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Veseljchak [2.6K]
3 years ago
6

a motorboat traveled for 2 hours with an 8km/h current. the return trip against the same current took 3 hours. find the speed of

the motorboat in still water.
Mathematics
1 answer:
Neporo4naja [7]3 years ago
6 0

Let x be the unknown speed, y the unknown distance.

distance equals speed times time.

"With" an 8kph current means our speed is x+8. 2 hours with an 8 kph current gets is a distance y:

y = 2(x + 8)

Against the current, speed x-8, took 3 hours to go y:

y = 3(x-8)

Equating,

2(x+8)=3(x-8)

2x + 16 =3x - 24

40 = x

Answer: 40 km/h

Check: 2(40+8)=96 km. 3(40-8)=3(32)=96 km. Equal, good.

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Each of the students at piano recital takes about 8 3/4 minutes to introduce themselves and play 3 songs. There are 9 students p
Tomtit [17]

For this case we have that each student takes 8 \ frac {3} {4} minutes to perform and play 3 songs. Then, we convert the mixed number to a fraction:

8 \frac {3} {4} = \frac {4 * 8 + 3} {4} = \frac {32 + 3} {4} = \frac {35} {4}

Thus, each student takes\frac {35} {4} minutes.

If there are 9 students in the recital then we have:

9 * \frac {35} {4} = \frac {315} {4} = 78.75 minutes.

Thus, the recital lasts at least 78.75 minutes.

Answer:

The recital lasts at least 78.75 minutes.

5 0
3 years ago
Find the measure of &lt;1. A) 104 degrees, B) 76 degrees , C) 38 degrees<br> Help due in 5 minutes
Annette [7]
It’s c because the triangle is a isosceles triangle meaning both base angles are the same! So a triangle equals 180°. So you subtract 104 from 180. Then divide it by 2 since the base angles are the same

180-104= 76

76/2=38°
3 0
3 years ago
Kelly pays $25/sweater wholesale.find the salling price if her mark-up is 65%?
gladu [14]
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41.25 is your answer
3 0
3 years ago
A sample of tritium-3 decayed to 94.5% of its original amount after a year.
Zolol [24]
(a) If y(t) is the mass after t days and y(0) = A then y(t) = Ae^{kt}.

y(1) = Ae^k = 0.945A \implies e^k = 0.945 \implies k = \ln 0.945

\text{Then } Ae^{(\ln 0.945)t} = \frac{1}{2}A\ \Leftrightarrow\ \ln e^{(\ln 0.945)t} = \ln \frac{1}{2}\ \Leftrightarrow\  ( \ln 0.945) t = \ln \frac{1}{2} \Leftrightarrow \\ \\&#10;t = - \frac{\ln 5}{\ln 0.945} \approx 12.25 \text{ years}

(b)
Ae^{(\ln 0.945) t} = 0.20 A \ \Leftrightarrow\ (\ln 0.945) t \ln \frac{1}{5}\ \implies \\ \\&#10;t = - \frac{\ln 5}{\ln 0.945} \approx 28.45\text{ years}
3 0
4 years ago
Help me solve for z, step by step if you can
zheka24 [161]

Answer:

z=6

Step-by-step explanation:

z/3 + 1/2 = 5/2

Subtract 1/2 from each side

z/3 + 1/2-1/2 = 5/2-1/2

z/3 = 4/2

z/3 =2

Multiply each side by 3

z/3*3 = 2*3

z = 6


5 0
3 years ago
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