Consider the paraboloid nd the point Upper P (10 comma 0 )on the level curve f (x comma y )equals0. 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.

Hannah is 3 years older than twice her brother joey’s age. joey is 2 years old. how old is hannah? show all of your work! the number of students is five more than seven times the number of teachers. there are 10 teachers. how many students are there? be sure to show all of your work!

Proceed as in example 3 in section 6.1 to rewrite the given expression using a single power series whose general term involves xk. ∞ n(n − 1)cnxn − 2 n = 2 − 4 ∞ ncnxn n = 1 + ∞ cnxn n = 0

Ageologist had two rocks on a scale that weighed 4.6 kilograms together.rock a was 0.5 of the total weight.how much did rock a weigh?