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3 years ago

The set of ordered pairs represents a function. Write a rule that represents the function.

Mathematics

1 answer:

Furkat [3]3 years ago

7 0

Answer:

y = 3x^3 is the rule representing the function.

Step-by-step explanation:

There are 4 points given.

(0,0), (1,3), (2,24), (3,81), (4,192)

We are asked to find the function or rule connecting x and y

On seeing the pair, first let us find y/x

We observe that y is a multiple of 3. Let us find the values of y/3

y/3 = 0, 1, 4, 9, 16

= 0^2,1^2,3^2,4^2,....

i.e. y/3 is the square of x.

Hence relation is y = 3x^2

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The product of which expression contains 4 decimal places

oee [108]

Answer:

14.2 x 0.784

Step-by-step explanation:

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3 years ago

Using a 5% level of significance and a sample size of 25, what is the critical t value for a null hypothesis, H0: µ ≤ 100? Selec

nadezda [96]

Answer:

D. 2.064

Step-by-step explanation:

Number of sample (n) = 25, degree of freedom = n - 1 = 25 - 1 = 24, significance level = 0.05

The critical t value corresponding to 24 degrees of freedom and 0.05 significance level is 2.064

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3 years ago

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A battery has enough energy to operate eight toy bears for 21 hours. For how long could the battery operate 15 toy bears?

il63 [147K]

Answer:

28 hours for 15 toy bears

Step-by-step explanation:

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4 years ago

The rod is made of A-36 steel and has a diameter of 0.22 in . If the rod is 4 ft long when the springs are compressed 0.7 in . a

ziro4ka [17]

The force in the rod when the temperature is 150 °F is 718.72 pounds-force.

<h3>How to determine the resulting the resulting force due to mechanical and thermal deformation</h3>

Let suppose that rod experiments a quasi-static deformation and that both springs have a linear behavior, that is, force ( $F$ ), in pounds-force, is directly proportional to deformation. Then, the elongation of the rod due to temperature increase creates a spring deformation additional to that associated with mechanical contact.

Given simmetry considerations, we derive an expression for the spring force ( $F$ ), in pounds-force, as a sum of mechanical and thermal effects by principle of superposition:

$F = k\cdot (\Delta x + 0.5\cdot \Delta l)$ (1)

Where:

$k$ - Spring constant, in pounds-force per inch.
$\Delta x$ - Spring deformation, in inches.
$\Delta l$ - Rod elongation, in inches.

The rod elongation is described by the following thermal dilatation formula:

$\Delta l = \alpha \cdot L_{o}\cdot (T_{f}-T_{o})$ (2)

Where:

$\alpha$ - Coefficient of linear expansion, in $\frac{1}{^{\circ}F}$ .
$L_{o}$ - Initial length of the rod, in inches.
$T_{o}$ - Initial temperature, in degrees Fahrenheit.
$T_{f}$ - Final temperature, in degrees Fahrenheit.

If we know $k = 1000\,\frac{lb}{in}$ , $\Delta x = 0.7\,in$ , $\alpha = 6.5\times 10^{-6}\,\frac{1}{^{\circ}F}$ , $L_{o} = 48\,in$ , $T_{o} = 30\,^{\circ}F$ and $T_{f} = 150\,^{\circ}F$ , then the force in the rod at final temperature is:

$F = \left(1000\,\frac{lb}{in} \right)\cdot \left[0.7\,in + 0.5\cdot\left(6.5\times 10^{-6}\,\frac{1}{^{\circ}F} \right)\cdot (48\,in)\cdot (150\,^{\circ}F-30\,^{\circ}F)\right]$

$F = 718.72\,lbf$

The force in the rod when the temperature is 150 °F is 718.72 pounds-force. $\blacksquare$

To learn more on deformations, we kindly invite to check this verified question: brainly.com/question/13774755

3 0

3 years ago

Find the next term for the following sequence 9,6,4

pav-90 [236]

Answer:

The next term for the following sequence is 8/3

8 0

4 years ago