Jar one has 133 pennies. Jar 2 has 127 times jar one. How many pennies does jar 2 have?

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

The Russian ice breaker you mall can move forward through 2.3 m thick ice at a speed of 5.5 km/h. Right and solve a multiplicati

viktelen [127]

Answer:

The Multiplication equation to find the number of hours taken to travel the distance is $5.5\times x=82.5$ .

It will taken 15 hours by Russian ice breaker to travel a distance of 82.5 km through the ice.

Step-by-step explanation:

Given:

Thickness of the ice = 2.3 m

Speed while moving forward = 5.5 km/h

Distance to travel through the ice = 82.5 km

We need to write and solve the multiplication equation to find the number of hours taken to travel the distance.

Solution:

Let the number of hours taken to travel the distance be 'x'.

Now We know that;

By Distance formula;

Distance traveled is equal to Speed while moving forward multiplied by the number of hours taken to travel the distance.

framing in equation form we get;

$5.5\times x=82.5$

Hence The Multiplication equation to find the number of hours taken to travel the distance is $5.5\times x=82.5$

On Solving above equation we get;

Dividing both side by 5.5 we get;

$\frac{5.5x}{5.5}=\frac{82.5}{5.5}\\\\x=15 \ hrs$

Hence It will taken 15 hours by Russian ice breaker to travel a distance of 82.5 km through the ice.

8 0

2 years ago

Sean is conducting an experiment with an isotope of a particular element that has a half life of 4 hours. He begins with a sampl

Alex Ar [27]

Answer:

/??

Step-by-step explanation:

5 0

3 years ago

What is the domain of the function..... {TIMED PLS HURRY}

timofeeve [1]

try c im sorry if im wrong i tried

6 0

2 years ago

What is the solution to the equation 2 (x-3) ^2 =13 help help ASAP !

olganol [36]

Answer:

3+sqrt(13/2)

3-sqrt(13/2)

Step-by-step explanation:

2 (x-3) ^2 =13

Divide each side by 2

2/2 (x-3) ^2 =13/2

(x-3) ^2 =13/2

Take the square root of each side

sqrt((x-3) ^2) =±sqrt(13/2)

x-3 = ±sqrt(13/2)

Add 3 to each side

x-3+3 = 3±sqrt(13/2)

x = 3±sqrt(13/2)

4 0

3 years ago

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