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Daniel [21]
3 years ago
10

Solve the initial-value problem. x' + 2tx = 5t, x(0) = 8 x(t) =

Mathematics
1 answer:
11111nata11111 [884]3 years ago
8 0

Multiply both sides of the ODE

x'+2tx+5t

by e^{t^2}:

e^{t^2}x'+2te^{t^2}x=5te^{t^2}

Now the left side can be condensed as the derivative of a product:

\left(e^{t^2}x\right)'=5te^{t^2}

Integrate both sides, then solve for <em>x</em> :

e^{t^2}x=\dfrac52e^{t^2}+C

\implies x(t)=\dfrac52+Ce^{-t^2}

Given that <em>x</em>(0) = 8, we find

8=\dfrac52+Ce^0\implies C=\dfrac{11}2

so that the particular solution to this IVP is

\boxed{x(t)=\dfrac{5+11e^{-t^2}}2}

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Bo Karah can run a race in 4 hours 33 minutes if he runs at 7 m/s. How long will it take in hours and minutes if
lidiya [134]

Answer:

7 hours and 9 minutes

Step-by-step explanation:

4 hours and 33 minutes is 273 minutes

7 m/s —> 273 minutes

11 m/s —> M

Criss cross to get M

11x273= 7M

3003=7M

M=429 minutes

==> 429 minutes is 7 hours and 9 minutes

8 0
2 years ago
A car travels 182 miles in 3 hours and 15 minutes. How many miles does it travel per hour?
timofeeve [1]
57 miles about I'm not positive but I think this is right
6 0
3 years ago
A cart travels 3.6 meters in 1.8 seconds. What is the average speed of the cart?
Lady_Fox [76]
For solving this we need the change in distance and the change in time.  You said that the change in time is 1.8 seconds and the change in distance is 3.6 meters.  ( This is assuming it started at 0 meters and started at 0 seconds )

Since the starting was 0,0 we can toss them out as they add no value.  Now since speed is labeled (in this case) m/s, we divide how many meters it traveled over how many seconds it took to travel it.

3.6 / 1.8 = 2

The average speed of the cart is 2 m/s
6 0
3 years ago
Need Help ASAP. Brent has two barcode printing machines. Each machine can print 25 barcodes per minute. On day 1, only the f
laila [671]
Hello!

As we can see, our first amount was 95 for the one machine. We are not multiplying it by anything from the second day as it was used the first. There is no 95 in B, and in C and D it is multiplied.

In A, we have a base of 95, plus 25 multiplied by x and y, and this fits the scenario perfectly. Our answer is A.

I hope this helps!


3 0
3 years ago
What is the area of the prism shown below?<br> prism<br> 10 in.<br> 8 in.<br> 11 in.
Gnom [1K]

Answer:

1180

Step-by-step explanation:

10* 8*11

you times all the figures to give you the right answer that is 1180

5 0
1 year ago
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