The identity in question is
cos(a - b) = cos(a) cos(b) + sin(a) sin(b)
so that
cos(a - b) = 12/37 cos(a) + 3/5 sin(b)
Since both a and b lie in the first quadrant, both cos(a) and sin(b) will be positive. Then it follows from the Pythagorean identity,
cos²(x) + sin²(x) = 1,
that
cos(a) = √(1 - sin²(a)) = 4/5
and
sin(b) = √(1 - cos²(b)) = 35/37
So,
cos(a - b) = 12/37 • 4/5 + 3/5 • 35/37 = 153/185
Answer:
1/3 cups of vanilla per teaspoon
Step-by-step explanation:
Answer:
Step-by-step explanation:
we know that
The algebraic expression is equal to
Remember that
and
so
substitute
Answer:
D., x= 19.7 or ≈20. g
Step-by-step explanation:
P(x) = [100(15+x)]/(100+x)
When 0 g additional salt is added, x=0. we have
P(0) = [100(15+0)]/(100+0)= 15
x=0, P=15
We can see this point only on the graph D.
P(x) =29 = [100(15+x)]/(100+x)
29 = [100(15+x)]/(100+x)
29(100+x) = 100(15+x)
2900+29x = 1500+100x
2900-1500=100x-29x
1400 = 71x
x ≈ 19.7 g or ≈20. g
From the graph D, we can see that to get 29% we need to add ≈ 20 g of salt.
