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The equation ​ yˆ=−6.2x2+51.5x+10.2 ​ approximates the average number of cars that pass through an intersection x hours after 3:00 p.m. What is the best estimate for the average number of cars that pass through the intersection at 6:30 p.m.?

Respuesta :

cerverusdante
Notice that form 3 pm to 6:30 pm 3.5 hours have passed.
Since the function [tex]y=-6 x^{2} +51.5x+10.2[/tex] represent the average number of cars that pass through an intersection x hours after 3:00 p.m, we are going to replace [tex]x[/tex] with 3.5 to find the average number of cars that pass through the intersection at 6:30 p.m
[tex]y=-6 x^{2} +51.5x+10.2[/tex]
[tex]y=-6 (3.5)^{2} +51.5(3.5)+10.2[/tex]
[tex]y=-6(12.25)+180.25+10.2[/tex]
[tex]y=-73.5+190.45[/tex]
[tex]y=116.95[/tex]

We can conclude that the average number of cars that pass through an intersection at 6:30 pm is approximately 117. 

Answer:

115 cars.

Step-by-step explanation:

We have been given an equation [tex]y=-6.2x^2+51.5x+10.2[/tex] which approximates the average number of cars that pass through an intersection x hours after 3:00 p.m.

Since we know that there will be 3.5 hours between 3:00 pm and 6:30 pm. So to find the average number of cars that pass through the intersection at 6:30 pm we will substitute [tex]x=3.5[/tex] in our given equation.

[tex]y=-6.2(3.5)^2+51.5(3.5)+10.2[/tex]

[tex]y=-6.2*12.25+180.25+10.2[/tex]

[tex]y=-75.95+180.25+10.2[/tex]

[tex]y=114.5\approx 115[/tex]

Therefore, approximately 115 cars will passe through the intersection at 6:30 pm.

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