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trapecia [35]
3 years ago
5

The height of an object launched upward from ground level is given by the function s(t) = -4.9t2 + 78.4t, where s(t) is the heig

ht in meters and t is the time in seconds. Arrange the time intervals in ascending order of the object's magnitude of average velocity over the interval.

Mathematics
1 answer:
Dahasolnce [82]3 years ago
4 0

Answer:

  • 6.5-8
  • 8-11
  • 9.5-10
  • 9-11
  • 4-4.5
  • 3-3.5
  • 2-2.5

Step-by-step explanation:

I'm always looking for ways to make problems like this simpler than computing 14 function values and doing a bunch of additional arithmetic.

Of course, all that could be done in a spreadsheet, which could then do the sorting for you. However, we'll try some mental math methods.

__

The average velocity on an interval for an object in ballistic motion is the slope of the height curve at the midpoint of the interval. The magnitude of velocity is symmetrical about the vertex of the height curve, which occurs at ...

  t = -b/(2a) = -78.4/(2(-4.9)) = 8

That is, the farther the center of the time interval is from t=8, the greater the magnitude of velocity.

Interval: 8-11, 6.5-8, 2-2.5, 4-4.5, 3-3.5, 9-11, 9.5-10

Midpoint: 9.5, 7.25, 2.25, 4.25, 3.25, 10, 9.75

Distance from 8: 1.5, 0.75, 5.75, 3.75, 4.75, 2, 1.75

So, the values of "distance from 8" in order are ...

  0.75, 1.5, 1.75, 2, 3.75, 4.75, 5.75

The corresponding intervals in order of increasing velocity magnitude are ...

  • 6.5-8
  • 8-11
  • 9.5-10
  • 9-11
  • 4-4.5
  • 3-3.5
  • 2-2.5

_____

For your edification, the spreadsheet solution is attached. Having the sort done automatically saved a bunch of time relative to that spent checking and double-checking the work by hand.

The magnitude of the average velocity on the interval [a, b] is

  |v| = |s(b)-s(a)|/(b-a)

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aliina [53]

Answer:

C) more than the absolute value of the critical value, we can conclude that the average monthly rate for an assisted-living facility is not equal to $3,300.

Step-by-step explanation:

Hello!

Interest hypothesizes is " the average monthly rate for one-bedroom assisted-living facility is equal to $3300" symbolically: μ = 3300

The study variable is:

X: Monthly rate for a one-bedroom assisted-living facility.

Since there is no information about the distribution of the variable, to be able to study the population mean, I'll assume that the variable has a normal distribution.

The hypothesis is:

H₀: μ = 3300

H₁: μ ≠ 3300

α: 0.05

The statistic to use, considering that there is no known population information and the sample size, is a Student t:

t= <u> X[bar] - μ </u> ~t_{n-1}

       S/√n

n= 12

X[bar]= $3690

S= $530

Using the sample data, calculate the statistic value:

t= <u> 3690 - 3300 </u> = 2.549

       530/√12

The rejection region for this test is two-tailed, with critical values:

t_{n-1; \alpha /2} = t_{11; 0.025} = -2.201

t_{n-1;1-\alpha /2} = t_{11; 0.975} = 2.201

The decision rule is:

Reject the null hypothesis if t ≤ -2.201 or if t ≥ 2.201

Not reject the null hypothesis if -2.201 < t < 2.201

Since the calculated value (2.549) is greater than the right critical value (2.201) the decision is to reject the null hypothesis.

With a signification level of 5%, there is enough evidence to reject the null hypothesis. This means that the population mean of the monthly rate for a one-bedroom assisted living facility is different from $3300.

I hope it helps!

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3 years ago
Need help with this lol
Kisachek [45]

Answer:

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Step-by-step explanation:

hope this helps with your work

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Step-by-step explanation:

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