Crystal solved the following equation incorrectly. In which step did she make a mistake? A Step 1 B Step 2 C Step 3 D Step 4
1 answer:
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Let x be the number of people that can be seated.
The value of x is some number 0 or greater, such that this number is a whole number (we can't have half a person). This means that
which is the same as saying 
The instructions state that we can seat up to 1200 people. This is the max capacity. We can't go over this amount. So we will also have
indicating that x can be less than 1200 or equal to 1200.
So putting the two inequalities together, we get
Note: if you haven't learned about compound inequalities yet, then the teacher may only want as the answer.
The value of x is some number 0 or greater, such that this number is a whole number (we can't have half a person). This means that
The instructions state that we can seat up to 1200 people. This is the max capacity. We can't go over this amount. So we will also have
So putting the two inequalities together, we get
Note: if you haven't learned about compound inequalities yet, then the teacher may only want
Answer:
- hits the ground at x = -0.732, and x = 2.732
- only the positive solution is reasonable
Step-by-step explanation:
The acorn will hit the ground where the value of x is such that y=0. We can find these values of x by solving the quadratic using any of several means.
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<h3>graphing</h3>The attachment shows a graphing calculator solution to the equation
-3x^2 + 6x + 6 = 0
The values of x are -0.732 and 2.732. The negative value is the point where the acorn would have originated from if its parabolic path were extrapolated backward in time. Only the positive horizontal distance is a reasonable solution.
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<h3>completing the square</h3>We can also solve the equation algebraically. One of the simplest methods is "completing the square."
-3x^2 +6x +6 = 0
x^2 -2x = 2 . . . . . . . . divide by -3 and add 2
x^2 -2x +1 = 2 +1 . . . . add 1 to complete the square
(x -1)^2 = 3 . . . . . . . . written as a square
x -1 = ±√3 . . . . . . . take the square root
x = 1 ±√3 . . . . . . . add 1; where the acorn hits the ground
The numerical values of these solutions are approximately ...
x ≈ {-0.732, 2.732}
The solutions to the equation say the acorn hits the ground at a distance of -0.732 behind Jacob, and at a distance of 2.732 in front of Jacob. The "behind" distance represents and extrapolation of the acorn's path backward in time before Jacob threw it. Only the positive solution is reasonable.
