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Anika [276]
2 years ago
5

In order to go on a kiddy ride at an amusement park, the

Mathematics
1 answer:
sasho [114]2 years ago
7 0

Using an absolute value inequality, it is found that the maximum height is of 90 pounds, that is:

W \leq 90

------------

  • The absolute value of a point or function is its distance to the origin.
  • That is, for example:

|x| \leq a means that:

-a \leq x \leq a

  • The recommended weight is of 80 pounds, with an allowance of at most 10 pounds. Thus, the absolute value of the weight W and the 80 must be at most 80, that is:

|W - 80| \leq 10

Solving the inequality:

-10 \leq W - 80 \leq 10

W - 80 \geq -10

W \geq 70

W - 80 \leq 10

W \leq 90

Thus, the minimum height is 70 pounds and the maximum height is 90 pounds.

Thus, the inequality representing the maximum height is:

W \leq 90

A similar problem is given at brainly.com/question/24514895

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Answer:

• multiplied by 4p: (x -h)² +4pk = 0

• zeros for k > 0: none

• zeros for k = 0: one

• zeros for k < 0: two

Step-by-step explanation:

a) Multiplying by 4p removes the 1/(4p) factor from the squared term, but adds a factor of 4p to the k term. (It has no effect on the subsequent questions or answers, so we wonder why we're doing this.) The result is ...

(x -h)² +4pk = 0

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b) The value of k is the vertical location of the vertex of the parabola with respect to the x-axis. The parabola opens upward, so for k > 0, the parabola does not cross the x-axis, and the number of real zeros is zero. (There are two complex zeros.)

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c) As in part b, the value of k defines the vertex location. When it is zero, the vertex of the parabola is on the x-axis, so there is one real zero (It is considered to have multiplicity 2.)

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d) As in part b, the value of k defines the vertex location. When it is negative, the vertex of the parabola is below the x-axis. Since the parabola opens upward, both branches will cross the x-axis, resulting in two real zeros.

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The attached graph shows a parabola with p=1/4 and h=2. The values shown for k are +1, 0, and -1. The coordinates of the real zeros are shown.

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