Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
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]
[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]
Answer:
- [tex]f(n)=0.5(0.52)^{n-1}[/tex]
- 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]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.