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laila [671]
2 years ago
10

What is the answer to 20t-10t+2t

Mathematics
1 answer:
n200080 [17]2 years ago
6 0

Answer:12t

Step-by-step explanation:

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A steamer travels 36 km upstream and 32 km downstream in 6.5 hours. The same steamer travels 4 km upstream and 40 km downstream
rewona [7]

Answer:

The streamer's speed in still water is 90.23 km/h while the stream's speed is 33.33 km/h

Step-by-step explanation:

Let v = streamer's speed in still water and v' = stream's speed. His speed upstream is V = v + v' and his speed downstream is V' = v - v'.

Since he travels 36 km upstream, the time taken is t = 36/V = 36/(v + v').

he travels 32 km downstream, the time taken is t' = 32/V' = 32/(v - v')

The total time is thus t + t' = 36/(v + v') + 32/(v - v')

Since the whole trip takes 6,5 hours,

36/(v + v') + 32/(v - v') = 6.5  (1)

Multiplying each term by (v + v')(v - v'), we have

(v + v')(v - v')36/(v + v') + (v + v')(v - v')32/(v - v') = 6.5(v + v')(v - v')  (1)

(v - v')36 + (v + v')32 = 6.5(v + v')(v - v')  (1)

36v - 36v' + 32v + 32v' = 6.5(v² + v'²)

68v - 4v' = 6.5(v² + v'²)        (2)

Also he travels 4 km upstream, the time taken is t" = 4/V = 4/(v + v').

he travels 40 km downstream, the time taken is t'" = 40/V' = 40/(v - v')

The total time is thus t" + t'" = 4/(v + v') + 40/(v - v')

Since the whole trip takes 180 minutes = 3 hours,

4/(v + v') + 40/(v - v') = 3  (3)

Multiplying each term by (v + v')(v - v'), we have

(v + v')(v - v')4/(v + v') + (v + v')(v - v')40/(v - v') = 3(v + v')(v - v')  (1)

(v - v')4 + (v + v')40 = 3(v + v')(v - v')  (1)

4v - 4v' + 40v + 40v' = 3(v² + v'²)

44v - 36v' = 3(v² + v'²)      (4)

Dividing (2) by (4), we have

(68v - 4v')/(44v - 36v') = 6.5(v² + v'²)/3(v² + v'²)      

(68v - 4v')/(44v - 36v') = 6.5/3

3(68v - 4v') = 6.5(44v - 36v')

204v - 12v' = 286v - 234v'

204v - 286v = 12v' - 234v'

-82v = -222v'

v = -222v'/82

v = 111v'/41

Substituting v into (2), we have

68v - 4v' = 6.5(v² + v'²)      

68(111v'/41) - 4v' = 6.5[(111v'/41)² + v'²]        

[68(111/41) - 4]v' = 6.5[(111/41)² + 1]v'²    

[68(111/41) - 4]v' = 6.5[(111/41)² + 1]v'²

[7548/41 - 4]v' = 6.5[12321/1681 + 1]v'²

[(7548 - 164)/41]v' = 6.5[(12321 + 1681)/1681]v'²

[7384/41]v' = 6.5[14002/1681]v'²

[7384/41]v' = [91013/1681]v'²

[91013/1681]v'² - [7384/41]v' = 0

([91013/1681]v' - [7384/41])v' = 0

⇒ v' = 0 or ([91013/1681]v' - 7384/41) = 0

⇒ v' = 0 or [91013/1681]v' - 7384/41) = 0

⇒ v' = 0 or v' =  7384/41 × 16841/91013

⇒ v' = 0 or v' =  180.097 × 0.185

⇒ v' = 0 or v' =  33.33 km/h

Since v' ≠ 0, v' = 33.33 km/h

Substituting v' into v = 111v'/41 = 111(33.33 km/h)/41 = 3699.63 km/h ÷ 41 = 90.23 km/h

So, the streamer's speed in still water is 90.23 km/h while the stream's speed is 33.33 km/h

5 0
3 years ago
A bag contains balls in a radio of 3 5 4 if there are twelve balls how many balls are in the bag!!
Elena-2011 [213]
Twelve balls are in the bag
4 0
2 years ago
Read 2 more answers
James can finish a job in 1.5 hours. Jane can finish the same job in one hour. How long will it take them to finish this job if
shusha [124]
An hour and 15 minutes i believe. not 100% though
4 0
3 years ago
The surface area of the triangular prism pictured below is 204 square centimeters. What is the height of the prism?
Fudgin [204]
The picture in the attached figure

we know that
surface area=2*area of the base+perimeter*height

area of the base=area of the triangle
area of the base=3*4/2----> 6 cm²

perimeter of the base=perimeter of triangle
perimeter=3+4+5----> 12 cm
height=x cm

surface area=2*6+12*x
surface area=204 cm²
12+12*x=204
12*x=204-12
12*x=192
x=192/12
x=16 cm

the answer is
16 cm

6 0
3 years ago
Please help & thank you.
MA_775_DIABLO [31]

Answer:

<em>9</em>

Step-by-step explanation:

2(5y°) = 90° ⇒ y = <em>9</em>

3 0
2 years ago
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