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FinnZ [79.3K]
3 years ago
11

In Still Water, Peters Boat Goes 4 Times as Fast as the Current of the River. He Took a Trip 15 Miles Up the River, Then Came Ba

ck. His Entire Trip Lasted 4 Hours. Find the Rate of the Rivers Current.
Mathematics
1 answer:
inn [45]3 years ago
3 0

Answer:

2 km/h

Step-by-step explanation:

Let

Rate of river current = x km/h

Speed of Peter's boat = 4x km/h

He takes 15 km trip up (opposite direction)

His speed upstream = 4x - x

= 3x

His speed is 3x and distance is 15 km

Time = Distance / Speed

15/3x

= 5/x

And

Moving downstream (same direction)

Speed will be 4x + x = 5x

Distance = 15km,

speed = 5x

Time = Distance / Speed

= 15/5x

= 3/x

Total time take for trip = 4 hours

Total time take for trip = upstream + downstream

4 =5/x + 3/x

4 = 8/x

Cross product

4 * x = 8

x = 8/4

x = 2

Rate of river current = x km/h

= 2 km/h

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a tank is 3/7 full of water.After removing 420 litres it became 12/35 full .how much can the tank hold when full? ​
insens350 [35]

Answer:

4900 Litres

Step-by-step explanation:

First we need a common demoninator:

3/7=15/35

Then we subtract the two to figure out how much 420 Litres is:

15/35-12/35=3/35

3/35=420 litres

Divide amount by the numerater for thow much 1/x is.

1/35=140

and multiply by the denomenator to get a full number on your fraction, and therefore a full tank.

140 x 35 = 4900

5 0
2 years ago
A rhombus has diagonals of 10cm and 6cm. Find the angles of the rhombus and its area.​
Marrrta [24]

Answer:

area =length ×breath =10×6=60

3 0
3 years ago
Keegan is priting and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total p
Damm [24]

Complete question is;

Keegan is printing and selling his original design on t-shirts. He has concluded that for x shirts, in thousands sold his total profits will be p(x) = -x³ + 4x² + x dollars, in thousands will be earned. How many t-shirts (rounded to the nearest whole number) should he print in order to make maximum profits? What will his profits rounded to the nearest whole dollar be if he prints that number of shirts?

Answer:

Number of t-shirts to make maximum profit = 2790 shirts

Maximum profit = $12,209

Step-by-step explanation:

From the question, we are given that the profit function is;

p(x) = -x³ + 4x² + x

For the maximum value of the profit function,

(dp/dx) = 0 and (d²p/dx²) < 0

Since, p(x) = -x³ + 4x² + x

Then,

(dp/dx) = -3x² + 8x + 1

at maximum point (dp/dx) = 0, thus;

-3x² + 8x + 1 = 0

Solving this using quadratic formula, the roots are;

x = -0.12 or 2.79

Also, (d²p/dx²) = -6x + 8

Now, let's put the roots of x into -6x + 8 and check for maximum value conditon;

at x = -0.12

(d²p/dx²) = -6(0.12) + 8 = 7.28 > 0

At x = 2.79

(d²p/dx²) = -6(2.79) + 8 = -8.74 < 0

Maximum has to be d²p/dx² < 0

So, the one that meets the condition is -8.74 < 0 at x = 2.79

Thus, the maximum of the profit function exists when the number of shirts, x = 2.79 (in thousands) = 2790

Now, the maximum profits that corresponds to this number of t-shirts of 2.79(in thousands) is obtained by putting 2.79 for x in the profit function;

So,

p(2.79) = -(2.79)³ + 4(2.79²) + 2.79

p(x) = -21.7176 + 31.1364 + 2.79

p(x) = 12.2088 (in thousand dollars) ≈ $12,209

6 0
3 years ago
Rick cuts a 12-foot-long ribbon into 2 pieces. One piece is 3.5 feet longer than the other. What is the length of each piece?
GREYUIT [131]

Its impossible there is no way to solve it because x+3.5= y no number can make 12 if one number is 3.5 ft longer than the other Ignore this i dont feel like erasing this part.

144 in. 42 in. greater than the other 42 + x = y Nvm if you convert the numbers too in. the numbers are 93 + 51 = 144 and if you convert it back it would be

7.75 + 4.25 = 12

3 0
2 years ago
Whats 407 divided by 47..<br>​
vovangra [49]

Answer:

8.65957446809

Step-by-step explanation:

8\frac{31 }{47}   8.7

6 0
3 years ago
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