A bird starts from the ground, flies at a certain speed for 5 seconds, and lands on a tree branch. The vector representing its position is (4,10). It continues to fly in the same direction and at the same speed for 5 or more seconds, and lands on another branch. What vector represents its new position?

The vector represents its new position is (10,25)

Step-by-step explanation:

A bird starts from the ground, that is (0,0) position and flies at a certain speed for 5 seconds, and lands on a tree branch.The vector representing its position is (4,10).

The rate of increase = slope will be

Slope = 10/4 = 2.5

It continues to fly in the same direction and at the same speed for 5 or more seconds

Since it is travelling at same speed and time, Slope will be the same

Slope = (y - 10)/(x - 4) = 5/2

The new x position = 4 × 5/2 = 10

The new y position = 10 × 5/2 = 25

The vector represents its new position is (10 , 25)

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt