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Rashid [163]
2 years ago
15

Given: XZ bisects ZYXW and ZYZW Prove: AXYZ 2 AXWZ

Mathematics
1 answer:
Rudiy272 years ago
5 0

Answer:

Step-by-step explanation:

Top Problem:

Reason:

1. Given

2. Definition of segment bisector ( segment bisector is a line, ray or segment that divides a segment into to congruent segments)

3. Vertical angles are congruent

4. SAS (Side ZP≅XP Angle ZPY ≅ WPX  Side WP≅YP)

Bottom Problem

Reason:

1. Given

2. Definition of angle bisector ( an angle bisector is a line, ray or line segment that divides an angle in two congruent angles)

3. Definition of angle bisector

4. Reflexive Property ( a line segment is congruent with itself)

5. ASA (Angle Side Angle Theorem of Congruency)

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Hi, am I supposed to find the stationary points of the f(x) and g(x) then use the distance formula to solve for the final answer
nikdorinn [45]

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Answer:

  maximum difference is 38 at x = -3

Step-by-step explanation:

This is nicely solved by a graphing calculator, which can plot the difference between the functions. The attached shows the maximum difference on the given interval is 38 at x = -3.

__

Ordinarily, the distance between curves is measured vertically. Here that means you're interested in finding the stationary points of the difference between the functions, along with that difference at the ends of the interval. The maximum difference magnitude is what you're interested in.

  h(x) = g(x) -f(x) = (2x³ +5x² -15x) -(x³ +3x² -2) = x³ +2x² -15x +2

Then the derivative is ...

  h'(x) = 3x² +4x -15 = (x +3)(3x -5)

This has zeros (stationary points) at x = -3 and x = 5/3. The values of h(x) of concern are those at x=-5, -3, 5/3, 3. These are shown in the attached table.

The maximum difference between f(x) and g(x) is 38 at x = -3.

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