MATHEMATICS HIGH SCHOOL

You drop a ball from a height of 0.5 meter. Each curved path has 52% of the height of the previous path.a. Write a rule for the sequence using centimeters. The initial height is given by the term n = 1.
b. What height will the ball be at the top of the third path?

Answers

Answer 1
Answer:

Answer:

  1. f(n)=0.5(0.52)^(n-1)
  2. 0.14 m

Step-by-step explanation:

The initial height of the ball is 0.5 m

Each curved path has 52% of the height of the previous path, i.e the height of the ball after one bounce will be,

=(52)/(100)* 0.5\n\n=0.52* 0.5\ m

The height of the ball after 2 bounces will be,

=(52)/(100)*(0.52* 0.5)

=0.52*0.52* 0.5

=0.52^2* 0.5\ m

Hence the series becomes,

0.5,0.5(0.52),0.5(0.52)^2,............

This is the case of Geometric Progression.

But as it is given that the initial height will be given by n=1, so the rules for finding the height f(n) after n bounces would be,

f(n)=0.5(0.52)^(n-1)

Putting n=3, we can get the height of the ball of the third path,

\Rightarrow f(3)=0.5(0.52)^(3-1)=0.5(0.52)^(2)=0.14\ m
Answer 2
Answer: This is a geometric sequence.  The first term is the max height of the first curved path, which is 0.5.  The second one is 52% of that meaning that it is 0.52 times the first term.  The third term is 0.52 times the second term. Thus, in this geometric sequence,

a = 0.5
r = 0.52

You will need to use the relation a_n = a \cdot r^(n-1)

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Answers

Answer:

slope of the line perpendicular to MN = 2/3

Step-by-step explanation:

slope = y2 - y1 / x2 - x1

the given co-ordinates are:

x1, y1 = -3, 4

x2, y2 = 5, -8

slope = -8 - 4 / 5 + 3

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slope of the line perpendicular to MN = -1 / slope

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                                                               = -1 * -2/3 = 2/3

Answer:

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Step-by-step explanation:

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Answers

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Answers

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Step-by-step explanation:
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