The first thing we must do in this case is find the derivatives:
y = a sin (x) + b cos (x)
y '= a cos (x) - b sin (x)
y '' = -a sin (x) - b cos (x)
Substituting the values:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
We rewrite:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
sin (x) * (- a-b-7a) + cos (x) * (- b + a-7b) = sin (x)
sin (x) * (- b-8a) + cos (x) * (a-8b) = sin (x)
From here we get the system:
-b-8a = 1
a-8b = 0
Whose solution is:
a = -8 / 65
b = -1 / 65
Answer:
constants a and b are:
a = -8 / 65
b = -1 / 65
Given:
Kelly purchased 5 containers of ice cream for a party.
Each container holds 8 cups of ice cream.
Her brother ate 2 cups of ice cream.
One serving of ice cream = 2/3 of a cup.
To find:
Number of servings of ice cream will be left for the party?
Solution:
We have,
1 container = 8 cups of ice cream
5 containers = 5×8 = 40 cups of ice cream
Her brother ate 2 cups of ice cream. So, remaining cups of ice cream is
cups
Now,
of a cup = 1 serving
1 cup = serving
38 cup = serving
= serving
= 57 serving
Therefore, 57 servings of ice cream will be left for the party.
Answer:
the answer is 250 million years
Step-by-step explanation:
Answer:
option A) y > 5/4x + 10
Step-by-step explanation:
Take any point in the shaded region
( -12 , 1)
y > 5/4 x + 10
1 > 5/4 * (-12) + 10
1 > 5*(-3) +10
1 > -15 + 10
1 > -5
(-12 , 5) satisfies the equation.
Answer:
D. $31,337.27
Step-by-step explanation:
We have that the initial amount of the loan is $5500.
Miranda took the loan for 4 years. So, the total present value is $5500×4 = $22,000.
The rate of interest on the loan is 7.5% i.e. 0.075 and it was for the duration of 10 years.
Also, it is given that the loan was compounded annually.
We have the formula as,
i.e.
Substituting the values, we get,
i.e.
i.e.
i.e.
i.e.
i.e.
i.e.
i.e.
i.e.
Thus, the total lifetime cost to pay of the loans compounded annually = 261.16 × 120 = $31,339.2
Hence, the total cost close to the answer is $31,337.27