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hoa [83]
2 years ago
11

Mrs.Peterson dropped a ball from the top of a tower. At the same time, her son, Drake, launches a rocket from a different level

of the tower.
The height of the tennis ball in feet after t seconds can be represented by the quadratic function: b(t)=-t^2-2t+26.
The height of Drakes rocket after t seconds can be represented by the linear function: p(t)=-2t+10.
What are the two solutions to this system? Show your work.
Explain which solution is not reasonable in this situation.
After how many seconds do the rocket and the ball reach the same height.
Mathematics
2 answers:
ss7ja [257]2 years ago
8 0

9514 1404 393

Answer:

  • two solutions: t = -4, t = 4
  • t = -4 is not reasonable
  • 4 seconds

Step-by-step explanation:

A graphing calculator shows the two solutions to be ...

  (t, h) = (-4, 18) and (4, 2)

__

The two heights will be equal when ...

  p(t) = b(t)

  -2t +10 = -t^2 -2t +26

  t^2 -16 = 0 . . . . subtract the right side expression

  (t -4)(t +4) = 0 . . . factor the difference of squares

  t = 4 or -4 . . . . values of t that make the factors zero

At these times, the heights will be ...

  p(t) = -2{4, -4} +10 = {-8, 8} +10 = {2, 18}

The solutions are ...

  (t, height) = (-4, 18) and (4, 2).

__

We generally discount solutions for negative time, because we start counting time when the objects are launched. t = -4 is an extraneous solution.

__

The rocket and ball reach the same height after 4 seconds.

katen-ka-za [31]2 years ago
3 0

Answer:

fxfyug

Step-by-step explanation:

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Meg lives in Indianapolis and wants to visit her mom in Lima. She has been meaning to go to a chiropractor in Dayton, so she is
ella [17]

Answer: 44 miles

WORKINGS

Given,
The distance between Indianapolis and Lima, IL = 173 miles
The distance between Indianapolis and Dayton, ID = 165 miles
The distance between Dayton and Lima, DL is unknown

Since there are straight roads connecting the three cities, the connection between them form a right angles triangle.

The right angle is at Dayton
The hypotenuse is the distance between Indianapolis and Lima, IL

Therefore IL^2 = ID^2 + DL^2
173^2 = 165^2 + DL^2
DL^2 = 173^2 – 165^2
DL^2 = 29929 – 27225
DL^2 = 2704
DL = 52 miles

Therefore, The distance between Dayton and Lima, DL = 52 miles

The question is asking how many more miles would Meg drive if she stopped in Dayton first than if she drove directly to Lima.

That is, Distance of Indianapolis to Dayton + Distance of Dayton to Lima – Direct distance of Indianapolis to Lima
That is, ID + DL – IL
= 165 miles + 52 miles – 173 miles
= 217 miles – 173 miles
= 44 miles

Therefore, Meg would drive 44 more miles if she stopped in Dayton first than if she drove directly to Lima.
7 0
3 years ago
What is the perimeter of the figure?
Fudgin [204]

Answer: C. 16.9

Step-by-step explanation: To find the perimeter you have to add all the sides of the figure.

6 0
3 years ago
Four members from a 45​-person committee are to be selected randomly to serve as​ chairperson, vice-chairperson,​ secretary, and
wariber [46]

Answer:

3575880

Step-by-step explanation:

We need to use Permutation method,

nPr= \frac{n!}{(n-r)!}

Where n is the sample of size and r the combination considered, so

n=45\\r=4\\45P4= \frac{45!}{(45-4)!}\\45P4 = 3575880

There is 3575880 possibilities to make leadership structures in that committee

6 0
3 years ago
2 5 ÷ 6 7 Give your answer as a fraction in its simplest form.
Bas_tet [7]

Answer:

2.68

Step-by-step explanation:

25/67 = 2.68

3 0
2 years ago
Kamrynn is looking at her five quiz scores of 96 90 94 93 and 90. Determine the mean rounded to the nearest tenth median mode an
Romashka [77]

Answer:

Mean = 90, Median = 93, Mode = 90, Range = 6

Step-by-step explanation:

Mean:

96 + 90 + 94 + 93 + 90 = 463

463 ÷ 5 = 92.5

92.5 to nearest tenth = 90

Mean = 90

Median:

<em>90, 90</em>, <u>93</u>, <em>94 ,96</em>

Median = 93

Mode

<em>96, </em><u>90</u><em>, 94, 93, </em><u>90</u><em> </em>

Mode = 90

Range:

96 - 90 = 6

Range = 6

8 0
2 years ago
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