March 2012
75 posts
So I walk into my calculus lecture, sit in the front row as always, and see three jokes about our Calc professor on the boards (his name is Vikram by the way):
- Vikram is the only one who can divide by zero
- Vikram doesn’t always drink, but when he does he prefers x^2.
- When Vikram does a pushup,…
satisfying the initial condition
oh, just saw the condition.
you would be able to figure it out by now then
:)
(dy/dx)[(x^2)/(y^2-6)]=1/2y
(2y dy)/(y^2 - 6) = x^(- 2) dx
( multiply both sides of your original equation by 2y dx and divide both sides by x^2)
Now, since the L.H.S. is of the form du/u (where u = y^2 - 6) and the R.H.S. is of the form u^n du, we can integrate, obtaining the following:
ln (y^2 - 6) = 1/x + C, where C is the constant of integration.
you will be needing some initial conditions like value of y or x to obtain value of c
February 2012
67 posts
in a school, 14% of students take drama and computer class, and 67% take drama class. what is the probability that a student takes computer class given that the student takes drama class?
Let’s say there are 300 students in school.
14% = combined drama/computer students = 42 students.
67% = 200 drama students.
Probability that ANY student is combined is 42/300 = 14%
Probability that DRAMA student is combined is 42/200 = 21%.
A particle moves according to a law of motion s = f(t). If f(t) = te^(-e/2), when is the particle moving in the positive direction?
v = ds/dt = df(t)/ dt = d[te^(-e/2)]/dt = e^(-e/2)= 1/[e^(e^2)]
so v >0 always.
so the particle moves in positive direction always.
This is a complete tutorial to solve Quadratic equations.
Quadratic equations can’t be simpler than this.
reblog or share it if you like it.
Pat is 20 years older than his son Patrick. In 2 years Pat will be twice as old as Patrick. How old are they now?
Pat is 20 years older than his son Patrick. In 2 years Pat will be twice as old as Patrick. How old are they now?
One number is nine more than twice another. If their sum is decreased by ten, the result is fourteen.
suppose patrick’s age is X. so pat’s age is 20+x
in two years, pat’s age will be 20+x+2
and patrick’s age will be x+2
given that 20+x+2 = 2(x+2)
22+x = 2x+4
or x = 18 i.e patrick’s age is 18 years. and pat’s age is 20+x = 20+18 = 38 years.
let first number be x
and
second number be y
it is given that x = = 2x+9
and x+y - 10 =14
solve these two equations and you would get the answer
Does anyone want to help me with my math homework?
you can direct your queries to me.
I need some help with equations.
shoot your queries. i will answer them.
welp?
Probability that a bus is ready for service is .84 = P1
probability that the bus is ready for service and has a working radio = . 67 = P2
probability that it has a working radio and is already ready for service
=P2/P1
=.67/.84=.798=79.8%
yeah. at point x= 0 and y = 0, i.e the origin, the curve has two tangents. By the defintion of a tangent, a tangent is a line that passes through one and only point of a curve.
hope that makes sense
IF YOU EXPLAIN TO ME HOW TO DO THIS QUESTION, I’LL LOVE YOU FOREVER.
So the original function is
http://www.wolframalpha.com/input/?i=2%28x%5E2%2By%5E2%29%5E2%3D25%28x%5E2-y%5E2%29
The derivative is
Man, thanks, how can I repay you, that is freaking awesome.
just share this tumblr blog. you don’t have to repay me anything.
if you have any further queries, feel free to ask.
I might reply late, but I do reply.
IF YOU EXPLAIN TO ME HOW TO DO THIS QUESTION, I’LL LOVE YOU FOREVER.
So the original function is
http://www.wolframalpha.com/input/?i=2%28x%5E2%2By%5E2%29%5E2%3D25%28x%5E2-y%5E2%29
The derivative is
http://www.wolframalpha.com/input/?i=%2825x-4x%5E3-4xy%5E2%29%2F%284x%5E2y%2B4y%5E3%2B25y%29
How do I find the points on the original function where the tangent line is horizontal.
Tangent is horizontal when dy/dx = 0
x (25 - 4x^2 - 4y^2) / [y (4x^2 + 4y^2 + 25)] = 0
x (25 - 4x^2 - 4y^2) = 0
x = 0 and 25 - 4x^2 - 4y^2 = 0
=> x^2 + y^2 = 25/4
put these values back into the original equation
x = 0
2(0+y^2)^2 = 25(0-y^2)
2y^4 + 25y^2 = 0
y^2 (2y^2 + 25) = 0
y = 0 or y^2 = -25/4( you reject this solution)
so you get a point x = 0 and y = 0 and at this point slope is indeterminate.
x^2 + y^2 = 25/4
2(x^2+y^2)^2 = 25(x^2-y^2)
2(x^2+y^2)^2 = 25(x^2+y^2-2y^2)
2(25/4)^2 = 25(25/4-2y^2)
625/8 = 625/4 - 50y^2
50y^2 = 625/4 - 625/8
50y^2 = 625/8
y^2 = 25/16
y = 5/4 and -5/4
put values of y so obtained here in this equation
x^2 + y^2 = 25/4
you would get values of x too.
