geometric

1. help with geometric distribution exercise

Hello dear forum members. I was requested to answer this exercise that requires the use of geometric distribution. "A bag contains 3 white and 5 black marbles. A marble is extracted with replacement until a black marble is selected. Find the probability that at least k-extractions are required"...
2. Two spheres of radii r1 and r2 cut orthogonally. Find radius of common circle.

Find the radius the common circle of intersection and show that it is equal to \frac{r_1 r_2}{\sqrt{r_1^{2} + r_2^{2}}}. When two sphere intersect they form a circle if you join all the points of intersection, that is the common circle. See this image, the silver portion is the common circle...
3. Geometric Series Equivalence

Hello, Why is this: Equivalent to this: Thank you.
4. Taylor series and Geometric series

To find the taylor series of a function you would usually use the formula $\sum_{n=0}^{\infty}\frac{f^{n}(c)}{n!}(z-c)^n$. However when computing the taylor series for $f(z)=\frac{1}{z+3}$ about $z=1$, I discovered that not only can you compute it using the above formula but you can also...
5. Geometric series, find the common ratio.

Given: a=1, 7th term = 4096. formula that we have to use: a_n=ar^n-1 if we plug it in we get: 1=ar^0 4096=ar^6 If we divide the 2nd equation by the first equation all we get is 4096=r^6..... now the answer...
6. Geometric distributions.

Question I am struggling on is attached. I can do all the questions bar the last one; apparently, P(X=3) (where X has a geometric distribution) is incorrect. I can't really see why this is as P(X=3) is defined as 'the probability of failing two times and then having a success on the third...
7. inverse geometric model arm robot : system equations non linear

Hi, i'm studying a robot arm i have done davenit and direct geometric model and i obtain this equations system eq1=335*cos(t2)* sin(t3) -77*sin(t2)-260*sin(t2)*sin(t4)+260*cos(t2)*cos(t3)*cos(t4)+85=x; eq2=335*cos(t3)-260* sin(t3)*cos(t4)=y; eq3=0-335*sin(t2)* sin(t3) -77*cos(t2)...
8. Using logarithms in a geometric distribution question involving inequalities.

The question goes like this: It is know that 9% of the population belongs to blood group B. How many people must a doctor - who is sampling random people - examine to be 99.8% confident of finding at least one person with blood group B? P(X\geqx)\leq0.002 where X = the no. of people examined...
9. Finding Ratios and First Term of Geometric Sums

Three integers x, y, and z (where x <= y <= z) form a geometric series with a common ratio r (which is also an integer). Given x + y + z = 741, what is the sum of all possible values of z? (Ans Key: 4870) I started doing some guess and check with my calculator and got z values of 247, 513, and...
10. Geometric Sequence Problem

We are working with the explicit formulas for arithmetic AND geometric sequences. I get for the most part, but it is the world problems that stump me a little. Here's one that confused me that I could use help on: John buys a computer for 1200 dollars. He predicts that the value of the...
11. Geometric Sequence

2nd term=3 4th term=1/3 6th term= unknown, find. 3=ar 1/3=ar^3 Then that equals 9=r^2 r=3 6th term= ar^n-1 6th term=a(3)^5 6th term=a243 Where did I mess up at ?
12. Arithmetic and Geometric Sequences.

Hi, I just did these problems for my final review. Does anyone mind checking them? Tyvm. 1) Find the 98th term of an arithmetic sequence whose first three terms are 2,6,10 Ans: 390 2)Write the 21st term in arithmetic sequence with a first term of 7, and a common difference of 5. Ans: 107 3)...

I am also stuck on this question. Let {b sub k} be a geometric sequence. Given that (b sub 4)= 80, (b sub 9)=1280, and (S sub 9)=2555. Find the first term (b sub 1). I have tried it every way I know how but I am getting nowhere. No amount of searching on the internet has helped either...
14. Geometric Progression

Hi, I came across a GP questions as follows- The difference between 5th term and 3rd term of GP is 72. If the 1st term is 1. Find the common ratio. I had solved it. Please correct me. Where am I wrong? a= 1 as its the 1st term. ar^4 - ar^2 = 72. This implies r^4- r^2 = 72. From here I can...
15. Geometric Progression

The sum of an infinite GP is 16, its second term is 4. Find the first term
16. Convergence of a geometric power series centered at x = 2

2 Questions I have located at the bottom of the attached image.
17. Understanding Arithmetic and Geometric series, help?

Below are a few examples i pulled from by book, i was wondering if i could get some help with so i can have a better understanding on how to solve the rest. 8+3-2-7-12-....-87 1a) What Kind of series is this? Arithmetic, Geometric, or Neither? Why? 1b) Use the appropriate formula to find...
18. Geometric Sequences

How many terms of the geometric sequence 1.2, 2.4, 4.8, 9.6, 19.2...are required for the sum to be greater than 10,000? Do you use the equation sn=a(1-r^n)/1-r? And how is logarithms included in this question?
19. Infinite geometric series word problem

Q: A ball is dropped from a height of 32 ft. Each time it strikes the ground it rebounds 3/8ths of the distance from which it had fallen. Theoretically, how far will the ball travel before coming to a rest? Because the ball rebounds up then falls back down again before rebounding a next time, I...
20. Geometric Progression Word Problem

Q: The sum of the first and last terms of a G.P. of fourteen real terms is 7. The fifth term is the mean proportional between the second and last terms. Find the third term. All I have been able to come up with thus far are the equations: t1 + t14 = 7 and t2/t5 = t5/t14 Then I plugged in a...