1. ## Calculus homework again...

I am still having terrible trouble with my class. Any help is greatly appreciated and I want to thank everyone who has helped me out in the past.

The first problem I am having trouble with is finding f prime of the function

((2x^2)(tan(x))/(sec(x))

Now my first inclination is ((sec(x))((4x)(sec^2(x)))-((2x^2(tan(x)))((sec(x))(tan(x)))))/(sec(x)(tan(x)))

But I input this and it comes out incorrect. Any ideas? Is it a typo or am I doing it wrong?

2. The first thing to do is simplify, then it's easy to work with

$\frac{2x^{2}tan(x)}{sec(x)}=2x^{2}sin(x)$

3. A farmer wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle (see the figure below). He has 470 feet of fencing available to complete the job. What is the largest possible total area of the four pens?

How does one solve this type of problem?

My professor has several of these and I want to figure out the general method.

4. anyone know how to do this one? It seems easy but I am unsure how to set up the equation: A bacteria culture starts with 720 bacteria and grows at a rate proportional to its size. After 2 hours there will be 1440 bacteria. Express the population after t hours as a function of t.
population:

5. Originally Posted by Pikeman85
anyone know how to do this one? It seems easy but I am unsure how to set up the equation: A bacteria culture starts with 720 bacteria and grows at a rate proportional to its size. After 2 hours there will be 1440 bacteria. Express the population after t hours as a function of t.
population:
Set up the model $y=Ce^{kt}$

now you are given two initial conditions

when t=0 y=770 which implies C=770

and when t=2 Y=1440 now put in your values we have foud as of yet and solve for k

6. Originally Posted by Pikeman85
A farmer wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle (see the figure below). He has 470 feet of fencing available to complete the job. What is the largest possible total area of the four pens?

How does one solve this type of problem?

My professor has several of these and I want to figure out the general method.
The general method for solving these optimization problem is setting up two equations, the first is the equation whhich contains both variables and a number

For example $x+y=1$

and then setting up the function you want to optimize

for example

$S=xy$

then you solve for a variable in the first one

$x+y=1\Rightarrow{x=1-y}$

and then sub into the optimizing equation

$S=(1-y)y$

now find the max/min for this equation, once found the y or x value, sub that back into your original equation to get the other value

now apply that here

7. A plane flying with a constant speed of km/min passes over a ground radar station at an altitude of km and climbs at an angle of degrees. At what rate, in km/min is the distance from the plane to the radar station increasing minutes later?

8. Originally Posted by Pikeman85
A plane flying with a constant speed of km/min passes over a ground radar station at an altitude of km and climbs at an angle of degrees. At what rate, in km/min is the distance from the plane to the radar station increasing minutes later?

Always draw a diagram

We can use the law of cosines to set up an equation

$y^2=12^2+x^2-2(12)x\cos(125^\circ)$

We know $\frac{dx}{dt}=24$

taking the derivative with respect to t we get

$2y\frac{dy}{dt}=2x\frac{dx}{dt}-24\cos(125^\circ)\frac{dx}{dt}$

Do you think you can finish from here?