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ahrayia [7]
2 years ago
5

Help please! Calculate the exact value of cos (a-b) given that sin a= 12/13 with pi/2

Mathematics
1 answer:
zloy xaker [14]2 years ago
4 0

Answer:

56/65

Step-by-step explanation:

First, we know that cos(a-b) = cos(a)cos(b) + sin(a)sin(b)

We know what sin(a) and sin(b) are, and to get cos(a), we can take the equation sin²a + cos²a = 1

Thus,

(12/13)² + cos²a = 1

1 - (12/13)² = cos²a

1- 144/169 = cos²a

cos²a = 25/169

cos(a) = 5/13

Similarly,

(3/5)² + cos²b = 1

1 - (3/5)² = cos²b

1 - 9/25 = cos²b

cos²b = 16/25

cos(b) = 4/5

Our answer is

cos(a-b) = cos(a)cos(b) + sin(a)sin(b)

cos(a-b)  = (5/13)(4/5) + (12/13)(3/5)

cos(a-b)  = 20/65 + 36/65

cos(a-b)  = 56/65

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The ratio of boys to girls in math classes is 5 :7. if there are 60 students in all or her classes, how many are boys
daser333 [38]
Total of ratio 5+7=12

60/12 = 5

For boys 5x5 = 25 boys in her class

(For girls 7x5 = 35)
6 0
3 years ago
Solve the system of equations and choose the correct ordered pair. 3y=4x+7 and 5y=4x+25​
Luba_88 [7]

Answer:

(5,9)

Step-by-step explanation:

3y=4x+7

5y=4x+25​

Subtract the two equations to eliminate x

5y=4x+25

-( ​3y=4x+7)

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

2y = 0x +18

Divide by 2

2y/2 = 18/2

y =9

Now find x

3y = 4x+7

3*9 = 4x+7

27 = 4x+7

Subtract 7

20 = 4x

Divide 4

20/4 = 4x/4

5 =x

(5,9)

7 0
3 years ago
Read 2 more answers
You have a 1 in 4 chance of winning a game. How would you calculate the probability that you will win 3 times in a row?
Ierofanga [76]

Answer:

<u>The probability of winning three games in a row is 1/64 or 1.6%</u>

Step-by-step explanation:

Probability of winning a game = 1/4

Probability of winning two games in a row = 1/4 * 1/4 = 1/16

Probability of winning three games in a row = 1/4 * 1/4 * 1/4 = 1/64

Probability of winning three games in a row = (1/4)³ = 1/64

1/64 = 0.015625

1/64 = 1.6% (rounding to the next tenth)

5 0
3 years ago
A lender will make an 80% loan-to-value loan on a property that is appraised for $72,250 and sells for $73,500. If the buyer has
anyanavicka [17]

Answer:

$1,250

Step-by-step explanation:

We are given;

Loan to value ratio;LTV = 80% = 0.8

Appraised value of property = $72,250

Selling value of property = $73,500

Now, the formula for Loan to value ratio is;

LTV = Loan amount/Appraised value of property

0.8 = loan amount/72250

Cross multiply to get;

Loan amount = 0.8 × 72250 = $57,800

Now,we are told that he has saved $14,450.

Thus, total money raised including loan = $57,800 + $14,450 = $72,250

Since the selling value = $73,500, then,

Amount left for him to save in order to make down payment = $73,500 - $72,250 = $1,250

7 0
3 years ago
The bigger
Arte-miy333 [17]

Answer:

See Explanation

Step-by-step explanation:

Required

Prove that Dexter is wrong

To prove that Dexter is wrong, we use the following numbers.

Number = 4

The factors are:

Factor = 1,2\ and\ 4

3 factors

Using a greater number:

Number = 5

The factors are:

Factor = 1\ and\ 5

2 factors

From the above analysis:

4 has 3 factors and 5 has 2 factors; which shows that 5 has fewer factors

This shows that Dexter is wrong

5 0
2 years ago
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