 # Get help with multivariable calculus equations

Recent questions in Multivariable calculus Brody Collins 2022-05-14 Answered

### for the function f(x,y)= $\sum _{i=1}^{n}\left[\left({x}_{i}{\right)}^{4\ast {y}_{i}}+\left(1-{y}_{i}\right)ln{x}_{i}\right]$, y are binary variables, x nonnegative real values with fixed upper bound C. Does the minimization min f(x,y) have a unique solution or not? Eve Dunn 2022-05-12 Answered

### How to solve for $a,b,c,d$ from two equations?Need to understand how to solve the following question:You have $50$ coins that add up to $1$ dollar. What are the possible combinations of pennys, nickels, dimes, and quarters that will satisfy these limits?$P+N+D+Q=50$$.01P+.05N+.10D+.25Q=1$ Govindennz34j 2022-05-10 Answered

### This is taken from one of the lecture slides, where a simplification of the quadratic formula is attempted:$\left(x-{x}_{A}{\right)}^{T}A\left(x-{x}_{A}\right)+{a}^{T}\left(x-{x}_{a}\right)+b$and from there I expand the brackets, which yields:$\left(x-{x}_{A}{\right)}^{T}A\left(x-{x}_{A}\right)+{a}^{T}\left(x-{x}_{a}\right)+b={x}^{T}Ax-{x}_{A}^{T}Ax-{x}_{A}^{T}A{x}_{A}+{a}^{T}x-{a}^{T}{x}_{a}+b$In the next step the factorization is used to rearrange the formula:$\left(x-{x}_{A}{\right)}^{T}A\left(x-{x}_{A}\right)+{a}^{T}\left(x-{x}_{a}\right)+b={x}^{T}Ax+\left(-{A}^{T}{x}_{A}-{x}_{A}^{T}{A}^{T}+a{\right)}^{T}x+\left({x}_{A}^{T}A{x}_{A}+b-{a}^{T}{x}_{a}\right)$I do not understand how the linear term has been transposed from $\left({x}_{A}^{T}{A}^{T}{\right)}^{T}x$. Can someone explain this ? Yaritza Oneill 2022-05-09 Answered

### Most statements of Constraint Qualification I have found in the literature mention a locally "locally optimal solution" of the problem:$\left\{\begin{array}{l}minf\left(x\right)\\ \text{s.t.}\\ {g}_{i}\left(x\right)\le 0\end{array}$It is stated that when a C.Q. holds at a local optimum, then there exist Lagrange multipliers that satisfy KKT conditions.But, I cannot get my head around this notion of local optimality. Does it mean locally optimal for the unconstrained problem? Does not local optimality imply the satisfaction of the KKT conditions? Brooklynn Hubbard 2022-05-09 Answered

### Could you help me solve this problem please ?1. Maximize ${x}^{t}y$ with constraint ${x}^{t}Qx\le 1$ (where $Q$ is definite positive)What I tried : I tried using KKT but I don't know why I get $-\sqrt{{y}^{t}{Q}^{-1}y}$ as the maximum instead of $\sqrt{{y}^{t}{Q}^{-1}y}$ (which I believe is the maximum). Also, since ${x}^{t}y$ is linear (convex and concave), I don't know how to conclude...2. Conclude that $\left({x}^{t}y{\right)}^{2}\le \left({x}^{t}Qx\right)\left({y}^{t}{Q}^{-1}y\right)$$\mathrm{\forall }x,y$ (generalized CS) pettingyg0 2022-05-03 Answered

### Solve for w: 0=-7w+5x-3. Davian Lawson 2022-05-03 Answered

2022-05-02

### use squeeze theorem find the following lim x,y-0,0 y^2(1-cos2x) /x^4 +y^2 ngihlungeqtr 2022-05-02 Answered

### Solve for x: 0=-4u-7x+4. Gage Potter 2022-05-02 Answered

### Solve for w in the equation y-1=4wy-6. dificultehcm 2022-05-01 Answered

### Solve for v in the equation -7=3uv+4. Jordin Olsen 2022-05-01 Answered

### Solve for x in the equation 3-3x=w+1. Jordin Olsen 2022-05-01 Answered

### Solve for w: 0=-6u-7w-6. broggesy9 2022-04-30 Answered

### Solve for x: 0=3u-7x-9. Judith Warner 2022-04-30 Answered

### Solve for y: 0=u-5y+1. Dania Robbins 2022-04-30 Answered

### Solve for x in the equation a-7x+4=0. Edith Mayer 2022-04-07 Answered

### I want to ask whether the following question has a closed form solution:We can write down the kkt condition as:$\begin{array}{rl}L& ={c}^{T}x-⟨{\lambda }_{1},{\mathbf{1}}^{T}x-b⟩-⟨{\lambda }_{2},x⟩\\ \mathrm{\partial }L/\mathrm{\partial }x& =c-\mathbf{1}{\lambda }_{1}-{\lambda }_{2}=0\\ \left[{\lambda }_{2}{\right]}_{i}\cdot {x}_{i}& =0\\ \left[{\lambda }_{2}{\right]}_{i}& \ge 0\end{array}$Denote ith component of $c$ as ${c}_{i}$. Now we can see that when $\left({c}_{i}-{\lambda }_{1}\right)\ge 0$, then we must have ${x}_{i}=0$ and $\left({c}_{i}-{\lambda }_{1}\right)=0$, we also must have ${x}_{i}>0$. But I am not sure how to proceed to the next. lasquiyas5loaa 2022-04-07 Answered

### $U$ is a random variable that follows Uniform distribution with interval  follows Bernoulli distribution with mean $U$. How do I find the function $f:\left(0,1{\right)}^{n}->R$ that minimizes $E\left[\left(U-f\left({X}_{1},...,{X}_{n}\right){\right)}^{2}\right)\right]$ ? I have no idea where to start solving. Thank you in advance. habib A 2022-04-02

2022-03-24

### As you start exploring calculus and analysis, you will encounter multivariable calculus equations that are self-explanatory as well because all of them will contain at least two questions related to each variable being involved. See our multivariable calculus examples to receive more help and information regarding how these are used. The answers to solving these multivariable calculus questions should be based on finding the deterministic behavior. These are used in engineering and those fields where the parametric equations solver will provide you an optimal control of time dynamic systems. As an interesting subject, applying at least one equation in practice will keep you inspired!