Angela and brian were measuring the length of each side of the same box, in order to find its volume. they both measured the sides to be 7.2, 3.5, and 8.7. angela, to avoid mistakes in rounding, first found the volume and then rounded to the nearest whole number. brian, on the other hand, decided to take the easy route and rounded the length of the sides to the nearest integers and then found the volume using the rounded lengths. what was the positive difference between angela's and brian's rounded volumes? (note: the volume of a box is defined to be the product of its three sides.)

33

Step-by-step explanation:

Using Angela's method, we first multiply, then round.

V = (7.2)(3.5)(8.7)

V = 219.24

V ≈ 219

Using Brian's method, we first round, then multiply.

V = (7.2)(3.5)(8.7)

V ≈ (7)(4)(9)

V ≈ 252

The positive difference between their answers is:

252 − 219 = 33

c

step-by-step explanation:

when in doubt choose

hshsndjdbdjdjdbdjdxj jd did ddn did and djd f ddnddjd fnf sbabs. d d

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}