer:

Iam going to do question 21

Step-by-step explanation:

1/7*x=2

1/7x=2

x=2:1/7

x=2*7/1

x=14

Help please!!!!!!!!!!!

Answers

Answer:

y = 14

Step-by-step explanation:

[tex] \frac{15}{21} = \frac{5}{7} [/tex]

[tex] \frac{10}{x} = \frac{5}{7} [/tex]

[tex]x = 14[/tex]

Now,

10/15 = y/21

15y = 10*21

y = 210/15

y = 14

This is a Right answer...

I hope you understand..

Mark me as brainliest...

calculate limits x>-infinity
-2x^5-3x+1

Answers

Given:

The limit problem is:

[tex]\lim_{x\to -\infty}(-2x^5-3x+1)[/tex]

To find:

The value of the given limit problem.

Solution:

We have,

[tex]\lim_{x\to -\infty}(-2x^5-3x+1)[/tex]

In the function [tex]-2x^5-3x+1[/tex], the degree of the polynomial is 5, which is an odd number and the leading coefficient is -2, which is a negative number.

So, the function approaches to positive infinity as x approaches to negative infinity.

[tex]\lim_{x\to -\infty}(-2x^5-3x+1)=\infty[/tex]

Therefore, [tex]\lim_{x\to -\infty}(-2x^5-3x+1)=\infty[/tex].

why was it difficult for the woman to cross the road​

Answers

Beacause it’s too dangerous for him so many cars,truck,motorcycle on the road, if the road have pedestrians it easy for her to cross the road

How would I solve the 4 questions on the picture?

Answers

Answer:

l don't know

Step-by-step explanation:

Suppose the sales (1000s of $) of a fast food restaurant are a linear function of the number of competing outlets within a 5 mile radius and the population (1000s of people) within a 1 mile radius. The regression equation quantifying this relation is (sales)

Answers

Answer:

[tex]Sales = 86.749[/tex]

Step-by-step explanation:

Given

[tex]Sales = 0.845*(competitors) + 5.79*(population) + 13.889[/tex]

[tex]Competitors = 4[/tex]

[tex]Population = 12000[/tex]

See comment for complete question

Required

The sales

We have:

[tex]Sales = 0.845*(competitors) + 5.79*(population) + 13.889[/tex]

Substitute values for competitors and population

[tex]Sales = 0.845*4 + 5.79*12 + 13.889[/tex]

[tex]Sales = 3.38 + 69.48 + 13.889[/tex]

[tex]Sales = 86.749[/tex]

Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible are possible

Answers

Answer:

10

Step-by-step explanation:

5C2 =5!

       2! (3)!

=1 x 2 x 3 x 4 x 5

(1 x 2) (1 x 2 x 3)

=4 x 5

   2

=20

  2

5C2 = 10

Why is underfind the square root of a negative number?​

Answers

Answer:

The square root of a negative number is undefined, because anything times itself will give a positive (or zero) result. Note: Zero has only one square root (itself). Zero is considered neither positive nor negative

Answer:

sjshzhshshdhdgdgdhdhdgshshshshshwywhwhw

How would I simplify the expressions on the picture?

Answers

Answer:

7. [tex]x^{11}[/tex]   8. [tex]y^{2}\\[/tex]  9. [tex]p^{12}[/tex]  10.[tex]a^{3} b^{2}[/tex]  11.[tex]g^{16}[/tex]  12.[tex]r^{9} h^{3}[/tex]  13.[tex]m^{15} p^{6}[/tex]  14.[tex]k^{6} y[/tex]  15.[tex]x^6 z^4[/tex]

Step-by-step explanation:

7. [tex]x^3[/tex] × [tex]x^8[/tex] = [tex]x^{11}[/tex] when multiplying with exponents you add

8. [tex]\frac{y^{6} }{y^{4} }[/tex] = [tex]y^{2}[/tex] when dividing with exponents you subtract

9. [tex](p^{3})^4[/tex] = [tex]p^{12}\\[/tex] when it's power to power, you multiply

10. [tex]\frac{a^{9} b^{4}}{a^{6} b^{2}}[/tex] = [tex]a^{3} b^{2}[/tex]  (subtract exponents)

11. [tex](g^{8})^2[/tex] = [tex]g^{16}[/tex]  (multiply exponents)

12. [tex]r^{4} h^{2} r^{5} h[/tex] = [tex]r^{9} h^{3}[/tex]  (add exponents [tex]r^4 + r^5\\[/tex] and [tex]h^2 +h^1\\[/tex] )

13. [tex](m^{5} p^{2})^3[/tex] = [tex]m^{15} p^{6}[/tex] (multiply exponents)

14. [tex]\frac{k^{7} y^{4}}{y^{3}k}[/tex] =  [tex]k^{6} y[/tex] (subtract exponents [tex]k^7-k^1[/tex] and [tex]y^4-y^3\\[/tex] )

15. [tex]x^3 z^2 x^3 z^2[/tex] = [tex]x^6 z^4[/tex] (add exponents same as #12)

What is the inverse of function f? f(x)=3-x/7

Answers

Answer:

[tex] {f}^{ - 1} (x) = \frac{x}{3} + \frac{7}{3} [/tex]

hence option d is the correct option.

Answer:

Option C is answer.

Step-by-step explanation:

Hey there!

Given;

f(x) = (3-x) /7

Let f(x) be "y".

y = (3-x) /7

Interchanging "x" and "y".

x = (3-y)/7

7x = 3-y

y = 3-7x

Therefore, f'(x) = 3-7x.

Hope it helps!

The circle P has a center at (0, 0) and a point on the circle at (0, 4). If it is dilated by a factor of 4, what is the distance of the diameter for circle P’.
A. 32

B. 4

C. 8

D. 16

Answers

Answer:

A. 32

Step-by-step explanation:

If the center is (0, 0) and a point is (0, 4) then the distance from the center to that point is 4 units. That distance is the radius. If you are dilating by a factor of 4, multiply the radius by 4 and you get 16. The new radius is 16 and the diameter= radius*2.

16*2=32

June, Gavyn and Alex share some sweets in the ratio 5:5:3. June gets 22 more sweets than Alex. How many sweets are there altogether?

Answers

Answer:

Let June's sweets be 5x.

Then Gavyn's sweets will be 5x.

And Alex's sweets will be 3x.

5x = 3x + 22

2x = 22

x = 11

So June has 5 x 11 = 55 sweets

Gavyn has 5 x 11 = 55 sweets

And Alex have 3 x 11 = 33 sweets

Total

= 55 + 55 + 33

= 143 sweets

What is the general form of the equation for the given circle centered at [0, 0)?

Answers

Answer:

x^2+y^2=r^2 is quation of circle whose centre is (0,0)

The owner of a busy coffee shop wanted to see if it was worth keeping tea on the menu. She logged the number of cups of tea she sold each day for seven days.
6 12 5 7 7 3 9
Calculate the mean, median, range, and midrange of the number of cups of tea sold for the week.

Answers

Answer:

mean = 7

median = 7

range = 9

mid range = 7.5

Step-by-step explanation:

3, 5, 6, 7, 7, 9, 12

Range is the difference between the highest and lowest values of a set of observations

Range = highest value - lowest value

12 - 3 = 9  

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order

3, 5, 6, 7, 7, 9, 12

median = 7

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

(6 + 12 + 5 + 7+  7 + 3 + 9) / 7 = 7

Mid range = (highest value + lowest value) / 2

(12 + 3) / 2 = 7.5

Suppose U1 and U2 are i.i.d. Unif(0,1) withU1=0.1 and U2=0.8. Use the "cosine" version of Box-Muller to generate a single Nor(-1,4) random variate. Don't forget to use radians instead of degrees.
a. 0.326
b. 0.326
c. 0.663
d. 1.96

Answers

Answer:

0.663 ( c )

Step-by-step explanation:

U1 = 0.1 , U2 = 0.8

using the "cosine" version of Box-Muller to generate a single Nor(-1,4) random variable

first step : generate single obsⁿ from N ( -1,4 )

attached below is the detailed solution

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Locate the participle (not the entire participial phrase) and the word it modifies.Reminding the younger children to walk carefully, the guide led the group into the cave.Participle:Modified: PLEASE HELP!! I NEED IT NOW!!Kevin has not seen much progress in his muscular strength even though he has been going to the gym each week. Describe specific ways your friend can use frequency, intensity, time, and type to safely apply the overload principle to his workout and break his plateau. Provide one way for each training principle.Sunday Pull Ups, Push Ups and Triceps Dips (3 sets of 15 reps)Monday RestTuesday 30-minute bike rideWednesday YogaThursday Wall Sits, Squats and Hamstring Curls (3 sets of 15 reps)Friday RestSaturday One-hour walk Konjugiere die verbenJana .... Schlerin. (sein) On January 1, 2019, Brooks Inc. borrows $90,000 from a bank and signs a 5% installment note requiring four annual payments of $25,381 at the end of each year. The first installment payment is made on December 31. Complete the necessary journal entry on 12/31 by selecting the account names from the drop-down menus and entering the dollar amounts in the debit or credit columns. Tell me a password. Your password must be at least 8 characters long and must include at least one uppercase letter, one lowercase letter, one special character, and one number.82 point question even tho its really easy WILL MARK BRAINLIESTPlease help solve problems with common tangents. Thank you. Conversion disorder can affect motor and sensory skills in all of the following ways except __________.A.loss of balanceB.loss of vision and hearingC.hallucinationsD.loss of memoryPlease select the best answer from the choices providedABCD # By selling 5 oranges, a shopkeeper gains the selling price of 1 orange. Find his profit percentage. O 50% O 25% O 15% O 20% Which function has a vertex at (2, 6)?O f(x) = 2|x 2| 6O f(x) = 2|x 2| + 6Of(x) = 2|x + 2| + 6Of(x) = 2|x + 2| - 6 any blinks at herei am blink also Which verb form correctly completes this sentence? Os pido que __________ con la persona encargada de esta biblioteca para inscribiros. A. hables B. hablis C. hable D. hablen The manager of an air conditioning manufacturing plant wants to train their service installers on the steps to follow to install the new units. Which visual aid listed below is the best option? which of the points lies on the curve y=x^3 Find an equation for the line below. 5 + 3bc = 9a + b = cd + bc = Find the sum (-4) + 2/3 o Calculate the pH of 500 ml of buffer solution containing .2M of ammonium sulphate and 0.3M ammonium hydroxide which 5 2.1% ionized in dilute solution. (kb of ammonium hydroxide is 1.810^-5) Select the correct answer.Which was NOT a reason the North began to lose interest in the Southern Reconstruction by the early 1870s?A. Southern intransigence was increasingly frustrating to the North, whose soldiers had fought for Black peoples' freedom.B. The violence in the South was increasingly disturbing and seemed to indicate that Black people would never really be free.C. Other issues, such as Indian Wars, western expansion, and others started to overtake Northerners' attention.D. Real and propagandized evidence of corruption in the reconstructed Southern governments discouraged the North.E. Northerners were not supportive of President Johnson's policies, and wanted change with President Grant. Which of the following is a best practice when weight training?A. only static stretch to warm upB. take as little rest as possible between sets C. use proper technique and weightD. eat a heavy meal before heavy lifting Be sure to answer all parts.Calculate the molarity of each of the following solutions:(a) 28.5 g of ethanol (C2H5OH) in 4.50 x 102 mL of solutionM Mes(b) 21.6 g of sucrose (C12H22011) in 67.0 mL of solutionM(c) 6.65 g of sodium chloride (NaCl) in 96.2 mL of solutionM