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Nutka1998 [239]
2 years ago
7

A ball is thrown vertically upward with an initial velocity of 64 feet per second. The distance s​ (in feet) of the ball from th

e ground after t seconds is s=64t-16t^2 (a) At what time t will the ball strike the​ ground? ​(b) For what time t is the ball more than 48 feet above the​ ground?
Mathematics
1 answer:
kow [346]2 years ago
6 0

Given:

The distance s​ (in feet) of the ball from the ground after t seconds is

s=64t-16t^2

To find:

(a) At what time t will the ball strike the​ ground?

(b) For what time t is the ball more than 48 feet above the​ ground?

Solution:

(a)

We have,

s=64t-16t^2

Substitute s=0, to find the time t when the ball strike the​ ground.

0=64t-16t^2

0=16t(4-t)

Using zero product property, we get

16t=0\Rightarrow t=0

4-t=0\Rightarrow t=4

Therefore, the ball strike the​ ground in initial condition (t = 0) and after 4 seconds (t = 4).

(b)

Now, s > 48, to find the time t when the ball will be more than 48 feet above the​ ground.

64t-16t^2\geq 48

0> 16t^2-64t+48

Divide both sides by 16.

0> t^2-4t+3

0> t^2-t-3t+3

0> t(t-1)-3(t-1)

0>(t-1)(t-3)

Related equation is (t-1)(t-3)=0. Zeroes are t=1,3. These two number divide the number line is three parts. (-∞,1),(1,3),(3,∞)

0>(t-1)(t-3) inequality is true for only (1,3).

It is only possible when t lies in the interval (1,3).

Therefore, the ball will be more than 48 feet above the​ ground between 1 and 3 seconds.

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Answer: 300/91

Step-by-step explanation:

1. Convert 4 1/3 to an improper fraction

13/3

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4. Simplify, if applicable. This fraction cannot be simplified any further.

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3 years ago
Mrs McCarr buys 9 packages of markers for an art project. Each packages has 10 markers. How many markers does Mrs McCarr buy?
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Question:

The box plots below show student grades on the most recent exam compared to overall grades in the class: two box plots shown. The top one is labeled Class. Minimum at 70, Q1 at 74, median at 83, Q3 at 92, maximum at 100. The bottom box plot is labeled Exam. Minimum at 60, Q1 at 81, median at 87, Q3 at 91, maximum at 95. Which of the following best describes the information about the medians? (1 point) Group of answer choices

•The exam outlier at 60 makes the IQR narrower and the median higher.

•The class data is more evenly spread, which pulls its median down.

•The class median is lower than the exam median.

•The class Q3 is higher than the exam Q3.

Answer:

•The class Q3 is higher than the exam Q3.

Step-by-step explanation:

In the question we have two box plots

a) Box plots for class is given as

Minimum at 70, Q1 at 74, median at 83, Q3 at 92,

b) Box plots for exam is given as Minimum at 60, Q1 at 81, median at 87, Q3 at 91, maximum at 95.

When we compare the median of the class which is 83 and the median of the exam plots 87, we can see that the median of the exam is higher than the median of the class, hence the option

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From the options given, the only correct option which best describes the information about the medians is

"•The class Q3 is higher than the exam Q3".

This is because when we compare the Q3 of the class which is 92 to the Q3 of the box which is 91 , we can see that the class Q3 is higher than the box Q3 hence the option is correct.

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