Respuesta :
The equation modeling this problem is given by:
y = mx + b
Where,
m: rate of change
x: time in seconds
b: initial height.
We must find the constants m and b.
For m we have:
"descends at a rate of two feet per second":
m = -2
For b we have:
"After 3 seconds it is 67 feet above the ground":
y = -2x + b
67 = -2 (3) + b
67 = -6 + b
67 + 6 = b
b = 73
The equation of the line is:
y = -2x + 73
For eight seconds we evaluate x = 8 in the function:
y = -2 (8) +73
y = -16 + 73
y = 57 feet
Answer:
The equation in point slope form that models the situation is:
y = -2x + 73
The height of the plane after eight seconds is:
y = 57 feet
y = mx + b
Where,
m: rate of change
x: time in seconds
b: initial height.
We must find the constants m and b.
For m we have:
"descends at a rate of two feet per second":
m = -2
For b we have:
"After 3 seconds it is 67 feet above the ground":
y = -2x + b
67 = -2 (3) + b
67 = -6 + b
67 + 6 = b
b = 73
The equation of the line is:
y = -2x + 73
For eight seconds we evaluate x = 8 in the function:
y = -2 (8) +73
y = -16 + 73
y = 57 feet
Answer:
The equation in point slope form that models the situation is:
y = -2x + 73
The height of the plane after eight seconds is:
y = 57 feet
Answer:
- The equation in point slope form is:
[tex]h-67=-2(x-3)[/tex]
where h is the height of the plane above ground and t is the time.
- The height of the plane after eight seconds is: 57 feet
Step-by-step explanation:
Let h denote the height of the plane above the ground.
and t denote the time.
Now, it is given that:
a remote control airplane descends at a rate of two feet per second.
This means that the rate is : -2
Also,
After 3 seconds it is 67 feet above the ground.
This means that the equation which models this situation passes through (3,67).
Hence, by using the point-slope form of the line.
i.e. any line passing through (a,b) and having slope m is given by:
[tex]y-b=m(x-a)[/tex]
Here we have:
y=h x=t , m=-2 and (a,b)=(3,67).
Hence, we have the equation as follows:
[tex]h-67=-2(x-3)[/tex]
Now, we are asked to find the height of the plane after t seconds i.e. we are asked to find the value of h when t=8 seconds.
[tex]h-67=-2(8-3)\\\\i.e.\\\\h-67=-2(5)\\\\i.e.\\\\h-67=-10\\\\i.e.\\\\h=-10+67\\\\i.e.\\\\h=57\ \text{feet}[/tex]
