# Questions and Answers

March 20, 2013

## How do you find the magnitude of a vector?

I am so confused about vectors. I have seen them listed as three numbers (1,5,3) or as two (3,4). I have read to find the magnitude of a vector you subtract (x1-x2) and I’ve read that you add (sqrt of u1^2 + u2^2 + u3^2) I am so confused. I know that magnitude is length, but I am so lost!

The magnitude is the “distance” or “length” of the vector. So to find the magnitude, you apply the distance formula. That is, the magnitude of a vector v = = sqrt{v1^2 + v2^2 + v3^2}

Keep in mind that you sometimes are given endpoints to find your vector coordinates. That is, if the endpoints are (x1, y1, z1) and (x2, y2, z2), then to find the vector v=
note that
v1 = x2 – x1,

v2 = y2 – y1 and

v3 = z2 – z1

## How do I find the arc length using the arc length formula for the following equation?

The equation is y=mx+b, and it goes from (x1,y1) to (x2, y2).
I get the integral(x1,x2) of sqrt(1+m^2).
m is a constant.
Help?

L = INTEGRAL OF [SQRT[1 + (f '(x))^2] dx] from x1 to x2

f(x) = mx + b
f ‘(x) = m
L = INTEGRAL OF [[SQRT[1 + m^2]] dx] from x1 to x2 <— just as you have
L = [SQRT[1 + m^2]] x evaluated from x1 to x2 since the SQRT term is a constant
L = [SQRT[1 + m^2]] x2 – [SQRT[1 + m^2]] x1 = [SQRT[1 + m^2]] (x2 – x1)
Since m = (y2 – y1) / (x2 – x1), then
L = [SQRT[1 + m^2]] (x2 – x1) = [SQRT[1 + [(y2 - y1) / (x2 - x1)]^2]] (x2 – x1)
L = [SQRT[ [(x2 - x1) / (x2 - x1)]^2+ [(y2 - y1) / (x2 - x1)]^2]] (x2 – x1)
L = SQRT[ (x2 - x1)^2+ (y2 - y1)^2 ] which is just the distance formula between the two points

## Can all modern laptops burn DVDs at x1?

Burning DVDs at a slow rate is the best for quality. I’m just wondering if new laptops burn at x1 or x2?

No it is not. Maybe among older machines where the technology for faster burn times was still in its infancy, but burning quality data to dvd’s involves quality discs, not slower write speeds.

## Let a fair die be rolled twice and let and be the outcomes of the first and?

Let a fair die be rolled twice and let X1 and X2 be the outcomes of the first and the second rolls. What is the distribution function of X1X2?

Tabulate all possibe outcomes in separate columns
X1 can be 1, x2 can be 1,2,3,4,5,6 etc
There are 36 possibles, and all have equal probability of 1/36.
Now create a third column: x1*x2
Group together any products that are the same. If 4 products are identical then the probability of that product is 4/36 (just add the individual probabilities).

X1*x2=5 can only be formed by throwing 1,5 or 5,1 so product 5 has probability 2/36.

That is how it is done. In the end, the probabilities assigned to each possible product must sum to 1. Good luck.

## What is the equation for finding the distance between two points on a graph?

Example: distance between point A (1,-3) and B (4,1). I am more concerned with the equation that is similar to (X2-X1)/(Y2-Y1)=?

Y-y1=m(x-x1)Point slope equation

y=mx+b Slope intercept equation

put the point on the graph and do RISE/RUN

## Which PCI Express x1 graphics card is the best?

Hey guys, I have a Dell 3100 which has a PCI E x1 slot and two PCI slots and i am planning to buy a PCI E x1 graphics card to enhance my gaming, which graphics card which goes into the PCI E x1 slot is best for me to get??

The only one on my mind so far is: NVIDIA GeForce 8400GS – graphics adapter – GF 8400 GS – 256MB

What do you guys think??

That’s fine but the Dell 3100 power supply is rated at 230 Watts

NVIDIA GeForce 8400GS
Minimum of a 300 Watt power supply.
(Minimum recommended power supply with +12 Volt current rating of 18 Amp Amps.)

## What is the best adhesive to mount mirror tiles on walls?

These are reused tiles, so they have 1″x1” foam pads on the corners, which would be very difficult to get off. So I can’t use the entire back surface for adhering. Also, it is in a bathroom — is humidity an issue?

Glass merchants sell a special mirror adhesive as some other types of adhesives can have acids in which will attack the silvering on the back

## How do I derive a cost function from a production function?

What is the general process? Here is the question it relates to:

A firm has the production function Q = X1^1/2*X2. In the short run it must use exactly 15 units of factor 2. The price of factor 1 is \$75 per unit and the price of factor 2 is \$2 per unit. The firm’s short run marginal cost function is

a. MC(Q) = 10Q 15.
b. MC(Q) = 30Q1 2.
c. MC(Q) = 30 + 75Q2.
d. MC(Q) = 2Q.
e. MC(Q) = 15Q1 2.

TC = cost*q = 75*x1 + 2*x2

In the short run Q = x1^(1/2)*x2; must use 15 units of x2
Q = x1^(1/2)*15 = 15×1^(1/2)
Q/15 = x1^(1/2)
x1 = (q^2)/225

TC = 75×1 + 2*15 = 75×1 + 30
TC = 75(Q^2)/225 + 30
TC = (Q^2)/3 + 30
MC(Q) = (2/3)Q (via differentiation)

I am not sure, but a) seems to be the closest answer.

I am also not sure whether the above is correct, but I hope it helps