The function h(t) = -16t^2 + 64t + 12 shows the height h(t) in feet of a baseball after t seconds. a second baseball moves in the air along a path represented by g(t)=10 + 10.4t, where g(t) is the height, in feet, of the object from the ground at time t seconds. part a: create a table using integers 1 through 4 for the first two functions. between what 2 seconds is the solution to h(t) = g(t) located? how do you know? part b: explain what the solution from part a means in the context of the problem.

The function H(t) = −16t2 + 64t + 12 shows the height H(t), in feet, of a baseball after t seconds. A second baseball moves in the air along a path represented by g(t) = 10 + 10.4t, where g(t) is the height, in feet, of the object from the ground at time t seconds.

Part A: Create a table using integers 1 through 4 for the 2 functions. Between what 2 seconds is the solution to H(t) = g(t) located? How do you know? (6 points)

Part B: Explain what the solution from Part A means in the context of the problem. (4 points)

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Answer and Explanation:

We have given that,

The function  shows the height H(t), in feet,of a baseball after t seconds.     

A second baseball moves in the air along a path represented by , where g(t) is the height, in feet, of the object from the ground at time t seconds.

We have to find,

Part A - Create a table using integers 1 through 4 for the first two functions. Between what 2 seconds is the solution to H(t) = g(t) located?  

Part B - Explain what the solution from Part A means in the context of the problem.

Solution :

For Part A - We have to substitute the value of t from 1 to 4 in the equation H(t) and g(t)

t                        

1                    

2                    

3            

4            

To determine the interval in which H(t)=g(t), we have to plot the equation and the table points and see the intersection.

Refer the attached figure below.

The intersection point of both the equations are (3.387,45.224).

This point lies between t at 3 to 4.

Therefore, H(t)=g(t) between t=3 to t=4.

For Part B -  The solution from Part A means in the context of the problem.

The Part A shows that the projectile along the path are same in interval [3,4] and gives the solution of equation.

Answer and Explanation:

We have given that,

The function  shows the height H(t), in feet,of a baseball after t seconds.     

A second baseball moves in the air along a path represented by , where g(t) is the height, in feet, of the object from the ground at time t seconds.

We have to find,

Part A - Create a table using integers 1 through 4 for the first two functions. Between what 2 seconds is the solution to H(t) = g(t) located?  

Part B - Explain what the solution from Part A means in the context of the problem.

Solution :

For Part A - We have to substitute the value of t from 1 to 4 in the equation H(t) and g(t)

t                        

1                    

2                    

3            

4            

To determine the interval in which H(t)=g(t), we have to plot the equation and the table points and see the intersection.

Refer the attached figure below.

The intersection point of both the equations are (3.387,45.224).

This point lies between t at 3 to 4.

Therefore, H(t)=g(t) between t=3 to t=4.

For Part B -  The solution from Part A means in the context of the problem.

The Part A shows that the projectile along the path are same in interval [3,4] and gives the solution of equation.

boxplot

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1