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
Answer:
10
Step-by-step explanation:
10 is the least of the numbers, it is the lowest
10<14,16,20,29
p = pennies
q= quarters
p = 2q+5 (1)
.25q+.01p=1.67 (2)
substitute the equation for pennies (1) into the 2nd equation
.25q+.01(2q+5)=1.67
distribute
.25q +.02q +.05 = 1.67
combine like terms
.27q +.05 =1.67
subtract .05 from each side
.27q = 1.62
divide by .27
q=6
p=2q+5
p=2(6)+5
p=12+5
p=17
There are 6 quarters and 17 pennies
Explanation:
Answer:
12.48 i think
Answer:
The required equation is 
Step-by-step explanation:
Consider the provided equation.
Solve the equation for b.
Square both the sides.
Subtract a² from both the sides.
Square root both the sides.
Hence the required equation is
