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3 years ago

A catapult launches a boulder with an upward velocity of 120 ft/s. The height of the boulder, h,

Mathematics

1 answer:

tekilochka [14]3 years ago

3 0

Answer:

The boulder's maximum height is:

a. Reaches a maximum height of 235.00 feet in 3.75 seconds.

Step-by-step explanation:

The easiest way to solve the unknown is to replace the time in the given equation, with the values given in the answer, look for the highest value and check if the height value decreases as the time increases or decreases.

First the equation provided is taken:

h = -16t ^ 2 + 120t + 10

The time values in the options are 3.75 seconds and 7.5 seconds, therefore we proceed to replace this formula with those values:

h (3.75) = - 16 (3.75) ^ 2 + 120 (3.75) + 10 = 235
h (7.5) = - 16 (7.5) ^ 2 + 120 (7.5) + 10 = 10

Since a higher height value is obtained with 3.75 seconds (235 feet), this time will be taken as appropriate, however, it is best to check that by using more time and less time, the height decreases from that value, so we will take two very close times: 3.74 seconds and 3.76 seconds:

h (3.74) = - 16 (3.74) ^ 2 + 120 (3.74) + 10 = 234.9984
h (3.76) = - 16 (3.76) ^ 2 + 120 (3.76) + 10 = 220.5884

As you can see, if slightly higher or lower time values are taken, the height of the rock still decreases from 235 feet, so we can be sure that the time in which it reaches its maximum height is 3.75 seconds.

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PolarNik [594]

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3 years ago

The average undergraduate cost for tuition, fees, and room and board for two-year institutions last year was $13,252. The follow

kipiarov [429]

Answer:

The p-value of the test is 0.0041 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean cost has increased.

Step-by-step explanation:

The average undergraduate cost for tuition, fees, and room and board for two-year institutions last year was $13,252. Test if the mean cost has increased.

At the null hypothesis, we test if the mean cost is still the same, that is:

$H_0: \mu = 13252$

At the alternative hypothesis, we test if the mean cost has increased, that is:

$H_1: \mu > 13252$

The test statistic is:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

13252 is tested at the null hypothesis:

This means that $\mu = 13252$

The following year, a random sample of 20 two-year institutions had a mean of $15,560 and a standard deviation of $3500.

This means that $n = 20, X = 15560, s = 3500$

Value of the test statistic:

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{15560 - 13252}{\frac{3500}{\sqrt{20}}}$

$t = 2.95$

P-value of the test and decision:

The p-value of the test is found using a t-score calculator, with a right-tailed test, with 20-1 = 19 degrees of freedom and t = 2.95. Thus, the p-value of the test is 0.0041.

The p-value of the test is 0.0041 < 0.05, which means that there is sufficient evidence at the 0.05 significance level to conclude that the mean cost has increased.

7 0

3 years ago

The first row of a theater has 16 seats. There are 3 more seats in each row thereafter. How many seats are in the 25th row/

inessss [21]

Answer: 88

Step-by-step explanation:

Given

The first row has 16 seats

then there are 3 more seats in each row

this follows an AP with the first term $a=16$ and common difference $d=3$