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3 years ago

In a class of 30 students, 12 have a cat and 19 have a dog. There are 6 students who

Mathematics

1 answer:

Anna007 [38]3 years ago

7 0

Answer:

19/30

Step-by-step explanation:

30 students

12 have cat , 19 have dog , 6 no cat or dog

P dog = 19 have dogs/30 students total = .633333...

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Find the solution the each of the following first order linear differential equations:

Cerrena [4.2K]

Answer:

a. $y=\frac{2}{3}x^7+cx^4$

b. $y=2e^{7x}-ce^{5x}$

c. $y=e^{-2x}arctan(e^{2x})+ce^{-2x}$

d. $i=e^{-2t}\left(\frac{8\left(3e^{2t}\sin \left(3t\right)+2e^{2t}\cos \left(3t\right)\right)}{13}+C\right)$

Step-by-step explanation:

a) xy' -4y = 2 x^6

$xy'-4y=2x^6\\y'-\frac{4}{x}y=2x^5\\p(x)=\frac{-4}{x}\\Q(x)=2x^5\\\mu(x)=\int P(x)dx=\int \frac{-4}{x}dx=Ln|x|^{-4}\\y=e^{-\mu(x)}\int {e^{\mu(x)}Q(x)dx}\\y=x^4 \int {x^{-4}2x^6}dx\\y=\frac{2}{3}x^7+cx^4$

b) y' - 5y = 4e^7x

$y'-5y=4e^{7x}\\p(x)=-5\\Q(x)=4e^{7x}\\\mu(x)=\int P(x)dx=\int-5dx=-5x\\y=e^{-\mu(x)}\int {e^{\mu(x)}Q(x)dx}\\y=e^{5x}\int {e^{-5x}4e^{7x}}dx\\y=2e^{7x}-ce^{5x}$

c) dy/dx + 2y = 2/(1+e^4x)

$\frac{dy}{dx}+2y=\frac{2}{1+e^{4x}}\\p(x)=2\\Q(x)=\frac{2}{1+e^{4x}}\\\mu(x)=\int P(x)dx=\int 2dx=2x\\y=e^{-\mu(x)}\int {e^{\mu(x)}Q(x)dx}\\y=e^{-2x}\int {e^{2x}\frac{2}{1+e^{4x}}}dx\\y=e^{-2x}arctan(e^{2x})+ce^{-2x}$

d) 1/2 di/dt + i = 4cos(3t)

$\frac{1}{2}\frac{di}{dt}+i=4cos(3t)\\\frac{di}{dt}+2i=8cos(3t)\\p(t)=2\\Q(t)=8cos(3t)\\\mu(t)=\int P(t)dt=\int 2dt=2t\\i=e^{-\mu(t)}\int {e^{\mu(t)}Q(t)dt}\\i=e^{-2t}\int {e^{2t}8cos(3t}dt\\i=e^{-2t}\left(\frac{8\left(3e^{2t}\sin \left(3t\right)+2e^{2t}\cos \left(3t\right)\right)}{13}+C\right)$

3 0

3 years ago

Least common denomiator of 7/9 and 11/6

Over [174]

9514 1404 393

Answer:

Step-by-step explanation:

The least common denominator (LCD) is the least common multiple (LCM) of the denominators.

Here, the denominators are ...

9 = 3·3

6 = 3·2

So, their LCM is 3·3·2 = 18.

The least common denominator of the given fractions is 18.

7/9 = 14/18

11/6 = 33/18

4 0

3 years ago

One step equations x/4 =9

Tamiku [17]

Hi Natalie

We have x/4 = 9

All you have to do is cross multiplication

x = 4*9

x= 36

That's all :)

I hope that's help:)

Now if you wanna check my answer just replace x by 36

36/4 = 9

9= 9

Because when you divide 36 by 4 you will find 9

I hope that's help:)

8 0

3 years ago

Read 2 more answers

Graph the function f(x) = -3/5x+8.

emmasim [6.3K]

Answer:

The y-intercept is at (0,8), so you can graph that point. Then the slope is -3/5. So the change in y coordinate divide the change in x coordinate is always -3/5. Thus 8-y/0-x=-3/5. You can choose any value for y and x as long as 8-y=-3. And 0-x=5. The point on the graph will just be (x,y) for the values you find.

6 0

3 years ago

WIll GIVE BRAINLYEST TO WHOEVER ANSWERS BOTH QUESTIONS FIRST CORRECTLY

omeli [17]

Answer:

1. 8.4 in 2. 33.6

Step-by-step explanation:

6 0

3 years ago