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harina [27]
3 years ago
7

Can someone give me the answer for this ​

Mathematics
1 answer:
ella [17]3 years ago
6 0

your answer is areas. area will be scaled by K^2

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Solve the differential equations dy/dx=((xy^2)+x)/y
arsen [322]

\displaystyle \dfrac{dy}{dx}=\dfrac{xy^2+x}{y}\\ \dfrac{dy}{dx}=\dfrac{x(y^2+1)}{y}\\ \dfrac{y}{y^2+1}\, dy=x\, dx\\ \int \dfrac{y}{y^2+1}\, dy=\int x\, dx\\ \dfrac{\ln (y^2+1)}{2}=\dfrac{x^2}{2}+C\\ \ln(y^2+1)=x^2+C\\ y^2+1=e^{x^2+C}\\ y^2=e^{x^2+C}-1\\ y=\sqrt{e^{x^2+C}-1} \vee y=-\sqrt{e^{x^2+C}-1}\\ \boxed{y=\sqrt{Ce^{x^2}-1} \vee y=-\sqrt{Ce^{x^2}-1}}\\

7 0
3 years ago
Michaels test scores for this semester were 83,80,91,74,66,99,87,72,95,98. What was the median of his scores
atroni [7]

Answer:

85

Step-by-step explanation:

Write the numbers in order

66, 72, 74, 80, 83, 87, 91, 95, 98, 99

Find the middle number

83 and 87 are in the middle, so find the mean of them. 83+87= 170

170/2 = 85.

5 0
2 years ago
Read 2 more answers
Solve the following differential equation: (2x+5y)dx+(5x−4y)dy=0 *Hint: they are exact<br><br> C=.
Tpy6a [65]

Answer with Step-by-step explanation:

The given differential equation is

(2x+5y)dx+(5x-4y)dy=0

Now the above differential equation can be re-written as

P(x,y)dx+Q(x,y)dy=0

Checking for exactness we should have

\frac{\partial P}{\partial y}=\frac{\partial Q}{\partial x}

\frac{\partial P}{\partial y}=\frac{\partial (2x+5y)}{\partial y}=5

\frac{\partial Q}{\partial x}=\frac{\partial (5x-4y)}{\partial x}=5

As we see that the 2 values are equal thus we conclude that the given differential equation is exact

The solution of exact differential equation is given by

u(x,y)=\int P(x,y)dx+\phi(y)\\\\u(x,y)=\int (2x+5y)dx+\phi (y)\\\\u(x,y)=x^2+5xy+\phi (y)

The value of \phi (y) can be obtained by differentiating u(x,y) partially with respect to 'y' and equating the result with P(x,y)

\frac{\partial u}{\partial y}=\frac{\partial (x^2+5xy+\phi (y)))}{\partial y}=Q(x,y))\\\\5y+\phi '(y)=(5x-4y)\\\\\phi '(y)=5x-9y\\\\\int\phi '(y)\partial y=\int (5x-9y)\partial y\\\\\phi (y)=5xy-\frac{9y^2}{2}\\\\\therefore u(x,y)=x^2+10xy-\frac{9y^2}{2}+c

5 0
3 years ago
A farmer sells four of his farm products Maize, Potatoes, carrots and tomatoes in each of 2 towns into classes of 3 customers. C
nordsb [41]

Answer:

Step-by-step explanation:

7 0
2 years ago
The population of a city is expected to
Furkat [3]

\huge\boxed{1.0925p}

Since the population is going to increase by a certain percentage, we have to add 100\% to the percentage to keep the original population.

9.25\%+100\%=109.25\%

Now, convert the percentage into a decimal. You can do this by moving the decimal place two places to the left.

109.25\longrightarrow 1.0925

Now, just multiply that by p.

\large\boxed{1.0925p}

8 0
3 years ago
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