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SCORPION-xisa [38]
2 years ago
9

The distance a coiled spring stretches varies directly with the amount of weight hanging on the spring. If a spring stretches 2

cm when a 30 gram weight is hung from it, how far will it stretch when a 75 gram weight is hung from the spring?
Mathematics
1 answer:
STALIN [3.7K]2 years ago
3 0

Answer:

5 cm

Step-by-step explanation:

The distance a coiled spring stretches varies directly with the amount of weight hanging on the spring.

Distance = D

Weight = W

Hence:

D ∝ W

D = kW

Where k is constant of proportionality

Step 1

We solve for k

If a spring stretches 2 cm when a 30 gram weight is hung from it.

2 = 30k

k = 2/30

k = 1/15

Step 2

how far will it stretch when a 75 gram weight is hung from the spring?

D = kW

We are solving for D

k = 1/15

D = 1/15 × 75

D = 5 cm

The spring would stretch 5cm with a weight of 75 gram.

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Which box is greater,a 1.5 lb box of raisins or a 650 gram box of raisins
ladessa [460]

First you would have to either make everything pounds or everything grams. If you chance everything into grams it would be about 680, so the 1.5 pound box of raisens would be more. 
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3 years ago
A diagram of Eric pool as shown below. He plans to fill this pool to a depth of 4ft with a garden hose that flows at 80ft expone
Alex777 [14]
<span>The Volume of a Cylinder  =   </span><span>π <span>• r² • height<span>
</span></span></span>radius = 13.5 feet
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volume = PI * 182.25 * 4
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6 0
3 years ago
Sarah is driving. Her distance in km from Tempe after t hours of driving is given by: x = D(t) = 13 + 57t
777dan777 [17]

Answer:

The solutions for your four question problem are:

a) t = D^-1(x) =  (1/57)*x -(13/57)

b) t = D^-1(x) =  1 h

c) D^-1(x) represents time.

d) The number of hours of driving needed for Sarah to be x km from Tempe. (option (c))

Step-by-step explanation:

a) Determine a formula in terms of x for: t = D^-1(x)

The distance in km from Tempe after t hours of driving is given by

x = D(t) = 13 + 57t.

We just need to find the value  t function of x

x = 13 + 57*t

x -13 =  57*t

57*t  = x -13

t = (1/57)*x -(13/57)

We can see the plots of both equation in the picture below.

b) Compute D^-1(70)

Once we find the expression for D^-1(x)

We substitute for x = 70 km

t = D^-1(x) =  (1/57)*x -(13/57)

t = D^-1(x) =  (1/57)*(70) -(13/57)

t = D^-1(x) =  (70/57) -(13/57)

t = D^-1(x) =  (1.228) -(0.228)

t = D^-1(x) = 1 h

c) In the expression D^-1(x) :  what quantity (distance or time) does the x represent?  what quantity (distance or time) does the entire D^-1(x) represent?

x represents Distance in both equations (D(t), and D^-1(x))

t represents Time in both equations (D(t), and D^-1(x))

Since t = D^-1(x),

D^-1(x) represents time.

d) Which of the following statements best describes D^-1(x)?

The number of hours of driving needed for Sarah to be x km from Tempe.

Since, t = D^-1(x), and t represents the amount of time elapsed since Sarah, parted from Tempe, the correct answer is option (c)

The expression for D^-1(x) can be found in the previous answers

t = D^-1(x) =  (1/57)*x -(13/57)

The input is x (distance) and the output is t (time)

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