Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Get quick and reliable solutions to your questions from knowledgeable professionals on our comprehensive Q&A platform. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

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?

Sagot :

ParthKohli
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,

[tex]a = 0.5 [/tex]
[tex]r = 0.52 [/tex]

You will need to use the relation [tex] a_n = a \cdot r^{n-1} [/tex]
InesWalston

Answer:

  1. [tex]f(n)=0.5(0.52)^{n-1}[/tex]
  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,

[tex]=\dfrac{52}{100}\times 0.5\\\\=0.52\times 0.5\ m[/tex]

The height of the ball after 2 bounces will be,

[tex]=\dfrac{52}{100}\times(0.52\times 0.5)[/tex]

[tex]=0.52\times0.52\times 0.5[/tex]

[tex]=0.52^2\times 0.5\ m[/tex]

Hence the series becomes,

[tex]0.5,0.5(0.52),0.5(0.52)^2,............[/tex]

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,

[tex]f(n)=0.5(0.52)^{n-1}[/tex]

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

[tex]\Rightarrow f(3)=0.5(0.52)^{3-1}=0.5(0.52)^{2}=0.14\ m[/tex]

We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.