Ski shop made 80,000 profit this is 250 precent of last year’s profit

avanturin [10]

By direct substitution and simplification, the trigonometric function z = cos (2 · x + 3 · y) represents a solution of the partial differential equation $\frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z$ .

<h3>How to analyze a differential equation</h3>

Differential equations are expressions that involve derivatives. In this question we must prove that a given expression is a solution of a differential equation, that is, substituting the variables and see if the equivalence is conserved.

If we know that $z = \cos (2\cdot x + 3\cdot y)$ and $\frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z$ , then we conclude that:

$\frac{\partial t}{\partial x} = -2\cdot \sin (2\cdot x + 3\cdot y)$

$\frac{\partial^{2} t}{\partial x^{2}} = - 4 \cdot \cos (2\cdot x + 3\cdot y)$

$\frac{\partial t}{\partial y} = - 3 \cdot \sin (2\cdot x + 3\cdot y)$

$\frac{\partial^{2} t}{\partial y^{2}} = - 9 \cdot \cos (2\cdot x + 3\cdot y)$

$- 4\cdot \cos (2\cdot x + 3\cdot y) + 9\cdot \cos (2\cdot x + 3\cdot y) = 5 \cdot \cos (2\cdot x + 3\cdot y) = 5\cdot z$

By direct substitution and simplification, the trigonometric function z = cos (2 · x + 3 · y) represents a solution of the partial differential equation $\frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z$ .

To learn more on differential equations: brainly.com/question/14620493

#SPJ1

3 0

1 year ago

Which ordered pairs are solutions to the inequality 4x+y>−6?

Bingel [31]

2,0 solution

-3,6no solution

4,-20 no solution

0,-9 no solution

-1,-1 solution

3 0

2 years ago

Read 2 more answers

Sam wants to meet his friend Beth at a restaurant before they go to the ththeaterThe restaurant is nine kilometers south of the

nata0808 [166]

I suppose the restaurant's coordinates are (0, -9), but it is all relative, unless the coordinates of the restaurant have a y-value 9 less than the coordinates of the theater

4 0

2 years ago

Suppose y varies directly with x,and y=30 when x=3.what direct variation equation relates x and y.

Olenka [21]

Hello here is a solution :

direct variation equation relates x and y is : y = 10x

8 0

3 years ago

Square the binomial (x + y).

Zepler [3.9K]

Answer:

$x^2 + 2xy + y^2$