In △ABC, AB=BC=29, and AC=42. What is the area of △ABC?

The area of △ABC is 420 square units.

The formula for calculating Heron's formula is expressed as √(s(s-a)(s-b)(s-c)  

where:

Get the value of "s"

s = (29+29+42)/ 2

s = 100/2

s = 50.

Get the required area:

Area = √50(50-29)(50-29(50-42)

Area = √176400

Area = 420.

Hence the area of △ABC is 420 square units.

Learn more on area of triangle here: link

420 unit^2.

Step-by-step explanation:

Use  the formula area = √(s(s-a)(s-b)(s-c)   where s = the semi-perimeter and ab and c are the 3 sides. (it is called Heron's Formula).

s = (29+29+42)/ 2

= 100/2

= 50.

Area = √50(50-29)(50-29(50-42)

= √176400

= 420.

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: