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3 years ago

Why 3^-7 x 3^7 = 1. . Someone please

Mathematics

1 answer:

irina [24]3 years ago

6 0

Answer:

see below

Step-by-step explanation:

3^-7 x 3^7 = 1

The negative exponents put it in the denominator

1/ 3*3*3*3*3*3*3 * (3*3*3*3*3*3*3) = 1

The 3's cancel leaving

1/1 = 1

1=1

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A motorboat travels 165 kilometers in 3 hours going upstream and 510 kilometers in 6 hours going downstream. What is the rate of

nikitadnepr [17]

<h3>Rate of the boat in still water is 70 km/hr and rate of the current is 15 km/hr</h3><h3><u>Solution:</u></h3>

Given that,

A motorboat travels 165 kilometers in 3 hours going upstream and 510 kilometers in 6 hours going downstream

Therefore,

Upstream distance = 165 km

Upstream time = 3 hours

<h3><u>Find upstream speed:</u></h3>

$speed = \frac{distance}{time}\\\\speed = \frac{165}{3}\\\\speed = 55$

Thus upstream speed is 55 km per hour

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Downstream time = 6 hours

<h3><u>Find downstream speed:</u></h3>

$speed = \frac{510}{6}\\\\speed = 85$

Thus downstream speed is 85 km per hour

<em><u>If the speed of a boat in still water is u km/hr and the speed of the stream is v km/hr, then</u></em>

Speed downstream = u + v km/hr

Speed upstream = u - v km/hr

Therefore,

u + v = 85 ----- eqn 1

u - v = 55 ----- eqn 2

Solve both

Add them

u + v + u - v = 85 + 55

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<em><u>Substitute u = 70 in eqn 1</u></em>

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