Consider the paraboloid f(x, y) = 1 - (x²/25) - (y²/9) and the point P (5, 0) on the level curve f(x, y) = 0.
Compute the slope of the line tangent to the level curve at P and verify that the tangent line is orthogonal to the gradient at that point.

The ratio of wooden bats to metal bats in the baseball coach’s bag is 2 to 1. if there are 20 wooden bats, how many metal bats are in the bag?

One number is 4 less than 3 times a second number. if 3 more than two times the first number is decreased by 2 times the second number, the result is 11. use the substitution method. what is the first number?

If the car had not hit the fence, how much farther would it have skidded? solve the skid-distance formula to find the extra distance that the car would have traveled if it had not hit the fence. round your answer to two decimal places. note that unit conversion is built into the skid distance formula, so no unit conversions are needed.