1. The tension t in a spring varies directly with the distance d the spring is stretched. If the tension is 46 pounds when the spring is stretched 4 inches, find the tension when the spring is stretched twice as far. 2. The time t it takes to fill a bucket varies directly with the volume g of the bucket. If it takes 2 minutes to fill a 8-gallon bucket, how long will it take to fill a 5-gallon bucket?

3. The power P in an electric circuit varies directly with the square of the current I. If P = 30 when I = 2, find P when I = 5.

4. The amount of money M a woman makes per week varies directly with the number of hours h she works per week. If she works 28 hours and earns $137, how much does she make if she works 42 hours?

5. The weight F of a body varies inversely with the square of the distance d between the body and the center of the Earth. If a man weighs 250 pounds 4,000 miles from the center of the Earth, how much will he weigh at a distance of 5,000 miles from the center of the Earth.

9514 1404 393

Explanation:

1. The tension is proportional to distance, so twice the distance will result in twice the tension:

  2 × 46 lbs = 92 lbs

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2. The fill time is proportional to the volume, so 5/8 of the volume will take 5/8 of the time:

  (5/8)(2 min) = 10/8 min = 5/4 min = 1 minute 15 seconds

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3. When the current increases by a factor of 5/2, the power increases by the square of that factor.

  (5/2)^2 × 30 = 187.5 . . . power at increased current

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4. Working 42/28 times as many hours will result in 48/28 times as much pay:

  (42/28) × $137 = $205.50

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5. The new distance is 5000/4000 = 5/4 times the reference distance, so the new weight will be 1/(5/4)^2 = (4/5)^2 = 16/25 times the reference weight.

  (16/25)(250 lbs) = 160 lbs

i need points

step-by-step explanation:

sorry bubs

the solution is x=1

step-by-step explanation:

we are given our   equation as

let's assume

left side function is

right side function is

now, we can draw graph

and then we can get intersection point

the intersection point will be solution

so, the solution is

x=1