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stira [4]
2 years ago
6

Sally launches a rocket off of a platform. The height of the rocket, in meters, can be modeled by the function, h(x) = -5(x - 3)

2 + 56, where x is in seconds. o What is the height of the platform? o What is the maximum height the rocket reaches? o How long does it take to reach this height?
Mathematics
1 answer:
Lorico [155]2 years ago
4 0

Answer:

Time = 3secs

Max height = 56m

Step-by-step explanation:

Given the height reached by the rocket modeled by the equation;

h(x) = -5(x - 3)² + 56 where;

x is in seconds

The rocket velocity at its maximum height is zero.

Hence dh/dx = 0

dh/dx = 2(-5)(x-3)

dh/dx = -10(x-3)

Since dh/dx = 0

0 = -10(x-3)

0 = -10x + 30

10x = 30

x = 3secs

<em>Hence it takes 3 secs to reach the maximum height.</em>

Get the maximum height reached by the rocket. Substitute x = 3 into the equation given;

Recall that:

h(x) = -5(x - 3)² + 56

If x  = 3

h(3) = -5(3 - 3)² + 56

h(3) = 0 + 56

h(3) = 56

<em>Hence the maximum height that the rocket reaches is 56m</em>

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Write the following numbers used in these statements in scientific notation. (Note: Some of these numbers have been rounded.)
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We have given that radius of earth is 4000 miles

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PART 1. HERE ARE THE NUMBERS I CAME UP WITH I JUST NEED THE REST DONE!!!
jarptica [38.1K]

Answer:

Part 2

The rate of change is 1 in increase in forearm length per 1 inch increase in foot length

Part 3

1) Foot length = 17.922 in.

2) The rate of change of the equation y = 0.860·x + 3.302 in part A is 0.860

3) No the data does not correspond with part A

4) The data  presented here has a greater rate of change

5) Different data sources

6) Yes

7) Yes

Step-by-step explanation:

Part 2

The data are as follows

Forearm             Foot

9.25                    8.5

10.25                   9.5

9.75                     9

10.75                    10

8.75                       8

To find the rate of change, we have;

For points

(x₁, y₁) = (9.25, 8.5) and (x₂, y₂) = (8.75, 8) we have;

Rate of change = (y₂ - y₁)/(x₂ - x₁) substituting the values we arrive at

(8.75 - 9.25)/(8 - 8.5) = 1

The rate of increase of foot to forearm is 1 to 1. That is there is an increase of 1 in in forearm length for every inch increase in foot length

The rate of change is 1 in increase in forearm length per 1 inch increse in foot length

Part 3

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Length of foot, y = 0.860·x + 3.302

Plugging in the values, we have;

y = 0.860×17 + 3.302 = 17.922 in.

2) The rate of change of the equation y = 0.860·x + 3.302 in part A is 0.860

3) No the data does not correspond with part A

4) The rate of change from part A = 0.860, Therefore, the data  presented here has a greater rate of change

5) The values are different because of they are derived from a non corresponding sources

6) Yes the relation is a function because the length of the foot is a function of the length of the forearm

From the equation of a straight line, we have;

y = mx + c

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m = Slope = 1

Therefore; for forearm, y = 9.25, we have

9.25 = 1×8.5 + c

∴ c = 9.5 - 8.5 = 1

The equation of the function becomes;

y = x + 1

7) for the equation in part A given by

y = 0.860·x + 3.302

Yes the equation in part A can represent a function because it maps each value of x to a unique value of y

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