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2 years ago

WILL GIVE POINTS

Mathematics

1 answer:

Nadusha1986 [10]2 years ago

3 0

Answer:

2x, (x-2), (x+6)

Step-by-step explanation:

I just took the quiz on plato and I got it correct

P.S Can you guys give me the brainliest please

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A boat travels 33 miles downstream in 4 hours. The return trip takes the boat 7 hours. Find the speed of the boat in still water

Paha777 [63]

<u>Answer:</u>

Speed of the boat in still water = 6.125 miles/hour

<u>Step-by-step explanation:</u>

We are given that a boat travels 33 miles downstream in 4 hours and the return trip takes the boat 7 hours.

We are to find the speed of the boat in the still water.

Assuming $S_b$ to be the speed of the boat in still water and $S_w$ to be the speed of the water.

The speeds of the boat add up when the boat and water travel in the same direction.

$Speed = \frac{distance}{time}$

$S_b+S_w=\frac{d}{t_1}=\frac{33 miles}{4 hours}$

And the speed of the water is subtracted from the speed of the boat when the boat is moving upstream.

$S_b-S_w=\frac{d}{t_2}=\frac{33 miles}{7 hours}$

Adding the two equations to get:

$S_b+S_w=\frac{d}{t_1}$

+ $S_b-S_w=\frac{d}{t_2}$

___________________________

$2S_b=\frac{d}{t_1} +\frac{d}{t_2}$

Solving this equation for $S_b$ and substituting the given values for $d,t_1, t_2$ :

$S_b=\frac{(t_1+t_2)d}{2t_1t_2}$

$S_b=\frac{(4 hour + 7hour)33 mi}{2(4hour)(7hour)}$

$S_b=\frac{(11 hour)(33mi)}{56hour^2}$

$S_b=6.125 mi/hr$

Therefore, the speed of the boat in still water is 6.125 miles/hour.

6 0

2 years ago

Read 2 more answers

The slope of the tangent line for the curve r=2 cos(3 theta) where theta = pi/6 is.

Phantasy [73]

as you already know, the slope of the tangent line is simply the derivative of the function, so

$r=2cos(3\theta )\implies \cfrac{dr}{d\theta }=2\stackrel{chain~rule}{\left[ -sin(3\theta )\cdot 3 \right]} \\\\\\ \left. \cfrac{dr}{d\theta }=-6sin(3\theta ) \right|_{\theta =\frac{\pi }{6}}\implies -6sin\left( 3\cdot \frac{\pi }{6} \right)\implies -6sin\left( \frac{\pi }{2} \right)\implies -6$