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kifflom [539]
3 years ago
8

Two trucks leave a warehouse at the same time. One travels due east at an average speed of 50 miles per hour, and the other trav

els due west at an average speed of 51 miles per hour. After how many hours will the two trucks be 707 miles apart?
Mathematics
1 answer:
Keith_Richards [23]3 years ago
8 0

Answer:Since the vehicles are travelling in the exact opposite direction, the sum of their rates is the rate at which they are separating. 48 + 64 = 112 miles per hour of separation.

728 miles ÷ 112 miles/hour = 6.5 hours

Step-by-step explanation:

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(b) dy/dx = (x - y+ 1)^2
Elanso [62]

Substitute v(x)=x-y(x)+1, so that

\dfrac{\mathrm dv}{\mathrm dx}=1-\dfrac{\mathrm dy}{\mathrm dx}

Then the resulting ODE in v(x) is separable, with

1-\dfrac{\mathrm dv}{\mathrm dx}=v^2\implies\dfrac{\mathrm dv}{1-v^2}=\mathrm dx

On the left, we can split into partial fractions:

\dfrac12\left(\dfrac1{1-v}+\dfrac1{1+v}\right)\mathrm dv=\mathrm dx

Integrating both sides gives

\dfrac{\ln|1-v|+\ln|1+v|}2=x+C

\dfrac12\ln|1-v^2|=x+C

1-v^2=e^{2x+C}

v=\pm\sqrt{1-Ce^{2x}}

Now solve for y(x):

x-y+1=\pm\sqrt{1-Ce^{2x}}

\boxed{y=x+1\pm\sqrt{1-Ce^{2x}}}

3 0
3 years ago
|3 - 5 + 7|.<br><br>O 15<br>O 5<br>O -15<br>O -5​
Aliun [14]

Answer:

5

Step-by-step explanation:

The answer is 5

because 3 - 5 = -2

and -2 + 7 = 5

so the answer is 5

4 0
3 years ago
The sum of two numbers is 53. If twice the 1st number minus 3 times the second number is 26, find both numbers.
zhannawk [14.2K]
F twice the 1st number minus 3 times the second number is 26<span>, </span>find both<span> ... </span>Twice the first number<span> is eleven more than </span>the sum<span> of the other </span>two numbers<span>.</span>
3 0
3 years ago
The new total is 60%, but the sales tax is 5% of the bill. how much is the salestax?
Nataly_w [17]

Answer:

Sales tax is 8.33 % of new total

Step-by-step explanation:

Let

Your bill =1000

New total 60%=1000*60/100=600

5% sale tax on whole bill price =1000*5/100=50

To deduct 5% sale tax in 60% of new total the % are=50/600=0.0833*100=8.33%

So,

Sale tax is 8.33% of new total 60%.

6 0
4 years ago
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DaniilM [7]

Answer:

7

Step-by-step explanation:

6 0
3 years ago
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