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3 years ago

A directed line segment begins at F(-8, -2), ends at H(6, 4), and is divided in the ratio 8 to 2 by G.

1 answer:

nataly862011 [7]3 years ago

5 0

You are given a directed line segment that begins at F(-8, -2), ends at H(6, 4), and is divided in the ratio 8 to 2 by G. To find the coordinates of G, you shall draw your line segment with points at FGH respectively. You have to calculate the distance first before getting the location of G.

distance = √[(x₂-x₁)² + (y₂-y₁)²]
distance = √[(-8-6)² + (-2-4)²]
distance = √[(-14)² + (-6)²]
distance = √[196 + 36]
distance = √232
distance = 2√58

and then multiply it with 8/2 to get the the distance of G
2√58 * 8/2
8√58

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Hank has to drain his pool so repairs can be done on a crack on the bottom. The company coming to fix the pool is scheduled to a

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Answer:

The answer to the question: "Will Hank have the pool drained in time?" is:

Yes, Hank will have the pool drained in time.

Step-by-step explanation:

To identify the time Hank needs to drain the pool, we can begin with the time Hank has from 8:00 AM to 2:00 PM in minutes:

Available time = 6 hours * 60 minutes / 1 hour (we cancel the unit "hour")
Available time = 360 minutes

Now we know Hank has 360 minutes to drain the pool, we're gonna calculate the volume of the pool with the given measurements and the next equation:

Volume of the pool = Deep * Long * Wide
Volume of the pool = 2 m * 10 m * 8 m
Volume of the pool = 160 m^3

Since the drain rate is in gallons, we must convert the obtained volume to gallons too, we must know that:

1 m^3 = 264.172 gal

Now, we use a rule of three:

If:

1 m^3 ⇒ 264.172 gal
160 m^3 ⇒ x

And we calculate:

$x = \frac{160 m^{3}*264.172 gal }{1m^{3} }$ (We cancel the unit "m^3)
x = 42267.52 gal

At last, we must identify how much time take to drain the pool with a volume of 42267.52 gallons if the drain rate is 130 gal/min:

Time to drain the pool = $\frac{42267.52gal}{130\frac{gal}{min} }$ (We cancel the unit "gallon")
Time to drain the pool = 325.1347692 minutes
Time to drain the pool ≅ 326 minutes (I approximate to the next number because I want to assure the pool is drained in that time)

As we know, Hank has 360 minutes to drain the pool and how it would be drained in 326 minutes approximately, we know Hank will have the pool drained in time and will have and additional 34 minutes.

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