Calculus Answers

Find the equation for the circle of curvature of the curve r(t)=(sqrt2)(t)(ihat) + (t^2)(jhat) at the point (sqrt8, 4) (this curve parameterizes the curve y=(1/2)(x^2) in the xy-plane)

Along with the problem please explain
1. What value of t corresponds to the indicated coordinates?
2. What elements will you need for the equation of the circle?
3. What values and vectors will aide you in finding the elements of the circle?
4. How will you use these values and vectors to obtain the necessary elements?

What is the integral of (x^3+1) / (x^3+4*x^2+5*x)?

Heidi has 3 times more books than Olga. And together they have 44 books. how much does each girl have?

the radius of the earth is 6.37 x 10 to the power of 6 metres. how do i convert this distance to metres?

if square tables are arranged in a restaurant so that only one person can sit on any side of the table, how many tables will it take to seat 40 people ?

A water tank of 1000 liters capacity is connected to a tap, which can fill at the rate of of 20 liters per minute and water is let out at the same time at the rate of 6 liters per minute.After an hour the outlet is shut off.Find how long will it take now for the tank to become full?

a curve has equation y=3x^2 -14x+5. the point q lies on the curve and the tangent at q is parallel to the line with equation y=x-42. find the x coordinate of q

find derivative of each function using first principles (use definition) and then evaluate the slope of the tangent line at the given point.

y= x/ (x-1) (-3, 3/4)

A triangle has side c=2 and angles A=pi/4 and B=pi/6. Find the length of the side opposite A.

Evaluate the trigonometric function for each value of theta
theta=(-3pi/4), find sin(theta),cos(theta),tan(theta),cot(theta),sec(theta),csc(theta).
theta=(-pi/4), find sin(theta),cos(theta),tan(theta),cot(theta),sec(theta),csc(theta).
theta=(2pi/3), find sin(theta),cos(theta),tan(theta),cot(theta),sec(theta),csc(theta).