1.To do a college visit, Wes must make a 240-mile trip by car. The time in hours required to complete time
the trip depends on the speed at which Wes drives, of course, as the table below shows. Fill in the miss- ing entries, and plot points on the grid provided. Are the quantities time and speed proportional? It makes sense to connect your plotted points with a continu- ous graph. Explain why.

2.Suppose that n represents an integer. What expression represents the next larger inte- ger? the previous integer? the sum of these three consecutive integers?

3. .The rectangle ABCD shown at right has sides y
that are parallel to the coordinate axes. Side AD is three times the length of side AB and the perimeter of ABCD is 56 units.
(a) Find the dimensions of ABCD.
(b) Given the information D = (9, 2), find the coor- dinates for points A, B, and C.

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}

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

nothjing

step-by-step explanation:

5

step-by-step explanation: