Assignment calculus,simultaneous equation and logarithm

1. Jan 24, 2012

maali5

1. The problem statement, all variables and given/known data

Hi, teachers

I have been doing some work but I am confused.

Have you ever heard of this great math website www.wolframalpha.com (Google for maths).

This is one questions I done differantiate 3e^-4tsin(5t) and here is the link for the answers from

http://www.wolframalpha.com/input/?i=differantiate++3e^-4tsin(5t)

Although what I did is confusing to what the answers there?

This my solution

y=3e^-4t sin(5t)

u=3e^-4t v =sin(5t)

dy/dt=-12e^-4t dv/dt=-5cos(5t)

chain rule/product rule (1 of them)

ds/dt= 3e^-4t x 5cos(5t) + sin(5t) x -12e^-4t

factor

=3e^-4t (5cos(5t) - 4sin (5t))

Am I or the computer correct ?

Also while you are there? May you look at these two questions below

1) The table gives a firm’s monthly profits for their first few months of business. The numbers are rounded to the nearest £100.

Number of months after start up (x) 1 2 3 4 5 6
Profit for this month (£y) 500 800 1200 1900 3000 4800

The firm’s profits, £y, for the xth month after start up are modelled by

y = k x 10ax

where a and k are constants.

Plot this data on semi log paper to verify if this relationship is true.

Its about plotting semi-log paper but am confused. Can you give me guide on where to start answering the question.

Thanx agin

2)
Simultaneos question
y = x2 – 5x + 5 a

5x + 3y = 30. b

Find location of points collide?

x2 + 2y -25=0

x= -2+ square root(2^2-(4x1x(-25))/2 x = 4.09901

or

x= -2 - square root(2^2-(4x1x(-25))/2 x=-6.09

subsitue y etc

2. Jan 24, 2012

Staff: Mentor

The first derivative is du/dt, not dy/dt.
In the other derivative, you have a sign error.
Why ds/dt? Your original function is y, so the derivative would be dy/dt.

Also, don't use x for multiplication. If there happens to be a variable named x, you will confuse yourself.
This looks fine to me.

Be sure to include the three parts of the homework template.
Again, don't use x for multiplication

3. Jan 24, 2012

SammyS

Staff Emeritus

Hello maali5. Welcome to PF !

I used the link. What you asked WolframAlpha to differentiate, 3e^-4tsin(5t) , is equivalent to differentiating
$\displaystyle\frac{3 t\sin(5 t)}{e^4}\,.$​
You need to put parentheses around the -4t if you want WolframAlpha to differentiate
$\displaystyle\frac{3 \sin(5 t)}{e^{4t}}\,.$​
Write your function as 3e^(-4t)sin(5t) .

4. Jan 25, 2012

maali5

Thanx for your help. I got it.