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ohaa [14]
3 years ago
8

Car A began a journey from a point at 9 am, traveling at 30 mph. At 10 am car B started traveling from the same point at 40 mph

in the same direction as car A. At what time will car B pass car A? PLEASE show work!
Mathematics
1 answer:
mafiozo [28]3 years ago
5 0

At 10 am, Car A is at 30 miles.

Then at 11 am, Car A is at 60 miles and Car B is at 40 miles

At 12 am, Car A is at 90 miles and Car B is at 80 miles

At 1 pm, Car A and B are tied for 120 miles

The very second after Car B passes Car A

Answer: 1:01 pm Car B Passes Car A

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Simplify (3^3 x 5^3)^-2
MatroZZZ [7]

(3^3 x 5^3)^-2

3^-6 x 5^-6

15^-6


7 0
3 years ago
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
4 years ago
Which of the values for x and y make the equation 2x + 3y + 4 = 15 true?
natima [27]
2(1)+3(3)+4=15
2+9+4=15
Or
2(4)+3(1)+4=15
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So either one would work
7 0
4 years ago
What is the remainder when 7^85 is divided by 41? How can you solve this without using a calculator?
Leto [7]

Answer:

you are supposed to divide it

Step-by-step explanation:

41divided by 85=

4 0
4 years ago
Doris made 80 cookies this week. She baked 4 less than three times the total she made last week. Which equation, when solved for
sertanlavr [38]

Answer:

The equation is  3x-4=80

The value of x is 28 cookies

Step-by-step explanation:

Let

x ---->  the number of cookies she baked last week

we know that

The number of cookies she baked last week multiplied by 3 minus 4 must be equal to 80 cookies

so

The linear equation that represent this situation is

3x-4=80

solve for x

3x=80+4\\3x=84\\x=28\ cookies

3 0
3 years ago
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