Mathematics - 28 October 2007

For the following problem we are asked to find an equation for the conic that satisfies the given conditions:

Hyperbola, foci (2,2) and (6,2), asymptotes y = x – 2 and y = 6 – x

I know that the center is (4,2), the halfway point between the two foci, and thus that c = 2. However, I am not sure how to use the given asymptotes to find a and b to get the equation. Please explain how to do this part of the problem step-by-step.

2007-10-28 21:48:57 · 1 answers · asked by Ryan_1770 1

For the following problem we are asked to find an equation for the conic that satisfies the given conditions:

1. Ellipse, foci (0, -1), (8, -1), vertex (9, -1)

For the solution I got:

[(x – 4)^2]/25 + [(y + 1)^2]/3 = 1

Is this correct?

2007-10-28 21:43:17 · 3 answers · asked by Ryan_1770 1

For this problem, we are asked to find the area of the region that lies inside the first curve and outside the second curve.

Note: I am using t instead of theta.

First curve: r = 2 + Sin(t)

Second curve: r = 3Sin(t)


I know pi/2 is one of the angles where these two curves intersect, but the problem is that I don’t know how to proceed from here since pi/2 is the only angle where these two curves are equal to one another for the interval between 0 and 2 pi. Please explain how to do the problem from this point forward step-by-step.

2007-10-28 21:09:34 · 3 answers · asked by Ryan_1770 1

it is known that 40% of the students in a certain college are girls and 50% of the students are above the median height.if 2/3 of the boys are above median height,what is the probability that a randomly selected student who is below median height is a girl?

2007-10-28 20:59:42 · 5 answers · asked by Anonymous

y'' - 5y' + 4y = 8e^(x) + x

2007-10-28 20:48:09 · 1 answers · asked by Anonymous

The radius of a circular disk is given as 28 cm with a maximum error in measurement of 0.2 cm.

a) Use differentials to estimate the maximum error in the calculated area of the disk.

b) What is the relative error?

What is the percentage error?

2007-10-28 20:35:16 · 2 answers · asked by Ana 1

y" + 2y' + 2y = 0
y(1) = 1, y'(1) = 2

Okay... i was able to find the general solution to this problem, but since the initial values are given at 1 (which involves taking the values of sin1 and cos1....) i couldn't solve for the constant coefficients. Can anyone help?

2007-10-28 20:24:31 · 2 answers · asked by Tas Chowdhury 2

and then it gets put backwards and goes like b_n =b_n-1+2b_n-2 ; where b0=1 and b1=2? How do you solve these?

2007-10-28 20:16:48 · 2 answers · asked by jimmy_castillo85 1

mm cu how to change to kg???

2007-10-28 20:11:24 · 2 answers · asked by rachel 1

2007-10-28 20:00:44 · 2 answers · asked by mustang5354@sbcglobal.net 1

e.g. a plane flies 100km from point A on a bearing of 060 degrees to point B then it changes it's direction on a bearing of 195 degrees and flies fro 120km to point C what is the distance and bearing between points A and C

2007-10-28 19:51:31 · 3 answers · asked by Anonymous

d [5e^x]
___ ______
dx [4+9e^x]





d [2x^7/5 - 8]
___ ______
dx [ e^x + 5]




d Cosx + x^3
___ ______
dx 7tanx




d
___ √tan(3x) (square root of all tan(3x) )
dx




d(e^x cosx (x^2 -1))
________________
dx

2007-10-28 19:45:07 · 1 answers · asked by Anonymous

1. A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline and its light makes four revolutions per minute, How fast is the beam of light moving along the shoreline when it is 1 km from P?

2. A ferris wheel with a radius of 10 m is rotating at a rate of one revolution every 2 minutes. How fast is a rider rising when his seat is 16 m above ground level.

2007-10-28 19:41:59 · 3 answers · asked by mickey g 1

List the possible rational roots of x^3 + 6x^2 +10x + 3 = 0. Then determine the rational roots.

please explain as you're solving, thankj you very much

2007-10-28 19:26:22 · 3 answers · asked by apromiseibroke 1

2007-10-28 18:48:48 · 1 answers · asked by Adam P 1

How would I go about finding the equation of a plane containing the lines:
x-3=4t, y-4=t, z-1=0
and x+1=12t, y-7=6t, z-5=3t

I'm stumped. Thanks.

2007-10-28 18:47:51 · 4 answers · asked by oiler110 2

find x.
thanks :)

2007-10-28 18:29:23 · 3 answers · asked by candy 3

Please show solutions...

2007-10-28 18:19:30 · 4 answers · asked by thankz10 1

So far I'm down to..

x2-2/5x+4/5=0

x2-2/5x+2/5=-2/5

Not sure if i'm going the right way thou. Would appreciate any help.

2007-10-28 18:04:47 · 2 answers · asked by sour_bank_s 1

Basically, I have no idea how to do the following problems.

1. f(x) = ln(e^-x - x)
2. f(x) = (x^2 + 5)^3 (3x^3 - 2)^2
3. f(x) = (5x^2 + 11)e^-21x
4. y = (x^2 + √x + 1 ) / x^3/2

Any help would be appreciated; thanks in advance!

2007-10-28 17:52:38 · 1 answers · asked by Anonymous

Given that log(xy^3)baseb = m and log(x^3.y^2) base b = p

Find log(√(xy)) base b in term of m and p.

The answer is (m+2p)/14 note that all above equation had log as a "base b" pls show working

2007-10-28 17:50:22 · 1 answers · asked by Anonymous

An item costs $500 at time t = 0 and costs $P in year t. When inflation is r% per year, the price is given by the following equation.

P = 500e^(rt/100)

(a) If r is a constant, at what rate is the price rising (in dollars per year) initially? 5r dollars per year

(b) At what rate is the price rising after 2 years? 5re^(r/50) dollars per year

(c) Now suppose that r is increasing by 0.3 per year when r = 3 and t = 2. At what rate (dollars per year) is the price increasing at that time?

I just need help with part C, but I put up the answers on the other parts in case it is helpful to get the answer to C. I've tried C already and I get an incorrect answer of 5.466356401 dollars per year.

2007-10-28 17:40:22 · 1 answers · asked by Christian 1

x + y = -8
x - 2y = 7

2007-10-28 17:37:38 · 8 answers · asked by Anonymous

3x+4(x-8)-x=3/5(10x+15)

2007-10-28 17:33:46 · 5 answers · asked by Anonymous

Solve the proportion: 1/8=7/2h

2007-10-28 17:32:45 · 5 answers · asked by Anonymous

solve for z.

2007-10-28 17:32:34 · 3 answers · asked by candy 3

-4/7s=-28

2007-10-28 17:24:50 · 6 answers · asked by Michele P 1

1.If the square of 2 less than an integer is 1 6, find the number(s).

2. Solar collector is 2.5m long by 2.0m wide. It is held in place by a frame of uniform width around its outside edge. If the exposed collector is 4m^2 , what is the width of the frame to the nearest tenth of a centimeter?

3. The length of a rectangle is 2cm more than 3 times its width. If the area of the rectangle is 95cm^2 , find the dimensions of the rectangle.

4. The hypotenuse of a given right triangle is 6 cm longer than the shorter leg. The length of the shorter leg is 2 cm less than that of the longer leg. Find the lengths of the three sides.

5. If a ball is thrown vertically upward from a height of 5 ft, with an initial velocity of 80ft/s, its height h after t s is given by . How long does it take the ball to return to the ground?

2007-10-28 17:22:54 · 1 answers · asked by Amanda K 1

the problem is as simple as 4elevated to "x" equals 5 elevated to "x+1". Solve the equation exactly. I looks like this: (notice that x+1 is a exponent from 5. not 5 elvated to x and then +1). Also where *=x
4*=5(*+1) ===} (*+1) is an exponent. PLEASE HELP

2007-10-28 17:21:40 · 2 answers · asked by JJ 1

a. ( x^3 - 7x^2 + 2x - 4 ) % ( x + 2 )

b. (4 x^3 - 2x^2 + 7x - 1 ) % ( x - 2 )

2007-10-28 17:15:22 · 1 answers · asked by Anonymous