A paper airplane was thrown from the top of a tall building. The height of the paper airplane above the ground can be found using the function y=—1.5x+60 , where x is the time in seconds the airplane has been in the air.

1) Since you have not provided the full question, I will work the quadratic expression that models the height of the paper airplane to find as much information as it gets.

2) Firstly, note that the quadratic function -2x^2 + 5x + 33 has these characteristics:

i) It is a parabola

ii) Since, the coefficient of x^2 is negative (-2) it opens downward and has a maximum, which indicates the maximum height of the airplane

iii) The, y-intercept, i.e. the y-value for x = 0, is the initial height of the ariplane, the height from which it was launched, and it is - 2 (0) + 5(0) + 33 = 33.

Then, the airplane was launched from a height of 33 units.

3) The vertex of the parabola is the maximum and it tells both the time to reach the maximum height and the value of that maximum.

4) You can easily find the vertex coordinates by completeing squares. This is how:

Start: -2x^2 + 5x + 33

Factor - 2 from the first two terms: - 2 (x^2 - 5/2x) + 33

Add and subtract the square of the half of x's coefficient:

- 2 ( x^2 - 5/2x + 25/16) + 25/8 + 33

Form the perfect square binomial: - 2 (x - 5/4)^2 + 289/8

By comparission with the vertex form of the equation of the parabola: A(x - h)² + k, the vertex is:

(h,k) = (5/4, 289/4) = (1.25, 36.125).

5) Then, the maximum height is 36.125 units, when the time is 1.25 seconds.

6) You can also find the time when the airplane lands on the ground by making -2x^2 + 5x + 33 = 0

For that you can factor the expression -2x^2 + 5x + 33

-2x^2 + 5x + 33 = - (x + 3) (2x - 11)

Equal to zero: - (x + 3)(2x - 11) = 0 ⇒ x = - 3 and x = 11/2 = 5.5.

That means that the airplane will land on the ground at 5.5 seconds.

7) You can also find the heights at different times, by just pluging in different values of x in the expression -2x^2 + 5x + 33.

1) Since you have not provided the full question, I will work the quadratic expression that models the height of the paper airplane to find as much information as it gets.

2) Firstly, note that the quadratic function -2x^2 + 5x + 33 has these characteristics:

i) It is a parabola

ii) Since, the coefficient of x^2 is negative (-2) it opens downward and has a maximum, which indicates the maximum height of the airplane

iii) The, y-intercept, i.e. the y-value for x = 0, is the initial height of the ariplane, the height from which it was launched, and it is - 2 (0) + 5(0) + 33 = 33.

Then, the airplane was launched from a height of 33 units.

3) The vertex of the parabola is the maximum and it tells both the time to reach the maximum height and the value of that maximum.

4) You can easily find the vertex coordinates by completeing squares. This is how:

Start: -2x^2 + 5x + 33

Factor - 2 from the first two terms: - 2 (x^2 - 5/2x) + 33

Add and subtract the square of the half of x's coefficient:

- 2 ( x^2 - 5/2x + 25/16) + 25/8 + 33

Form the perfect square binomial: - 2 (x - 5/4)^2 + 289/8

By comparission with the vertex form of the equation of the parabola: A(x - h)² + k, the vertex is:

(h,k) = (5/4, 289/4) = (1.25, 36.125).

5) Then, the maximum height is 36.125 units, when the time is 1.25 seconds.

6) You can also find the time when the airplane lands on the ground by making -2x^2 + 5x + 33 = 0

For that you can factor the expression -2x^2 + 5x + 33

-2x^2 + 5x + 33 = - (x + 3) (2x - 11)

Equal to zero: - (x + 3)(2x - 11) = 0 ⇒ x = - 3 and x = 11/2 = 5.5.

That means that the airplane will land on the ground at 5.5 seconds.

7) You can also find the heights at different times, by just pluging in different values of x in the expression -2x^2 + 5x + 33.

It takes 46 seconds for the plane to reach the ground.

Step-by-step explanation:

We are given the following in the question:

The height of the paper airplane above the ground is given by a function:

where f(x) is the height above the ground and x is the time in seconds.

a) The attached image shows the graph for the given equation.

As clear from the graph the unction has a y-intercept of 69 and x-intercept of 46.

b) We have to find the time taken by he plane to reach the ground.

The height of plane on ground is 0

Thus, we can write:

c) Thus, it takes 46 seconds for the plane to reach the ground from the top of the tall building to reach a height of 0.

How many seconds did it take the paper airplane to reach the ground?

40 Seconds.

Step-by-step explanation:

When the paper airplane touches the ground is equivalent to having a height equal to zero (y=0). So replacing in the equation:

It takes 46 seconds for the plane to reach the ground.

Step-by-step explanation:

We are given the following in the question:

The height of the paper airplane above the ground is given by a function:

where f(x) is the height above the ground and x is the time in seconds.

a) The attached image shows the graph for the given equation.

As clear from the graph the unction has a y-intercept of 69 and x-intercept of 46.

b) We have to find the time taken by he plane to reach the ground.

The height of plane on ground is 0

Thus, we can write:

c) Thus, it takes 46 seconds for the plane to reach the ground from the top of the tall building to reach a height of 0.

Part a) The graph in the attached figure

Part b) It takes the paper airplane 46 seconds to get to the ground.

Step-by-step explanation:

we have

where

x -----> x is the time in seconds the airplane has been in the air.

f(x) ----> the height of the paper airplane above the ground

Part a) Draw the graph of the function

This is a linear function (is a line)

To graph the line plot the intercepts and join the points

Find the y-intercept

The y-intercept is the value of the function f(x) when the value of x is equal to zero

For x=0

The y-intercept is the point (0,69)

Find the x-intercept

The x-intercept is the value of x when the value of the function is equal to zero

For f(x)=0

The x-intercept is the point (46,0)

using a graphing tool

Plot the points (0,69) and (46,0) and join to graph the line

see the attached figure

Part b) How many seconds did it take the paper airplane to reach the ground?

we know that

When the paper airplane reach the ground, the height is equal to zero

so

Determine the x-intercept

For f(x)=0

The x-intercept is the point (46,0)

therefore

It takes the paper airplane 46 seconds to get to the ground.

The answer is in the image 

The answer is in the image 

The answer is in the image 

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

Approximately it is aqual to 1300kg