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steposvetlana [31]
2 years ago
6

Communicate Mathematical Ideas Why do you subtract exponents

Mathematics
1 answer:
zysi [14]2 years ago
5 0

Answer:

We subtract exponents when diving powers with the same base because they eventually get canceled out when written in expanded form.

Step-by-step explanation:

For example, if we expand the given fractions:

10^3/10^1 = 1000/10 = 100 = 10^2

Now, if we subtract the exponents we get the same result.

10^3-1 = 10^2

So, a^m/a^n = a^m-

n is one of the exponent rules which saves time and makes calculation easier.

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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
200 cans of food were distributed to 3 charity homes. 2/5 of the cans were given to the first home, 1/3 of the remainder to the
Mrrafil [7]
I believe 80 cans were given
8 0
3 years ago
A jar contains 2 red marbles, 5 blue marbles, and 1 green marble. What is the probability of selecting a red
mixer [17]

Answer:

1/4

Step-by-step explanation:

2+5+1=8

8 divided by 100% =12.5%

5 0
3 years ago
Some other person's sales tax is $1.61. How much was their subtotal?
sleet_krkn [62]
I tried helping but failed ☹️ your guess is as good as mine
6 0
3 years ago
Read 2 more answers
Please help me with this I'm stuck,
algol [13]
Y = -2x -5 


why?
-2x is found since in the table the x value is 0 and the y = -2

-5 because you are adding -5 every time 

0= -2
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-3 = -17
8 0
3 years ago
Read 2 more answers
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