Kiran and mai are standing at one corner of a rectangular field of grass looking at the diagonally opposite corner. kiran says that if the field were twice as long and twice as wide, then it would be twice the distance to the far corner. mai says that it would be more than twice as far, since the diagonal is even longer than the side lengths. do you agree with either of them?

Kiran is correct. (I agree with Kiran.)

Suppose the length and width are L and W. The Pythagorean theorem says the diagonal distance is ...

... d = √(L² +W²)

If the dimensions are doubled, the the diagonal distance becomes ...

... D = √((2L)² +(2W)²) = √(4(L² +W²)) = 2√(L² +W²)

... D = 2d

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}

step-by-step explanation: 4 cause 2+2=4