5 In the diagram, rhombus ABCD has sides of length 5 cm each and the length of the
diagonal AC is 8 cm.
(a) Find ABC
(b) Calculate the area of rhombus ABCD

a) the angle ABC is approximately 106 degrees b) 24

Step-by-step explanation:

1) Using the law of cos

AC*AC= AB*AB+BC*BC-2*AB*BC*cosB

8*8= 5*5+5*5-2*5*5*cosB

64= 50- 50c0sB

cosB= 14/(-50)= -7/25.

B= arccosB= arccos(-7/25)= 106degrees.

2) sinB*sinB= 1- CosB*cosB= 1-49/625= 576/625

sinB= 24/25 (SinB doesn't equal -24/25, because B is between 0 and 180 degrress, so sin B is positive)

3) S= AB*BC*sinB= 5*5*24/25= 24 (area of the rhombus is 24)

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}

answer: 0.64

step-by-step explanation: