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Serjik [45]
3 years ago
14

A rocket is launched with an initial upward velocity of 320 feet per second from an initial height of 15 feet.

Mathematics
1 answer:
liberstina [14]3 years ago
5 0

Answer:

The height of the rocket is greater than or equal to 1.039 feet during first 19.936 seconds.

Step-by-step explanation:

The height of the rocket launched from the ground is modelled after the following expression:

h(t) = -16.087\cdot t^{2}+320\cdot t +15 (1)

Where:

t - Time, measured in seconds.

h - Height, measured in feet.

After a careful reading to the statement, we translate all relevant information into the following mathematical inequation:

-16.087\cdot t^{2}+320\cdot t +15\ge 1.039 (2)

After some algebra, we get the equivalent inequation:

-(16.087\cdot t^{2}-320\cdot t -13.961)\ge 0

16.087\cdot t^{2}-320\cdot t -13.961 \le 0

(x-19.936)\cdot (x+0.044)\le 0

Which means that the following conditions must be observed to satisfy the inequation above:

x-19.936\le 0\,\land\,x+0.044\ge 0

x\le 19.936\,s\,\land\,x\ge -0.044\,s

0\,s\le x \le 19.936\,s

The height of the rocket is greater than or equal to 1.039 feet during first 19.936 seconds.

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Answer:

C) p(x) has a zero between x=2 and x=4

Step-by-step explanation:

For a polynomial p(x), p(a)=R means that, when p(x) is divided by x-a, the remainder is R.

This is called the remainder theorem

Therefore p(2)=1, p(4)=-1 means that when p(x) is divided x-2 and x-4 is 1 and -1 respectively.

Also the Intermediate value theorem says that, if p(a) and p(b) have opposite signs then there is a certain c on (a,b) where f(c)=0 i.e there is a zero between a and b

Therefore the correct answer is C

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3 years ago
Is 4 5/12 a terminating or repeating decimal?
Vesnalui [34]

Answer:

repeating

Step-by-step explanation:

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5 0
3 years ago
A composite shape is shown.
kodGreya [7K]

Answer:

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Step-by-step explanation:

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The following stem-and-leaf plot represents the test scores for
rewona [7]

Considering the given stem-and-leaf plot, the quartiles are given as follows:

  • The first quartile is of 67.5.
  • The second quartile, which is the median, is of 84.5.
  • The third quartile is of 91.5.

<h3>What are the median and the quartiles of a data-set?</h3>

  • The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.
  • The first quartile is the median of the first half of the data-set.
  • The third quartile is the median of the second half of the data-set.

There is an even number of elements(26), hence the median is the mean of the 13th and 14th elements, which are 83 and 86, hence:

Me = (83 + 86)/2 = 84.5.

The first half has 12 elements, hence the first quartile is the mean of the 6th and 7th elements, which are 67 and 68, hence:

Q1 = (67 + 68)/2 = 67.5.

The third half also has 12 elements, starting at the second 86, hence the third quartile is the mean of the 6th and 7th elements of this half, hence:

Q3 = (91 + 92)/2 = 91.5.

More can be learned about the quartiles of a data-set at brainly.com/question/28017610

#SPJ1

7 0
1 year ago
Find an equation for the nth term of the arithmetic sequence.<br> 8,6,4,2,…
jarptica [38.1K]

Answer:

1st term= 8 2nd term=6 3rd term=4 4th term=2 5th term=0 6th term=-2 7th term=-4 8th term=-6 9th term=-8 10th term=-10

Step-by-step explanation:

hope this helps

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2 years ago
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