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3 years ago

Which equation below represents exponential decay?

Mathematics

1 answer:

8_murik_8 [283]3 years ago

8 0

C. y=2(1/4)^x

B is just a linear functions and the other two aren't exponential functions

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Solve the linear differential equation 2xy' + y = 2√x

77julia77 [94]

Answer:

Step-by-step explanation:

General form of the linear differential equation can be written as:

$\frac{dy}{dx}+P(x)y=Q(x)$

For this case, we can rewrite the equation as:

$\frac{dy}{dx}+\frac{1}{2x}y=\frac{\sqrt{x}}{x}$

Here $P(x) =\frac{1}{2x}; Q(x)=\frac{\sqrt{x}}{x}$

To find the solution (y(x)), we can use the integration factor method:

$Fy(x)=\int Q(x)Fdx+C \rightarrow F=e^{\int P(x)dx$

Then $F=e^{\int \frac{1}{2x}dx}=e^{\frac{1}{2}\ln|x|\right}=\sqrt{|x|}$

So, we can find:

$y\sqrt{|x|}=\int \frac{\sqrt{x}\sqrt{|x|}}{x}dx+C$

Suppose that $x\in \double R$ , then $\sqrt{|x|}=\sqrt{x}$ , and we find:

$y\sqrt{x}=x+C \rightarrow y(x)=\sqrt{x}+\frac{C\sqrt{x}}{x}$

To check our solution is right or not, put your y(x) back to the ODE:

$y' = \frac{1}{2\sqrt{x}}-\frac{C}{2\sqrt{x^{3}}}$

$2xy'=\frac{x-C}{\sqrt{x}}$

$2xy'+y=\frac{x-C}{\sqrt{x}}+\sqrt{x}+\frac{C\sqrt{x}}{x}=2\sqrt{x}$

(it means your solution is right)

3 0

2 years ago

Please help me in the question of commission ! Grade - 9 .

AlladinOne [14]

Answer:

Step-by-step explanation:

Commission for amount Rs. 5,00,00 = $\frac{2}{100}*500000$

= 2* 5000

= Rs. 10,000

total commission = Rs. 32,000

Remaining commission = 32500 - 10000

= Rs. 22500

Let remaining amount of the restaurant = Rs. x

Commission on Rs. x = 22500

3% of x = 22500

$\frac{3}{100}*x=22500\\\\x=22500*\frac{100}{3}\\\\x = 7500*100$

x = Rs. 750000

Price of the restaurant = 750000 + 500000

=Rs . 1250000

7 0

3 years ago

from the top of a cliff 20m high,a boat can be sighted at sea 75m from the foot of the cliff.calculate the angle of depression o

r-ruslan [8.4K]

Answer:

The angle of depression will be= 14.9 degrees

Step-by-step explanation:

tanx=20/75=0.267

x=tan−10.267=14.93°

x= 14.9°

3 0

3 years ago

Somebody please help me:(

Varvara68 [4.7K]

How do you need help?

3 0

3 years ago

Read 2 more answers

Which property justifies the following statement? If 12x = 84, then x = 7

makkiz [27]

Answer:

<h2>B. Division Property of Equality </h2>

Step-by-step explanation:

$12x=84\qquad\text{divide both sides by 12}\\\\\dfrac{12x}{12}=\dfrac{84}{12}\\\\x=7$

7 0

3 years ago