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iVinArrow [24]
3 years ago
9

Use Hooke's Law to determine the work done by the variable force in the spring problem. A force of 450 newtons stretches a sprin

g 30 centimeters. How much work is done in stretching the spring from 30 centimeters to 60 centimeters?
Mathematics
1 answer:
vlada-n [284]3 years ago
7 0

Answer:

The work done is 202.50Nm

Step-by-step explanation:

Given

F =450N

x_1 = 30cm

x_2 = 60cm

Required

The work done

First, we calculate the spring constant (k)

F = kx_1

450N = k *30cm

k = \frac{450N}{30cm}

k =15N/cm

So:

F = kx_1

F(x) = 15x

The work done using Hooke's law is:

W =\int\limits^a_b {F(x)} \, dx

This gives:

W =\int\limits^{60}_{30} {15x} \, dx

Rewrite as:

W =15\int\limits^{60}_{30} {x} \, dx

Integrate

W =15 \frac{x^2}{2}|\limits^{60}_{30}

This gives:

W =15 *\frac{60^2 - 30^2}{2}

W =15 *\frac{2700}{2}

W =15 *1350

W =20250N-cm

Convert to Nm

W =\frac{20250Nm}{100}

W =202.50Nm

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trapecia [35]
Substitute 5 into both the equations...
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7 0
3 years ago
Sandra decided to bake blackberry pies to sell at the county fair. She had $180 in her savings
Hatshy [7]

Answer:

275

Step-by-step explanation:

180-130=50

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2 years ago
An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you th
aliya0001 [1]

Answer:

0.227 = 22.7% probability that the mean printing speed of the sample is greater than 18.12 ppm.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 17.42 ppm and a standard deviation of 3.25 ppm.

This means that \mu = 17.42, \sigma = 3.25

Sample of 12:

This means that n = 12, s = \frac{3.25}{\sqrt{12}}

Find the probability that the mean printing speed of the sample is greater than 18.12 ppm.

This is 1 subtracted by the p-value of Z when X = 18.12.

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{18.12 - 17.42}{\frac{3.25}{\sqrt{12}}}

Z = 0.75

Z = 0.75 has a pvalue of 0.773.

1 - 0.773 = 0.227

0.227 = 22.7% probability that the mean printing speed of the sample is greater than 18.12 ppm.

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3 years ago
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In the data set below, what is the mean absolute deviation?
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here are the steps

1. you would take all the numbers and add them and u would get 18.

2. you want to then divide by 5 since that is how many numbers there are

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4 0
2 years ago
Read 2 more answers
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