Mike

The end of a retractable extension cord is fastened to a swivel 12 feet above the floor on the ceiling of an automotive repair shop. The other end of the cord is an outlet that can be moved around the floor of the shop. Let x represent the distance (in feet) that a point on the floor is from the point directly under the swivel. Write a formula for L(x), the length of cord needed to reach a point that is x feet from the point directly under the swivel.

I was asked this problem by another student, and I wasn't sure how what do to. Any help?

Given two sides and a non-included angle of a triangle, which of the following CANNOT happen:

A. There could be no solutions.

B. There could be one solution.

C. There could be two solutions.

D. Any of these could happen.

Consider the following diagram:

http://i46.tinypic.com/vifx9i.jpg

This is a multiple choice question. They want you to find x, (FC) to the nearest foot.

The possible answers are:

A. 204

B. 205

C. 206

D. 207

I was able to come up with 204.48. If this is correct, would this round to 204 or 205?

A plane leaves LA traveling 200 mph at a bearing fo N 30 E. After 3 hours, how much horizontal distance has the plane traveled to the nearest tenth?

I came up with 520 mi, is this correct?

Point A revolves counterclockwise around a point, making 7 complete rotations in 12 seconds. If A is 19 cm away from its center of rotation, what is the linear velocity of A to the nearest tenth?

What is the angular velocity of A to the nearest tenth?

Any help would be greatly appreciated.

Suppose you have three metal rods of length 9, 11, and 15 inches, and you want to form a triangle out of these three rods. What can be said about this triangle?

A. It's a right triangle (which I know it's not due to not satisfying the pythagorean theorem)

B. It's an acute triangle

C. It's an obtuse triangle

D. It is impossible to form a triangle from these three rods.

I need to find the maximum radius of a disk centered at 0 where each function is locally one-to-one.

A. f(z) = z + az, for any real number a

B. f(z) = z^2 + z

C. f(z) = e^(z) - 1

Let f 1 ,f 2 ,… be a sequence of continuous positive functions on [0,1] and let an = sup{fn(x) : x∈[0,1]} .

In class, we showed that if ∑fn uniformly converges on [0,1] , then it is not always true that ∑an <∞ .

We did this by visually constructing a sequence of continuous functions of disjoint support on [0,1] such that an =1/n .

My question is: Does the same conclusion hold if fn is a decreasing sequence of continuous positive functions on [0,1] , or not?

I know that I have to find the 2nd partial derivatives with respect to x and y and figure out when their sum equals 0.

So far, I have:

uxx = -(k-1)*k*x^(k-2)

uyy = (k-2)*(k-1)*k*x*y^(k-3)

When trying to solve the equation uxx + uyy = 0, I get k*(k-1)*[-x^(k-2)+k*x*y^(k-3)-2*x*y^(k-3)] = 0.

This means k = 0 or (k-1) = 0 or the third factor = 0.

Is it possible to solve the third factor?

Prove that [Kc : K] is infinite. Prove that [Kc : Ksep] is infinite. Is it true that [Ksep: K] must be infinite?

Also, is A noetherian?

Prove that H is normal and the order of G/H is a power of 2.

My laptop is over 5 years old and needs to be replaced. The hard drive is fairly new and works perfectly. I was wondering if I can insert it into a new dell laptop and have it run like it does now, except on a new machine.