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Lubov Fominskaja [6]
3 years ago
10

Brynn and Denise launch their rockets at the same time. The height of Brynn’s rocket, in meters, is given by the function f(x)=-

4.9x^2+75x , where x is the number of seconds after the launch.
The height of Denise’s rocket, in meters, is given by the function
g(x)=_4.9x^2+50x+38
,  where x is the number of seconds after the launch.
There is a moment when the rockets are at the same height.
 
What is this height?
Enter your answer, rounded to the nearest tenth of a meter, in the box.
Mathematics
2 answers:
Vladimir [108]3 years ago
8 0

Answer:

The height of rocket is 102.7 meter.

Step-by-step explanation:

Given : Brynn and Denise launch their rockets at the same time.

The height of Brynn’s rocket, in meters, is given by the function f(x)=-4.9x^2+75x , where x is the number of seconds after the launch.  

The height of Denise’s rocket, in meters, is given by the function  

g(x)=-4.9x^2+50x+38,  where x is the number of seconds after the launch.

There is a moment when the rockets are at the same height.

To find : The height

Solution :

When the rockets have same height

So, f(x)=g(x)

-4.9x^2+75x=-4.9x^2+50x+38

-4.9x^2+75x+4.9x^2-50x=38

25x=38

x=\frac{38}{25}

x=1.52

Now, we put x value in any of the function to find height.

f(x)=-4.9x^2+75x , x=1.52

f(x)=-4.9(1.52)^2+75(1.52)

f(x)=-11.32096+114

f(x)=102.67

Nearest tenth = 102.7

Therefore, The height of rocket is 102.7 meter.

Y_Kistochka [10]3 years ago
8 0

Answer:  102.7 meters

Step-by-step explanation:

Given: Brynn and Denise launch their rockets at the same time.

The height of Brynn’s rocket, in meters, is given by the function f(x)=-4.9x^2+75x , where x is the number of seconds after the launch.  

The height of Denise’s rocket, in meters, is given by the function  

g(x)=-4.9x^2+50x+38,  where x is the number of seconds after the launch.

The moment when both rockets are on same height, then f(x)=g(x)

\Rightarrow-4.9x^2+75x=-4.9x^2+50x+38\\\\\Rightarrow\ 75x=50x+38\\\\\Rightarrow\ 25x=38\\\\\Rightarrow\ x=1.52

It means at 1.52 seconds  the rockets are at the same height.

To calculate the height substitute, the value of x in any of the function.

f(1.52)=-4.9(1.52)^2+75(1.52)=102.67904\approx102.7 meters

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