Let us put

and substitute it into the differential equation. Then the characteristic equation is

So, the general equation can be written as

The correct answer is E.

the correct answer is A.

the correct answer is C.

Substituting

into suggested equations, we find that the only equation that is satisfied is D) indeed

Correct answer is  D .

h(2)=2^.2²+2a-1=7+2a. Since h(2)=15, then 7+2a=15. If we solve this equation 2a=8. And we obtain a=4.

The area under the graph of the supply function corresponds to the expected income, so

The antiderivative of the integrand is

As before   we only need to apply the formula for the future value of income . Since the time period is

 and the interest rate gives

we have

Correct answer is A

Let u=x³+4 then du=3x²dx. Thus we obtain

In a certain market, if a producer who is willing to sell a product at a certain price may sell the product higher than the price he asks, then he has increased his revenue. This extra amount gained is called the producer surplus (PS). In other words, the producer surplus is the difference of the price the producer is willing to sell and the actual price he sells his product.

Since given parabola intersects

at

and the required area is under the

then we evaluate required area by the definite integral below:

Thus, the right answer is D.

Let us use the integration by parts method. Let u=4x+10 which gives du=4dx. Also, let dv=e^2xdx which gives

.

Substituting these values into ∫udv=uv-∫vdu  we get;

for any arbitrary real number c.

on the interval [-2, 1], therefore the sought for area A can be calculated by definite integral:

The antiderivative of 

is

so 

Therefore the correct answer is the C option.

First, we must find q₀:

Since the area under the graph of the supply function corresponds to the expected income, we can evaluate it by integrating the supply function from q = 0 to q = 3 which gives

Substituting

in the equation we get

Hence

so the general solution of the  equation is

The solution is quite straightforward. Using the integral formula for Gini index, we get