Math Answers

Hello, I need help with one of my assignment questions. How do you calculate the diameter of a pipe needed to water a track with only knowing the flow rate of 0.7 l/sec

Examine whether lim x to 0 (e^1/x)/(e^1/x +1) exist or not.

state whether the following statements are true or false. justify your answers.
1) lim x to 0 (1/x^2 -1/sin^2x)is in (0/0) form.
2) f(x,y)={sin(x^2y/x^3 +y^3)}/ln(x+y/x) is a homogeneous funtion of degree 2.
3) Domain of f(x,y)=xy/(x^4 +y^4) is R^2.
4) The funtion f(x,y)=(x^3y +1, x^2 +y^2) is locally invertible at (1,2).
5) The funtion f(x,y)=x^3 +y^3 is integrable on [1,2]*[1,3].

Find the equation of circle with center at the origin and tangent to the line 2x - 5y =8.

Find the standard form of the equation of circle whose center is at (4,3) which passes through the origin. Draw the circle

If you save three pennies on January 1, six pennies on January 2, nine pennies on January 3, and continue this pattern for one year (not a leap year), what will be the value of your entire savings, in dollars, at the end of that one year? Express your answer as a decimal.

Write an odd natural number as a sum of two integers m_1 and m_2 in a way that m_1 m_2 is maximum.

Prove that 1/2 (x+y+z ) <= ( x^2/y+z) +( y^2/x+z)+ ( z^2/x+y) , for x, y, z >0.

Show that 1+(1/√2)+...+(1/√n)>= √2 √(n-1) , for n belongs to N , n>1.

Is Cramer 's Rule applicable for solving the linear system below? If yes, apply it. Otherwise, alter the last equation in the system so that the solution can be obtained by applying the rule.
x+y+z=π
-πx +πy+ √2 z =0
π^2 x+ π^2 y+2z =0.