Calculate the exact value of cos(a−b) given that sin a=12/13 with π/2

Calculate The Exact Value Of Cos(ab) Given That Sin A=12/13 With /2

Answers

Answer 1

Answer:

Step-by-step explanation:

[tex]sin ~a=\frac{12}{13} ,\frac{\pi}{2} <a<\pi\\a ~is~in~2nd~quadrant.\\sin~b=\frac{3}{5} ,0<b<\frac{\pi}{2} \\b~is~in~1st~quadrant.\\cos~b=\sqrt{1-sin ^2b} \\=\sqrt{1-(\frac{3}{5} )^2} \\=\sqrt{\frac{25-9}{25} } \\=\sqrt{\frac{16}{25} } \\=\frac{4}{5} ,\\cos~a=-\sqrt{1-sin^2 a} \\=-\sqrt{1-(\frac{12}{13} )^2} \\=-\sqrt{\frac{169-144}{169} } \\=-\sqrt{\frac{25}{169} } \\=-\frac{5}{13} \\cos(a-b)=cos~acos~b+sin~a sin~b\\=\frac{-5}{13}* \frac{4}{5} +\frac{12}{13}* \frac{3}{5} \\=?[/tex]


Related Questions

Cellular phone service is available for $37 per month for 1847 minutes. What is the monthly cost per minute? Round your answer to the nearest tenth of a cent.

The cost for the phone service is cents per minute.

Answers

The cost per minute is .02 cents

At the time of her​ grandson's birth, a grandmother deposits $2000 in an account that pays 6.5% compounded monthly. What will be the value of the account at the​ child's twenty-first​ birthday, assuming that no other deposits or withdrawals are made during this​ period?

Answers

Answer:

$41, 863. 50

Step-by-step explanation:

$2000 - 6.5% = $1,993.50

$1,993.50 x 21 = $41, 863. 50

if we use the quadratic expression below to complete a diamond, what value will go at every bottom of the diamond

a. -4
b. 4
c. 1
d. 5​

Answers

Answer:

if we use the quadratic expression below to complete a diamond, what value will go at every bottom of the diamond

is -4

Answer:

if we use the quadratic expression below to complete a diamond, what value will go at every bottom of the diamond

its 1 because

What is its potential energy when compressed by 0.25 m?

a. 1.25 Joules b. 33.33 Joules
c. 8.33 Joules d. 5.0 Joules​

Answers

For me the answer was C.

Give another real object for the following solid figures. Write your answer in the blank
provided
1. Sphere -
2. Cube -
3. Cylinder -
4. Rectangular Prism -
5. Triangular Prism -
matinong sagot po rereport ko ung di matinong sagot​

Answers

Answer:

1 bowling ball

2 box

3 can

4 book

5 pyramid

13. Find the measure of angle ABC. B 8x 6x 6x A С​

Answers

Answer

Angle A = 54 degree

Angle B = 72 degree

Angle C = 54 degree

Explain

It is a triangle, so the total of angle is 180 degree

Find X

8x + 6x + 6x = 180

20x = 180

x = 180/20

x = 9°

Value of x is 9°

Substitute a score of x for every angle =

Angle A

= 6x

= 6(9)

= 54°

Angle B

= 8x

= 8(9)

= 72°

Angle C

= 6x

= 6(9)

= 54°

#LearnWithBrainly

a. find the area

b. find the perimeter​

Answers

Answer:

Area= 4y^2 + 14y + 12

Perimeter = 10y + 16

Step-by-step explanation:

Area of a reactangle = length × width

= (4y+6) × (y+2)

= 4y^2 + 6y + 8y + 12

= 4y^2 + 14y + 12

Perimeter of a rectangle = 2 × (a +b)

= 2 × ( 4y + 6 + y+ 2)

= 2 × ( 5y + 8)

= 10y + 16

When you solve x^2 - 8x + 7 = 0 what is the last step of the equation
before you simplify to get the two answers? *
O x = -4 13
O x = 3 + 4
O x = 4 + 3

Answers

Answer:

x = 1 and x = 7

Step-by-step explanation:

The given equation is [tex]x^2 - 8x + 7 = 0[/tex].

We need to solve the equation.

It is a quadratic equation whose solution is given by :

[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]

Here, a = 1, b = -8 and c = 7

Put values,

[tex]x=\dfrac{-(-8)\pm \sqrt{(-8)^2-4(1)(7)} }{2(1)}\\\\=\dfrac{8\pm \sqrt{64-28}}{2}\\\\=\dfrac{8\pm 6}{2}\\\\=\dfrac{8+6}{2},\dfrac{8-6}{2}\\\\=7,1[/tex]

So, the values of x are x = 1 and x = 7.

433.54 in terms of pi​

Answers

Answer:

138.0700636942675[tex]\pi[/tex]

Step-by-step explanation:

7.5667004391


Is the answer


433.54 x π/180.

a sunglasses store bought $5,000 worth of glasses the store made $9,000 making a profit of $20 per sunglasses there were How many pairs of sunglasses involved?

Answers

Answer:

150 pairs

Step-by-step explanation:

so total money spent Is equal to 5000

profit is equal to 3000

profit on each pair is equal to 20

so 3000 divided by 20

which gives 150

so 150 pairs of sunglasses were involved

pls give me brainliest I need it

Answer:

The sunglasses involved are 200

First answer gets brainest. 8th grade math root question

Answers

Answer:

9

Step-by-step explanation:

Answer: 9

Step-by-step explanation:

Square Rooting is basically going down to the origins of the number, trying to figure out what times (x) would give you your current number. In order it get 81, you would need  to do 9*9, therefore making the square root 9

Please help me on this question! And explain how you got your answer please!

Answers

Answer:

she has a total of 140 coins

Step-by-step explanation:

x is coins in total

5/100 times x = 7

0.05 times x = 7

x = 7/0.005

x = 700/5

divide that you get 140

Answer:

Maybe 7.14285714?

Step-by-step explanation:

50% divided by 7?

I'm sorry I just guessed

Hey, I need help!

What is 56/2?

Answers

Answer:

28

Step-by-step explanation:

Answer:

56 divided by 2 would be 28.

Step-by-step explanation:

[tex]\frac{56}{2}[/tex] is the same thing as half of 56, since two 28s added together is 56, which means [tex]\frac{56}{2}[/tex] is equivalent to 28.

find the given polynomial by finding the greatest common monomial factor or the ñegative of the greatest common monomial factor and rewrite the expression. ​

Answers

Answer:

1. The greatest common monomial factor is xy

2. xy(6 + 2y² + 3x²)

Step-by-step explanation:

6xy + 2xy³+ 3x³y

1. Determination of the greatest common monomial (GCM) factor.

6xy + 2xy³+ 3x³y

6xy => 2 × 3 × x × y

2xy³ = 2 × x × y × y × y

3x³y = 3 × x × x × x × y

GCM => xy

2. Rewrite the expression

6xy + 2xy³+ 3x³y

GCM => xy

6xy + 2xy³+ 3x³y = xy(6 + 2y² + 3x²)

A ratio of the number of boys to the number of girls in a choir is 5 to 4. There are 60 girls in the choir

Answers

the ratio is 4/5 girls to boys. if there are 60 girls you would divide 60 by 4 and get 15. you would then multiply that 15 by 5 to get the number of boys in the choir. your answer would be 75 because 15x5=75. there are 75 boys in the choir

A rectangle has a perimeter of 66 inches. The length is 5 inches longer than the width. What is the length of the rectangle?
A.19 in
B.14 in
C.30.5 in
D.28 in

Answers

Answer:

I think that it is A. 19

Step-by-step explanation:

I think it is A. because 19x2=38. 19-5=14, 14x2=28. 28+38=66.

P=66

L=19

W=14

Sorry if I'm wrong.

A quantity with an initial value of 140 decays continuously at a rate of 4% per decade. What is the value of the quantity after 98 years, to the nearest hundredth?
(pls answer)

Answers

9514 1404 393

Answer:

  93.84

Step-by-step explanation:

The exponential function will be of the form ...

  q = a×b^t

where 'a' is the initial quantity and b is the growth factor per time period t.

If we use decades as the time period, then the growth factor is 1 more than the growth rate of -4%. For the initial value 140, the function is ...

  q = 140×(1 -4%)^t

  q = 140×0.96^t

98 years is 9.8 decades, so the quantity q remaining will be ...

  q = 140×0.96^9.8 ≈ 93.84

The quantity remaining will be 93.84 after 98 years.

Answer:

94.6

Step-by-step explanation:

Which choice is equivalent to the fraction below?
5/16

O A. 5.16
O B. 5 divided 16
O C. 5-16
O D. 16 divided 5

Answers

Answer:

I think A

Step-by-step explanation:

   But im not sure

The drawing below shows a side view of a picture frame on Mary's desk support 16 4.2 which of the following is the closest to the length of the frame support

Answers

Answer:

17 cm

Step-by-step explanation:

Math STAAR Readiness 8 grade Quiz: The drawing below shows a side view of a picture frame on Mary’s desk.  Closest to the length of the frame support.

Answer:

17 or D

Step-by-step explanation:

a^2+b^2=c^2

4.2^2+16^2=c^2

17.64+25.6=c^2

c^2=273.64

c=√273.64

c=16.5 which can be rounded up to 17 or D

and I am reviewing for the math staar.

The diagram shows a rhombus inside a regular hexagon

Work out the size of x

Answers

Answer:

add a picture

Step-by-step explanation:

Need help with this if possible ​

Answers

Answer:

hope it helps...

Step-by-step explanation:

Please help ! Please help! I put extra points! And I will heart you!

Answers

Answer:

89 degrees

Step-by-step explanation:

Answer:

91 degrees

Step-by-step explanation:

180-89=91 degrees

180 is the line that 89 degrees is on.

13. Using figure 1, angles 5 and 6 form a linear pair, If mz6=95", find m25.
a. 5°
b. 85"
c. 90°
d.95"
14. In figure 1, 25 and 28 are vertical angles. If m2s 2x + 45 and m28= 7x - 15
What is the value of x ?
a.6
b. 12
c.9
d. 21



paki answer po plss​

Answers

In the figure, angles 1 and 5 are alternate exterior angles. Use the Alternate Exterior ... each pair of alternate interior angles is congruent. ... 1 and 3. SOLUTION: If the radiation rays form parallel lines, then ∠1 and ... supplementary; since 3 and 5 are a linear pair, ... ∠8, ∠9 and ∠10, ∠11 and ∠12, and ∠13 and ∠14.

Solve for y please will mark brainly

Answers

Answer:

y = -4

Step-by-step explanation:

since f(y) = 9, you know the equation is equal to 9

9 = [tex]\sqrt{y+29}[/tex] - y

81 + 18y + y^2 = y + 29

y = -4

Kelly paid $45.36 for a sweater that was on sale for 25% off the original price. She paid 8% sales tax on the sale price.

What was the original price of the sweater, in dollars​

Answers

The sales tax is determined by computing a percent of the purchase price. To find the sales tax multiply the purchase price by the sales tax rate. Remember to convert the sales tax rate from a percent to a decimal number. Once the sales tax is calculated, it is added to the purchase price.

Step-by-step explanation: Sorry if this doesn't help....

The answer of 4.38 x 10^4 in ordinary notation is

Answers

4,38 * 10⁴ = 4,38 * 10 000 = 43 800

- 63 y^5
27y^7
- 18y^9
Take out the common factor ​

Answers

Answer:

[tex]Factor = 9y^5[/tex]

Step-by-step explanation:

Given

- 63 y^5  , 27y^7  and 18y^9

Required

Remove the common factor

Factorize each expression:

[tex]- 63 y^5 = -3*3*7*y*y*y*y*y[/tex]

[tex]27y^7 = 3 * 3 * y * y * y * y * y * y * y[/tex]

[tex]-18y^9 =-2 * 3 * 3 * y * y * y * y * y * y * y * y * y[/tex]

The common factor in the above expression is:

[tex]Factor = 3 * 3 * y*y*y*y*y[/tex]

[tex]Factor = 9y^5[/tex]

Can someone help me pls

Answers

Answer:

57°

Step-by-step explanation:

180-56=114

114÷2=57

Answer:

57°

Step-by-step explanation:

AO and BO are both the radius of the circle, so they are equal.  Since it makes an iscosoles triangle, angles A and B are equal.

180-66=114

114/2=57

17% off a $35 dresser

Answers

Answer:

Sale Price = $29.05 (answer). This means the cost of the item to you is $29.05. You will pay $29.05 for a item with original price of $35 when discounted 17%. In this example, if you buy an item at $35 with 17% discount, you will pay 35 - 5.95 = 29.05 dollars

Discount of $5.95. You would be paying $29.05

A study of 420,027 cell phone users found that 133 of them developed cancer of the brain or nervous system. Prior to this study of cell phone​ use, the rate of such cancer was found to be ​0.0414% for those not using cell phones. Complete parts​ (a) and​ (b). a. Use the sample data to construct a ​90% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system.

Answers

Answer:   (0.00027144,  0.00036176)

Step-by-step explanation:

The sample proportion of cell phone users who develop cancer of the brain or nervous system = [tex]\dfrac{133}{420027}=0.0003166[/tex]

Sample size : 420027

Confidence interval for p: [tex]\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex], where [tex]\hat{p}[/tex]= sample proportion , n= sample size , z* = crirical z value.

For 90% confidence interval , z*= 1.645

Required confidence interval:

[tex]0.0003166\pm (1.645)\sqrt{\dfrac{0.0003166(1-0.0003166)}{420027}}\\\\=0.0003166\pm 0.00004516\\\\=(0.0003166-0.00004516,\ 0.0003166+ 0.00004516)\\\\=(0.00027144, \ 0.00036176)[/tex]

A ​90% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system = (0.00027144,  0.00036176)

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