5. One of the two parallel sides of a trapezium is half of the length of the other. If the height of the trapezium is 7cm and its area is 52.5cm^2. The length of the parallel sides are

5 and 10 cm

Step-by-step explanation:

The area (A) of a trapezium is calculated as

A = h (a + b)

where h is the height and a, b the parallel bases

Here A = 52.5, h = 7 and b = 0.5a ( half the length of the other ), thus

× 7 × (a + 0.5a) = 52.5, that is

3.5 × 1.5a = 52.5

5.25a = 52.5 ( divide both sides by 5.25 )

a = 10

Thus

The parallel sides are 10 cm and 5 cm

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}

it could be 1,3 and more others to create a cylinder.

step-by-step explanation: