Math Answers

Reduce the following PDE to a set of three ODEs by the method of separation of
variables (1/r)(∂/∂r)(r(∂V/∂r)+(1/r^2)(∂^2V/∂θ^2)+(∂^2V/∂z^2)+(k^2)V=0

Bonnie claims single with 2 federal withholding allowances, and contributes state tax of 20% of her federal tax. Below is a copy of Bonnie's biweekly statement of earnings. Bonnie knows that her gross earnings and federal tax are correct, but she thinks that her net pay is not correct.


Earnings
Deductions

Week Ended
Regular
FED. SOC. MED STATE
WITH. WITH. CARE. WITH.
NET PAY
4/15
$760.00
$50.00 $47.12 $110.20 $10.00
$542.68

Using the fact that Social Security is 6.2% and Medicare is 1.45% of gross pay, explain why the given net pay is not correct. Determine how the error can be corrected, and what the net pay should be.

1. Evaluate the following integrals.

a) ∫_1^4▒√(5/x ) dx

b) ∫_1^9▒〖(3x-2)/√x dx〗

Having earned a bonus at his​ work, Rick placed the money in an investment earning
6.86% compounded monthly. He withdrew ​$370 at the end of every month for the next
4 years.
​(a) What was the amount of the​ bonus?
​(b) If he made all of the withdrawals as​ planned, how much interest was​ paid?

Let f(x,y)=x^2y/(x^4+y^2) if x^4+y^2not=0
=0. if x=y=0
examine whether
lim(x,y) tends to(0,0) f(x,y) exist or, not.

Let the function f:R^2-->R is defined as follow
f(x,y)=[xy(x^2-y^2)]/x^2+y^2 if(x,y )not=(0,0)
=0 if (x,y)=(0,0)
Then show that
1)fx(0,y)=y for all y

2)fx(x,0)=x for all x.
So that fxy(0,0)not=fyx(0,0)

Prove that
lim x tend to 0 xsin (2/x)=0

Find the point on the ellipse,(x^2/4)+y^2=1
that is nearest to the origin.

Find the massof an object which is in the form of a cuboid [0,1]×[2,4]×[1,3]Thedensity at any point(x,y,z)on the cuboid is given by del(x,y,z)= x^2+y^2+z^2.

Let x=e1+e2-2e3,y=2e1-e2+e3 where e1,e2,e3 are unit vector .find |x+y| and|x+2y|