Ninenine times the reciprocal of a number equals 33 times the reciprocal of 99. find the numbe

A fisherman traveled in a boat from point N upstream. After having traveled 6 km, he stopped rowing and 2 hour 40 min after firs

Nat2105 [25]

Answer:

The speed of the river's current is 4.5 km/hr.

Step-by-step explanation:

Given : A fisherman traveled in a boat from point N upstream.

After having traveled 6 km, he stopped rowing and 2 hour 40 min after first leaving N, he was brought back to N by the current.

Knowing that the speed of the boat in still water is 9 km/hour

To find : The speed of the river’s current.

Solution :

Let the speed of current = x km/h

Speed of boat = 9 km/h

Thus, the speed in upstream = (9 - x) km/h

Also, the speed in downstream = x km/h (because the boat is stationary in downstream)

Total distance = 6 km ( from N to the point he reached )

Total time = 2 hours 40 minutes

$\text{2 hours 40 minutes}=2\frac{40}{60}=2 \frac{2}{3} \\\\\text{2 hours 40 minutes}=\frac{8}{3} \text{ hours}$

We know, $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

According to the question,

$\frac{6}{9-x}+\frac{6}{x}=\frac{8}{3}$

Taking LCM and 6 common

$6[\frac{x+9-x}{(9-x)x}]=\frac{8}{3}$

Take 6 to another side,

$\frac{9}{9x-x^2}=\frac{8}{3\times 6}$

Cross multiply,

$9\times 18=8\times(9x-x^2)$

$162=72x-8x^2$

Taking 4 common and cancel out

$4x^2-36x+81=0$

Solve quadratic equation by middle term split,

$4x^2-18x-18x+81=0$

$2x(2x-9)-9(2x-9)=0$

$(2x-9)(2x-9)=0$

$\Rightarrow 2x-9=0$

$\Rightarrow x=\frac{9}{2}=4.5$

Therefore, The speed of the river's current is 4.5 km/hr.

6 0

2 years ago

Simplify the expression 5x-8(3+2x)

krek1111 [17]

Answer:

-11x - 24

Step-by-step explanation

7 0

3 years ago

Read 2 more answers

The battery on McKenzies old computer can last 4(1/5) hours. She bought a new computer that has a battery that can last 40% long

Solnce55 [7]

Answer:

$5\frac{22}{25}\ hours$

Step-by-step explanation:

we know that

$4\frac{1}{5}\ hours=\frac{4*5+1}{5}=\frac{21}{5}\ hours$

$100\%+40\%=140\%=\frac{140}{100}$

Let

x ------> new battery life

The equation that represent this situation is

$x=\frac{140}{100} (\frac{21}{5})=\frac{2,940}{500}\ hours$

convert to mixed number

$\frac{2,940}{500}=\frac{2,500}{500}+\frac{440}{500}=5\frac{22}{25}\ hours$

4 0

3 years ago

A boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water. Luis measur

Crazy boy [7]

Using the slope concept, it is found that the distance from point A to point B is of 465 feet.

<h3>What is a slope?</h3>

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

To find the horizontal position at point A, we have that:

tan(10º) = 107/dA

dA = 107/tan(10º)

dA = 607.

For the horizontal position at point B, we have that:

tan(37º) = 107/dB

dB = 107/tan(37º)

dB = 142.

Hence the distance is given by:

D = dA - dB = 607 - 142 = 465.

More can be learned about the slope concept at brainly.com/question/18090623

#SPJ1

6 0

1 year ago

Please help! thank you!

anyanavicka [17]

Answer:

B. r=7.5

yan po ang correct answer

7 0

2 years ago