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2 years ago

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A rocket was launched into the air from a podium 6 feet off the ground. The rocket path is represented by the equation h(t)=-16t

^2+120t+6, where h(t) represents the height, in feet, and t is the time, in seconds. Find the average rate of change from the initial launch to the maximum height.

1 answer:

Arte-miy333 [17]2 years ago

6 0

Answer:

60

Step-by-step explanation:

The given function is:

$h(t)=-16t^2+120t+6$

The average rate of change of h(t) from t=a to t=b is given by:

$\frac{h(b)-h(a)}{b-a}$

We can rewrite this function as: $h(t)=-16(t-3.75)^2+231$

The maximum height of the rocket is 231 and it occurs at t=3.75

$\implies h(3.75)=231$

The initial launch occurs at: t=0

and $h(0)=-16(0)^2+120(0)+6=6$

The average rate of change from the initial launch to the maximum height is

$\frac{h(3.75)-h(0)}{3.75-0}=\frac{231-6}{3.75-0} =60$

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<h2>Answer:</h2>

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<h2>Step-by-step explanation:</h2>

Let A denote the event that the defective component was from shipment I

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and B denote the event that the defective component was from shipment II.

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Answer:

a) $P(X$

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$P(z$

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And we can find this probability with this difference:

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And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

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Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the velocities of a population, and for this case we know the distribution for X is given by:

$X \sim N(46.8,1.75)$

Where $\mu=46.8$ and $\sigma=1.75$

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using the normal standard table or excel and we got:

$P(z$

Part b

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And we can find this probability using the complement rule, the normal standard table or excel and we got:

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Part c

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And we can find this probability with this difference:

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And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.

$P(-1.5$

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