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2 years ago

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The mass varies directly as the Kinetic energy (K) and inversely as the square of the velocity (V). if the kinetic energy is 80

Joules and the velocity is 4 meters per second, then the mass is 10 kilograms. Express the mass as a function of kinetic energy and velocity.

1 answer:

Alex73 [517]2 years ago

3 0

Answer:

m = $\frac{2K}{v^2}$

Step-by-step explanation:

Given mass (m ) varies directly as K and inversely as v² then the equation relating them is

m = $\frac{kK}{v^2}$ ← k is the constant of variation

To find k use the condition m = 10 when K = 80 and v = 4 , then

10 = $\frac{80k}{4^2}$ = $\frac{80k}{16}$ ( multiply both sides by 16 to clear the fraction )

160 = 80k ( divide both sides by 80 )

2 = k

m = $\frac{2K}{v^2}$ ← equation of variation

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Answer:

$E(X)=16\cdot 0.3+18\cdot 0.1+20\cdot 0.6=18.6$

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$V(X) = E(X^2)-[E(X)]^2=349.2-(18.6)^2=3.24$

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Step-by-step explanation:

From the information given we know the probability mass function (pmf) of random variable X.

$\left|\begin{array}{c|ccc}x&16&18&20\\p(x)&0.3&0.1&0.6\end{array}\right|$

<em>Point a:</em>

The Expected value or the mean value of X with set of possible values D, denoted by <em>E(X)</em> or <em>μ </em>is

$E(X) = $\sum_{x\in D} x\cdot p(x)$

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$E[h(X)] = $\sum_{D} h(x)\cdot p(x)$

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The variance of X, denoted by V(X), is

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From the rules of expected value this proposition is true:

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We have a = 60, b = -650, and <em>E(X)</em> = 18.6. Therefore

The expected price paid by the next customer is

$60\cdot E(X)-650=60\cdot 18.6-650=466$

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