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2 years ago

I NEED CORRECT ANSWER

Mathematics

1 answer:

RUDIKE [14]2 years ago

4 0

Answer:

Step-by-step explanation:

Activity 3

Q1) consistent, independent

Q2) inconsistent

Q3) consistent, dependent

Q4) consistent, independent

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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

olganol [36]

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.

3 0

3 years ago

How do you find direct variation? im having trouble understanding this subject

rodikova [14]

I was too just a couple of weeks ago. So direct variation is the constant way to variables change together. EX:
x y
1 2
2 4
3 6
Direct variation must be in the format b=ka where k is a constant. So the direct variation here could be y=2x. Understand?

5 0

3 years ago

Please help me if you can. Please also write how you got the answer thank you.

babunello [35]

Answer:

Question 9: Variables: (smallest) s, q, r (largest)

Question 10: 5 whole numbers (7, 8, 9, 10, and 11)

Step-by-step explanation:

For question nine, there are two given statements... s=q-2 and q<r. Say we plug in 10000 (a really big #) in for q, then we would get s=9998 and r>10000. This way, we can see that s would be the smallest, then q, and r is the largest. <em>(q<r can be written as r>q)</em>

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For question 10, it states $\frac{1}{4}$ . This can be split into $\frac{3}{x}$ and $\frac{3}{x}$ . When x is 12 in the first equation then $\frac{3}{12} = \frac{1}{4}$ and when x is 6 in the second equation $\frac{3}{6} =0.5$ (0.5 is also $\frac{1}{2}$ ). Therefore, x must be a whole number less than 12 and greater than 6, and it cannot be either 12 or 6. Whole numbers between 6 and 12 are 7, 8, 9, 10, and 11 or 5 whole numbers.