Write the statement as an absolute value equation or inequality n is no more than 9 units from 7

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

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3 0

2 years ago

For f(x) = 6x + 20, what is the value of x for which f(x)= -4 ?

Ymorist [56]

Answer:

x = -4

Step-by-step explanation:

Plug in -4 into the function and solve for x:

f(x) = 6x + 20

-4 = 6x + 20

-24 = 6x

-4 = x

So, the answer is x = -4

3 0

2 years ago

Is it Giveaway time? Why are you making me add more text :/

givi [52]

I hope it is giveaway time cause I need points

7 0

2 years ago

Read 2 more answers

Can someone explain (d) and (e) please?

muminat

Part (d)

Answer: 180 degrees

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Explanation:

QS is a diameter, which makes angle SPQ to be 180 degrees (ie a straight angle). Arc QTS is also going to be 180 degrees, because all semicircles are half of the full circle of 360 degrees. So (1/2)*360 = 180.

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Part (e)

Answer: 50 degrees

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Explanation:

Angle QPR is a central angle that subtends (cuts off) the minor arc RQ, which is shown to be 50 degrees. The central angle is equal to this arc measure, so angle QPR is also 50 degrees

8 0

3 years ago

Please help, this was due yesterday. Ill give brainliest :) the red numbers (in order from top to bottom, left to right) are 112

ivolga24 [154]

I pretty sure it’s 116

6 0

2 years ago