Recent content by mirandasatterley

Homework Statement Find the volume of the region bounded by z=x+y, z=10, and the planes x=0, y=0 The Attempt at a Solution If I want to integrate with respect to z,y, then x; Then I think the limits of integration would be 0≤x≤z-y, so for x the be its largest, set y=0 and z to be...

So, ∫0-9∫Square root of x -3 f(x,y) dydx

In a similar situation where i have to switch the order of integration from ∫0-3∫y2-9 f(x,y) dxdy to dydx, Is this also a parabola on it's side, with intercepts through (3,9) and (0,9), meaning that I would be setting up the new limits of integration, fro the portion of the parabola above y=0?

Homework Statement Find the volume of the region under the graph of f(x,y) = x+y and above the region y2≤x, 0≤x≤9 The Attempt at a Solution From these equations, x will be integrated from 0-9, but I'm not sure about y. My thinking is that y will be intgrated from 0-3 because y2≤x...

Homework Statement Use lagrange multipliers to find the maximum and minimum values of f subject to the given constraint, if such values exist. f(x,y) = x+3y, x2+y2≤2 Homework Equations grad f = λ grad g The Attempt at a Solution to find critical points in the interior region...

I think I understand, so when I solve z=a, and plug this into the addition definition, I am proving that (0,a) is the zero vector since (x,y) ++ (0,a) := (x,y)?

For the existence of a negative: there exists a -v such that v + (-v) = 0, does the following proof make sense? Let me know if I am missing something. Thanks. (x,y) is a vector v (w,z) is the vector -z, so I need to prove that (w,z) = -(x,y), so I have the equation, (x,y) + (w,z) = (0,0)...

So, if (w,z) is the zero vector and (x,y) is any vector, then (x,y) + (w,z) = (x,y), and addition is defined as (x,y) ‡ (w,z) := (x+w, y+z-a) Can I set these equations equal to each other? to get (x,y) = (x+w, y+z-a) therefore, x= x+w, and subtracting x from both sides gives w=0, and...

Homework Statement Let F be any field, and fix a є F. Equip the set V = F2 with two operations as follows. Define addition by (x, y)‡(x', y') := (x + x', y + y' − a), for all x, x', y, y' є F, and define the scalar multiplication by scalars by c * (x, y) := (cx, cy − ac + a), for all x...

Homework Statement True or False: The intersection of two planes in R3 is always a line. The Attempt at a Solution I'm pretty sure that this statement is true because two planes can only be parallel, or they must intersect in a line because the are infinite. But I have no ideas on...

I have tried quite a few different things and it seems that If both A and B are diagonals this works, but since diagonal matrices can be row reduced to the Identity matrix, does this make number 3 true? When only one of A or B are diagonals, it doesn't seen to work out unless one is the...

My question has 5 short parts and for each, I'm supposed to give a counterexample if the statement is false or give an argument to prove that a statement is true. 1.Q: Linear system with m equations and n variables. If m> or = to n, then the system can have at most 1 solution. A: I think...

Homework Statement When heating the methyl methacrylate reaction (methyl methacrylate and dibenzoyl peroxide) to 90-95oC, why do bubbles evolve from the solution? Homework Equations None The Attempt at a Solution I'm not sure why the bubbles form. Any hints or helpful websites?

[SOLVED] Cross-linking polymers Homework Statement What changes in consistency (if any) do you expect when adding more borax solution to your slime? Why? Homework Equations None The Attempt at a Solution Slime is a cross-linked polymer. Borax (borate ion) is the cross-link. So...

Okay - it's 1 right? Thank you for all of your help!