Quadrilateral ERGF is inscribed in a circle Find the measure of angle E (Remember to show formulas equations and numbers in those formulasequations receive creditAlso, make sure to include units on your answer ) R - 2 + 6x G EK 7x - 13

The measure of angle E is 75°.

Solution:

Given data:

∠E = 5x, ∠F = 7x – 13 and ∠R = –2 + 6x

A quadrilateral inscribed in a circle is called cyclic quadrilateral.

∠R and ∠G are opposite angles in a cyclic quadrilateral.

In cyclic quadrilateral, opposite angles are supplementary.

⇒ m∠R + m∠F = 180

⇒ –2 + 6x + 7x – 13 = 180

⇒ 13x – 15 = 180

Add 15 from both sides of the equation, we get

⇒ 13x = 195

Divide by 13 from both sides of the equation, we get

⇒ x = 15

To find the measure of angle E:

m∠E = 5x

m∠E = 5(15)

m∠E = 75

The measure of angle E is 75°.

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}