# Get help with multivariable calculus equations

Recent questions in Multivariable calculus
Multivariable functions

### 4.3-16. Two random variables X and Y have a joint density $$\displaystyle{{f}_{{{x},{y}}}{\left({x},{y}\right)}}={\frac{{{10}}}{{{4}}}}{\left[{u}{\left({x}\right)}-{u}{\left({x}-{4}\right)}\right]}{u}{\left({y}\right)}{y}^{{3}}{\exp{{\left[-{\left({x}+{1}\right)}{y}^{{2}}\right]}}}$$ Find the marginal densities and distributions of X and Y.

Multivariable functions

### Which interval is wider: (a) the 95% confidence interval for the conditional mean of the response variable at a particular set of values of the predictor variables or (b) the 95% prediction interval for the response variable at the same set of values of the predictor variables?

Multivariable functions

### Determine an elliptic cylinder such that the length of its major axis length is 5/3 times of its minor axis. Find the complex potential , F(z) , and complex velocity, W(z) , for a uniform flow stream (at zero angle of attack) past the cylinder without circulation. You can use a=1 , and U=20 for your baseline flow parameters.

Multivariable functions

### Finding the Square Roots of a Complex Number In Exercises 31–38, find the square roots of the complex number. 31. 2i

Multivariable functions

### Use the discriminant to determine whether the quadratic equation has two equal real number solutions, two unequal real number solutions, or two complex number solutions. $$\displaystyle{9}{z}^{{2}}-{6}{z}+{1}={0}$$ two equal real number solutionstwo unequal real number solutions two complex number solutions

Multivariable functions

### Differentials with more than two variables Write the differential dw in terms of the differentials of the independent variables. $$\displaystyle{w}={f{{\left({x},{y},{z}\right)}}}={\sin{{\left({x}+{y}-{z}\right)}}}$$

Multivariable functions

### Find the complex zeros of the following polynomial function. Write f in factored form. $$\displaystyle{x}^{{4}}+{2}{x}^{{3}}+{22}{x}^{{2}}+{50}{x}-{75}$$ The complex zeros of f are ? Use the complex zeros to factor f.

Multivariable functions

### Convert the equation into a first-order linear differential equation system with an appropriate transformation of variables. $$y"+4y'+3y=x^2$$

Multivariable functions

### The joint probability distribution of thr random variables X and Y is given below: $$f(x,y)=\begin{cases}cxy & 0 a.Find the value of the constant. b.Calculate the covariance and the correlation of the X and Y random variables. c. Calculate the expected value of the random variable \(Z= 2X-3Y+2$$

Multivariable functions

### Describe in general terms how to solve a system in three variables.

Multivariable functions

### Let $$\displaystyle{\left({X}_{{1}},{X}_{{2}}\right)}$$ be two independent standard normal random variables. Compute $$\displaystyle{E}{\left[\sqrt{{{{X}_{{1}}^{{2}}}+{{X}_{{2}}^{{2}}}}}\right]}$$

Multivariable functions

### For each of the systems of equations that follow, use Gaussian elimination to obtain an equivalent system whose coefficient matrix is in row echelon form. Indicate whether the system is consistent. If the system is consistent and involves no free variables, use back substitution to find the unique solution. If the system is consistent and there are free variables, transform it to reduced row echelon form and find all solutions. $$\displaystyle{2}{x}_{{1}}-{3}{x}_{{2}}={5}$$ $$\displaystyle-{4}{x}_{{1}}+{6}{x}_{{2}}={8}$$

Multivariable functions

### Simplify all fractions! $$3^{-4}=?$$ $$x^{-6}=?$$ $$\frac{16x^{-10}}{2x^{-2}}=?$$

Multivariable functions

### Solve each equation over the set of complex numbers, find the magnitudes of the solutions and draw them in the complex plane. Hint: For some of the equations , to get n roots you must use $$\displaystyle{a}^{{3}}+{b}^{{3}}={\left({a}+{b}\right)}{\left({a}^{{2}}-{a}{b}+{b}^{{2}}\right)}$$ and $$\displaystyle{a}^{{3}}-{b}^{{3}}={\left({a}-{b}\right)}{\left({a}^{{2}}+{a}{b}+{b}^{{2}}\right)}$$ $$\displaystyle{x}^{{3}}+{1}={0}$$

Multivariable functions

### Exercise No. 10 (D.E. with coefficient linear in two variables) Find the general / solution of the following D.E. 4. $$(2x+3y-5)dx+(3x-y-2)dy=0$$

Multivariable functions

### Combine variables for this equation $$\displaystyle{f{{\left({x}\right)}}}={x}^{{2}}+{7}{x}-{9}$$

Multivariable functions

### Let $$\displaystyle{f{{\left({t}\right)}}}={t}+{i}$$ where $$\displaystyle-\pi{<}{t}{<}\pi$$ and has period $$\displaystyle{2}\pi$$. Why is it impossible to express the Fourier series of f(t) in real form? A. Because f(t) is a complex function with $$Re(f(x)) < 0$$ B. Because f(t) is a complex function with $$Im(f(x)) \neq 0$$ C. Because f(t) is a complex function with $$Im(f(x))=0$$ D. Because f(t) is a complex function with $$Re(f(x)) > 0$$

Multivariable functions

### Use the following linear regression equation to answer the questions. $$\displaystyle{x}_{{1}}={1.3}+{3.0}{x}_{{2}}-{8.3}{x}_{{3}}+{1.6}{x}_{{4}}$$ (a) Which variable is the response variable? (b) Which number is the constant term? List the coefficients with their corresponding explanatory variables. (c) If $$\displaystyle{x}_{{2}}={8},{x}_{{3}}={2},{\quad\text{and}\quad}{x}_{{4}}={6}$$ , what is the predicted value for $$x_1$$? (Use 1 decimal place) (d) Explain how each coefficient can be thought of as a "slope" under certain conditions.

Multivariable functions