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Find the volume of the solid whose base is the region enclosed by y=x^2 and y=2, and the cross sections perpendicular to the y-axis are squares.

Approximate the arc length of the curve y=(1/4)x^4 over the interval [1,2] using the Trapezoidal Rule T8. I was never taught how to use the Trapezoidal Rule, so I was surprised to find this problem in my most recent Calculus assignment. How would you solv...

Let r(t) = < sin(6t), cos(6t), sin(6t)cos(12t) >. Find the point where r(t) intersects the xy-plane on the interval π/6 < t < 3/12π.

Find the point on the plane z = 8x + 10y + 1 closest to the point P=(1, 0, 0).

Find the point (x0, y0) on the line 12x+12y=2 that is closest to the origin. I set ∇f to ∇g to get: <2x,2y> = λ<12,12> I then found λ = x/6 and λ = y/6, meaning that x = y Once I plugged that back into the constraint, I found the answer to be:(1/12,1/12)...

Convert the following point from rectangular to spherical coordinates: (1, −√3, 2√3). I found the answer to be (4, -pi/3, 0.5235987755983), but my online homework is stating that my middle coordinate (-pi/3) is incorrect. I put this into an online calcula...

Use spherical coordinates to calculate the triple integral of f(x, y, z)=y over the region x^2+y^2+z^2≤8, x, y, z ≤ 0.

A box contains 19 yellow, 29 green and 37 red jelly beans. If 14 jelly beans are selected at random, what is the probability that 5 are yellow?

Given that P(A)=0.81 and P(B|A)=0.23, find the joint probability P(A and B):

A foreman for an injection-molding firm admits that on 46% of his shifts, he forgets to shut off the injection machine on his line. This causes the machine to overheat, increasing the probability that a defective molding will be produced during the early...

This is a WebWork problem for my Calculus 2 class and all the answers I got from online calculators weren't considered correct, which is why I'm asking for some help on here.

I got 19C5 * 66C5 / 85C14 = 0.0000273503, but my online hw is saying this answer's incorrect. Am I missing something?

Yeah, I just realized my mistake, it was 66C9 for the remainder of the selections, not 66C5. Thank you though