What is 7p-(-5)+(-1)

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

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3 0

1 year ago

30% of all the students in a school are in a play all students except for 140 are in the play how many students are in the schoo

Bezzdna [24]

To figure out how many kids are in the school, you must set up an equation with x representing the number of students. 30% of the students are in the play, so that would be represented by 0.3x. We also know that 140 students are not in the play, that could be represented by x-140. These two equations will equal each other since they both represent the same information, which is the number of children in the play. You set those two equations equal to one another (0.3x = x-140). You then can add 140 to the left side of the equation and subtract 0.3x from the right side. We do this in order to get both values of x on the same side of the equation. We then can simplify the right side of the equation by subtracting 0.3x from 1x. We get 0.7x. Our equation now looks like 140 = 0.7x. We must now divide each side of the equation by 0.7 in order to get the x all by itself and find its value. 140 divided by 0.7 is 200. The number of students in the school is 200.

3 0

2 years ago

Carl has 3 1/2 cups of blueberries. He is storing them in containers that each hold 2/3 cup. How many containers can he fill? Fi

aivan3 [116]

Answer:

The total number of containers than can be filled = $5\frac{11}{50}$

Step-by-step explanation:

The amount of blueberries Carl has = 3 1/2 cups

Now, $3\frac{1}{2} = 3 + \frac{1}{2} = 3 + 0.5 = 3.5$

⇒The amount of blueberries Carl has = 3. 5 cups

Also,the amount of blueberries each container can store = 2/3 cups

Now, $\frac{2}{3} = 0.67$

⇒The amount of blueberries each container can store = 0.67 cups

So, \textrm{Total cpus that can be filled by blueberries} = \frac{\textrm{Toaal amount of blueberries to be stored}}{\textrm{Bluebeeries stored in 1 cup}}

= $\frac{3.5 cup}{0.67 cup} = 5.22$

Now, $5.22 = 5 + 0.22 = 5 + \frac{22}{100} = 5 + \frac{11}{50} = 5 \frac{11}{50}$

Hence, the total number of cups than cen be filled with the blue berries = 5 11/50

⇒ Blueberries can fill 5 full cups and 11/50th of the 6th cup.

3 0

3 years ago