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umka2103 [35]
3 years ago
8

A motorboat travels 448 kilometers in 8 hours going upstream and 440 kilometers in 5 hours going downstream. What is the rate of

the boat in still water and what is the rate of the current?
Mathematics
1 answer:
liubo4ka [24]3 years ago
4 0

9514 1404 393

Answer:

  • boat: 72 km/h
  • current: 16 km/h

Step-by-step explanation:

The speed difference between boat and current is the upstream rate:

  (448 km)/(8 h) = 56 km/h

The sum of speeds of boat and current is the downstream rate:

  (440 km)/(5 h) = 88 km/h

The rate of the boat is half the sum of these:

  (56 +88)/2 = 72 . . . km/h

The rate of the current is half their difference:

  (88 -56)/2 = 16 . . . km/h

The rate of the boat is 72 km/h; the rate of the current is 16 km/h.

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What is 30/ 100 plus 50
zhuklara [117]

Answer:

50.3x is the right answer

Step-by-step explanation:

30/100 + 50x = 50.3x

8 0
2 years ago
Will mark brainliest! Answer quickly please.
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1400kg.
Force=ma
2100N= m*1.5
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Please mark me brainliest :)
3 0
2 years ago
the half life of c14 is 5730 years. Suppose that wood found at an archeological excavation site contains about 35% as much C14 a
Furkat [3]

Answer:

The wood was cut approximately 8679 years ago.

Step-by-step explanation:

At first we assume that examination occured in 2020. The decay of radioactive isotopes are represented by the following ordinary differential equation:

\frac{dm}{dt} = -\frac{m}{\tau} (Eq. 1)

Where:

\frac{dm}{dt} - First derivative of mass in time, measured in miligrams per year.

\tau - Time constant, measured in years.

m - Mass of the radioactive isotope, measured in miligrams.

Now we obtain the solution of this differential equation:

\int {\frac{dm}{m} } = -\frac{1}{\tau}\int dt

\ln m = -\frac{1}{\tau} + C

m(t) = m_{o}\cdot e^{-\frac{t}{\tau} } (Eq. 2)

Where:

m_{o} - Initial mass of isotope, measured in miligrams.

t - Time, measured in years.

And time is cleared within the equation:

t = -\tau \cdot \ln \left[\frac{m(t)}{m_{o}} \right]

Then, time constant can be found as a function of half-life:

\tau = \frac{t_{1/2}}{\ln 2} (Eq. 3)

If we know that t_{1/2} = 5730\,yr and \frac{m(t)}{m_{o}} = 0.35, then:

\tau = \frac{5730\,yr}{\ln 2}

\tau \approx 8266.643\,yr

t = -(8266.643\,yr)\cdot \ln 0.35

t \approx 8678.505\,yr

The wood was cut approximately 8679 years ago.

5 0
3 years ago
Which of the following best describes the algebraic expression x/3 -15
Dennis_Churaev [7]

Answer:

A. A number divided by three minus fifteen.

7 0
3 years ago
PLS HELP What is the quotient?
ryzh [129]

Answer:

Step-by-step explanation:

2\frac{1}{5}dividedby\frac{-1}{10}=2\frac{1}{5}*\frac{-10}{1}\\\\=\frac{11}{5}*\frac{-10}{1}\\\\=11*-2=-22\\

Keep the first fraction, change division to multiplication and find the reciprocal(multiplicative inverse) of the second fraction

\frac{11}{50}dividedby\frac{11}{50}=\frac{11}{50}*\frac{50}{11}\\\\ =1

3 0
3 years ago
Read 2 more answers
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