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Arisa [49]
3 years ago
8

A boat's crew rowed 15 kilometers downstream, with the current, in 1 hours. The return trip upstream, against the current, cover

ed the same distance, and it took 3 hours. Find the crew's rowing rate in still water.
Mathematics
1 answer:
Mandarinka [93]3 years ago
3 0
B and c are the speeds of the boat (in still water) and the current.

Traveling with the current, the boat goes b+c km per hour.
1 hour * (b+c km)/hour = 15 km
b+c = 15

Traveling against the current, the boat goes b-c km per hour.
3 hours * (b-c km)/hour = 15
b-c = 5

Add the two equations
b = 10 km per hour
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Which number is a solution of a² +4= 6a – 1?<br> 07<br> 6<br> 7<br> 8
LuckyWell [14K]

Answer:

a=1 or a=5

Step-by-step explanation:

a^{2}+4=6a−1

Step 1: Subtract 6a-1 from both sides.

a^{2}+4−(6a−1)=6a−1−(6a−1)

a^{2}−6a+5=0

Step 2: Factor left side of equation.

(a−1)(a−5)=0

Step 3: Set factors equal to 0.

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a=1 or a=5

(is it helpful rate me according to that

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2 years ago
Find the indefinite integral using the substitution provided.
Nady [450]

Answer:  7\text{Ln}\left(e^{2x}+10\right)+C

This is the same as writing 7*Ln( e^(2x) + 10) + C

=======================================================

Explanation:

Start with the equation u = e^{2x}+10

Apply the derivative and multiply both sides by 7 like so

u = e^{2x}+10\\\\\frac{du}{dx} = 2e^{2x}\\\\7\frac{du}{dx} = 7*2e^{2x}\\\\7\frac{du}{dx} = 14e^{2x}\\\\7du = 14e^{2x}dx\\\\

The "multiply both sides by 7" operation was done to turn the 2e^(2x) into 14e^(2x)

This way we can do the following substitutions:

\displaystyle \int \frac{14e^{2x}}{e^{2x}+10}dx\\\\\\\displaystyle \int \frac{1}{e^{2x}+10}14e^{2x}dx\\\\\\\displaystyle \int \frac{1}{u}7du\\\\\\\displaystyle 7\int \frac{1}{u}du\\\\\\

Integrating leads to

\displaystyle 7\int \frac{1}{u}du\\\\\\7\text{Ln}\left(u\right)+C\\\\\\7\text{Ln}\left(e^{2x}+10\right)+C\\\\\\

Be sure to replace 'u' with e^(2x)+10 since it's likely your teacher wants a function in terms of x. Also, do not forget to have the plus C at the end. This is a common mistake many students forget to do.

To verify the answer, you can apply the derivative to it and you should get back to the original integrand of \frac{14e^{2x}}{e^{2x}+10}

4 0
2 years ago
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