The maximum rpm for the car can be determined by finding the vertex of the parabola represented by the equation y = -2x^2 + 8x. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = -2 and b = 8. Plugging in the values, we get x = -8 / (2*-2) = 2.
Substitute x = 2 back into the equation to find the maximum rpm: y = -2*(2)^2 + 8*2 = -2(4) + 16 = -8 + 16 = 8,000 rpm.
So, the correct answer is 8,000 rpm.
1)
A car magazine wants to determine the maximum rpm of a car. The following graph shows the equation y=−2x2+8x
. The equation represents the function for the rpm of the car in thousands, where the rpm is y
and the number of seconds is x
.
The maximum rpm for the car is
(1 point)
Responses
6,000 rpm
6,000 rpm
8,000 rpm
8,000 rpm
10,000 rpm
5 answers
The engine returns to idle and the rpm becomes 0 at(1 point)
Responses
2 seconds
2 seconds
3 seconds
3 seconds
4 seconds
Responses
2 seconds
2 seconds
3 seconds
3 seconds
4 seconds
The engine returns to idle and the rpm becomes 0 when y = 0.
0 = -2x^2 + 8x
0 = -2x(x - 4)
This equation will be true when either x = 0 or x = 4.
So, the engine returns to idle at 4 seconds.
Therefore, the correct answer is:
4 seconds
0 = -2x^2 + 8x
0 = -2x(x - 4)
This equation will be true when either x = 0 or x = 4.
So, the engine returns to idle at 4 seconds.
Therefore, the correct answer is:
4 seconds
The rpm of the car increases for the first(1 point)
Responses
2 seconds
2 seconds
3 seconds
3 seconds
4 seconds
Responses
2 seconds
2 seconds
3 seconds
3 seconds
4 seconds
The rpm of the car increases when the value of y is positive. Therefore, we need to find when y (the rpm) is greater than 0. Going back to the equation -2x^2 + 8x:
-2x^2 + 8x > 0
Solving this inequality gives us x > 0 or x < 4. The rpm is increasing in the interval from 0 to 4 seconds.
Therefore, the rpm of the car increases for the first 4 seconds.
So, the correct answer is:
4 seconds
-2x^2 + 8x > 0
Solving this inequality gives us x > 0 or x < 4. The rpm is increasing in the interval from 0 to 4 seconds.
Therefore, the rpm of the car increases for the first 4 seconds.
So, the correct answer is:
4 seconds