DIRECTIONS:  Complete all problems on notebook paper, scan/take a picture then submit it as an attachment where indicated.  Provide as much work as possible to earn all points.  If I can’t see your work clearly, I will not make assumptions. The test is worth 85points. The percent grade will be posted.    First Order ODEs and IVPs Theorem: M(x,y) dx + N(x,y) dy = 0 is an exact equation if dM/dy = dN/dx. Exact Equations: dy/dx + P(x)y = Q(x)   10 pts each  Classify each equation below as linear or exact.  Then solve each problem. (ex + y) dx + (x – 2 – yey ) dy = 0 (y + x2 sin x) dx – x dy = 0 x dy/dx = 2y + x3 cos x,      y(π2)=0   II.  Mixing Application  dx/dt = input rate(concentration in) – output rate (concentration out) concentration out = x / (volume + (in rate – out rate)t )   20 pts The Love Dough Company makes delicious Valentine cookies and cookie dough ice cream to sell during the month of February. The thing that makes their cookie dough stand out from the rest is their secret ingredient! Initially there is 100 lbs of cookie dough mixture with no secret ingredient in a tank. The company adds 1 kg/lb of the secret ingredient in the mixture at a constant rate of 5 lbs\min. The mixture inside the tank is kept well stirred and it flows out of the tank at a rate of 4 lbs\min.  This is set aside to go into the cookie dough ice cream!  How much of the secret ingredient is in the tank at time t?  How much special ingredient is in the take after 60 minutes?   III. Homogeneous ODEs Solve the following.   a. 7pts y ” +2y’ + 5y = 0 b. 8pts y ‘” + y ’’ – y ‘ – y = 0   IV. Nonhomogeneous ODEs For undetermined coefficients: yp = generic expression of f(t)   20pts Consider the differential equation given by ay ” + by’ + cy = f(t).   Solve the initial value problem using undetermined coefficients:                                                                    y ” – 6y’ + 9y = 9×2 – 3x +14            y(0)=0              y’(0)=0  

At the number 10 position of the microscope, what is the name for the part?  

Human population growth has always been exponential. 

The following is what type of tissue?  

In some situations, the death rate of a population declines before the birth rate begins to decline. What can be concluded about the population?

Which type of tissue is this?  

High year round temperatures and high precipitation amounts is indicative of temperate grasslands

What was the trend of the rainfall in the Gorongosa national park?  

What influence does temperature have on the savannah biome of Gorongosa national park?

Monocots have central taproots and dicots have fibrous roots