The speed of the ball is
ds/dt = 32t
At t =1/2 s
ds/dt = 16 ft/s
The distance from the ground
50 - 16(1/2)^2 = 46 ft
The triangles formed are similar
50/46 = (30 + x)/x
x = 345 ft

50 / (50 - s) = (30 + x)/x
Taking the derivative and substituing
ds/dt = 16
and
Solve for dx/dt

7 0

3 years ago

Consider a geometric sequence with a first term of 4 and a fourth term of -2.916.

Orlov [11]

Answer:

a) Find the common ratio of this sequence.

Answer: -0.82

b) Find the sum to infinity of this sequence.

Answer: 2.2

Step-by-step explanation:

nth term in geometric series is given by $4\ th \ term = ar^n-1\\-2.196 = 4r^{4-1} \\-2.196/4 = r^{3} \\r = \sqrt[3]{0.549} \\r = 0.82$

where

a is the first term

r is the common ratio and

n is the nth term

_________________________________

given

a = 4

4th term = -2.196

let

common ratio of this sequence. be r

$4\ th \ term = ar^n-1\\-2.196 = 4r^{4-1} \\-2.196/4 = r^{3} \\r = \sqrt[3]{-0.549} \\r = -0.82$

a) Find the common ratio of this sequence.

answer: -0.82

sum of infinity of geometric sequence is given by = a/(1-r)

thus,

sum to infinity of this sequence = 4/(1-(-0.82) = 4/1.82 = 2.2

4 0

2 years ago