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netineya [11]
3 years ago
8

Suppose that 5 J of work is needed to stretch a spring from its natural length of 36 cm to a length of 51 cm. (a) How much work

is needed to stretch the spring from 41 cm to 46 cm? (Round your answer to two decimal places.) 5 Incorrect: Your answer is incorrect. J (b) How far beyond its natural length will a force of 25 N keep the spring stretched? (Round your answer one decimal place.) cm
Mathematics
1 answer:
olganol [36]3 years ago
3 0

Answer:

a) 0.6 joules of work are needed to stretch the spring from 41 centimeters to 46 centimeters.

b) The spring must be 5.6 centimeters far from its natural length.

Step-by-step explanation:

a) The work done to stretch the ideal spring from its natural length is defined by the following definition:

W = \frac{1}{2}\cdot k\cdot (x_{f}-x_{o})^{2} (1)

Where:

k - Spring constant, measured in newtons.

x_{o}, x_{f} - Initial and final lengths of the spring, measured in meters.

W - Work, measured in joules.

The spring constant is: (W = 5\,J, x_{o} = 0.36\,m, x_{f} = 0.51\,m)

k = \frac{2\cdot W}{(x_{f}-x_{o})^{2}}

k = \frac{2\cdot (5\,J)}{(0.51\,m-0.36\,m)^{2}}

k = 444.44\,\frac{N}{m}

If we know that k = 444.44\,\frac{N}{m}, x_{o} = 0.41\,m and x_{f} = 0.46\,m, then the work needed is:

W = \frac{1}{2}\cdot \left(444.44\,\frac{N}{m} \right)\cdot (0.46\,m-0.41\,m)^{2}

W = 0.555\,J

0.6 joules of work are needed to stretch the spring from 41 centimeters to 46 centimeters.

b) The elastic force of the ideal spring (F), measured in newtons, is defined by the following formula:

F = k\cdot \Delta x (2)

Where \Delta x is the linear difference from natural length, measured in meters.

If we know that k = 444.44\,\frac{N}{m} and F = 25\,N, then the linear difference is:

\Delta x = \frac{F}{k}

\Delta x = \frac{25\,N}{444.44\,\frac{N}{m} }

\Delta x = 0.056\,m

The spring must be 5.6 centimeters far from its natural length.

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Parallel / Perpendicular Practice
deff fn [24]

The slope and intercept form is the form of the straight line equation that includes the value of the slope of the line

  1. Neither
  2. ║
  3. Neither
  4. ⊥
  5. ║
  6. Neither
  7. Neither
  8. Neither

Reason:

The slope and intercept form is the form y = m·x + c

Where;

m = The slope

Two equations are parallel if their slopes are equal

Two equations are perpendicular if the relationship between their slopes, m₁, and m₂ are; m_1 = -\dfrac{1}{m_2}

1. The given equations are in the slope and intercept form

\ y = 3 \cdot x + 1

The slope, m₁ = 3

y = \dfrac{1}{3} \cdot x + 1

The slope, m₂ = \dfrac{1}{3}

Therefore, the equations are <u>neither</u> parallel or perpendicular

  • Neither

2. y = 5·x - 3

10·x - 2·y = 7

The second equation can be rewritten in the slope and intercept form as follows;

y = 5 \cdot x -\dfrac{7}{2}

Therefore, the two equations are <u>parallel</u>

  • ║

3. The given equations are;

-2·x - 4·y = -8

-2·x + 4·y = -8

The given equations in slope and intercept form are;

y = 2 -\dfrac{1}{2}  \cdot x

Slope, m₁ = -\dfrac{1}{2}

y = \dfrac{1}{2}  \cdot x - 2

Slope, m₂ = \dfrac{1}{2}

The slopes

Therefore, m₁ ≠ m₂

m_1 \neq -\dfrac{1}{m_2}

The lines are <u>Neither</u> parallel nor perpendicular

  • <u>Neither</u>

4. The given equations are;

2·y - x = 2

y = \dfrac{1}{2} \cdot   x +1

m₁ = \dfrac{1}{2}

y = -2·x + 4

m₂ = -2

Therefore;

m_1 \neq -\dfrac{1}{m_2}

Therefore, the lines are <u>perpendicular</u>

  • ⊥

5. The given equations are;

4·y = 3·x + 12

-3·x + 4·y = 2

Which gives;

First equation, y = \dfrac{3}{4} \cdot x + 3

Second equation, y = \dfrac{3}{4} \cdot x + \dfrac{1}{2}

Therefore, m₁ = m₂, the lines are <u>parallel</u>

  • ║

6. The given equations are;

8·x - 4·y = 16

Which gives; y = 2·x - 4

5·y - 10 = 3, therefore, y = \dfrac{13}{5}

Therefore, the two equations are <u>neither</u> parallel nor perpendicular

  • <u>Neither</u>

7. The equations are;

2·x + 6·y = -3

Which gives y = -\dfrac{1}{3} \cdot x - \dfrac{1}{2}

12·y = 4·x + 20

Which gives

y = \dfrac{1}{3} \cdot x + \dfrac{5}{3}

m₁ ≠ m₂

m_1 \neq -\dfrac{1}{m_2}

  • <u>Neither</u>

8. 2·x - 5·y = -3

Which gives; y = \dfrac{2}{5} \cdot x +\dfrac{3}{5}

5·x + 27 = 6

x = -\dfrac{21}{5}

  • Therefore, the slopes are not equal, or perpendicular, the correct option is <u>Neither</u>

Learn more here:

brainly.com/question/16732089

6 0
3 years ago
The greater of two consecutive integers is 15 more than twice the smaller. Find the integers.
Vlad [161]

Well, we know that the two consecutive numbers have to be negative, because if it was positive, the smaller number multiplied by two would be much greater. (unless 1 and 2). So, by guessing and checking, we will get -13 and -14 :)

3 0
3 years ago
Solve 5 / 6 ÷ 1 / 12 ?​
Tema [17]

Answer:

10

Step-by-step explanation:

5/6 ÷ 1/12 ➡ 5/6 × 12/1 = 60/6 ➡ 10

5 0
3 years ago
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Suppose your statistics professor reports test grades as​ z-scores, and you got a score of 2.49 on an exam. ​(a) Write a sentenc
Oduvanchick [21]

Answer:

a) A z-score of 2.49 means that your grade was 2.49 standard deviations above the mean of all grades.

b) 1.39% of the class scored lower than your​ friend.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

You got a score of 2.49 on an exam. ​

(a) Write a sentence explaining what that means

A z-score of 2.49 means that your grade was 2.49 standard deviations above the mean of all grades.

(b) Your friend got a​ z-score of negative 2−2. If the grades satisfy the Nearly Normal​ Condition, about what percent of the class scored lower than your​ friend? ​

This percentage is the pvalue of Z = -2.2

So 0.0139 = 1.39% of the class scored lower than your​ friend.

7 0
3 years ago
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patriot [66]
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