Math, asked by mj7979, 1 year ago

A spiral formed by semicircles have radii 0.5,1.0,1.5.... respectively.What is the total length of 13 semicircles?

Attachments:

Answers

Answered by Shreya2002
1
Circumference of first semicircle = πr = 0.5π

Circumference of second semicircle = πr = 1π = π

Circumference of third semicircle =πr = 1.5π





It is clear that a = 0.5 π, d = 0.5π and n = 13

Hence; length of spiral can be calculated as follows:

sum of n terms
10 arithmetic progression exercise solution

mj7979: answr this question
Light1729: i think the question is wrong
mj7979: y?
Light1729: Using distance formula,

√[{x-2}²+{y+3}²]=√[{x+4}²+{y-5}²]

Squaring both sides,

x²-4x+4+y²+6y+9=x²+8x+16+y²-10y+25

So, 12x-16y+28=0
mj7979: This question was there in our first term exam
Light1729: i got 3x-4y+7=0
mj7979: i also got the same
Light1729: its wrong question, then
Light1729: don't worry about it
mj7979: ok. i will ask my teacher
Answered by Light1729
1
Length of one semicircle = πr

So, length of 13 semicircles is π{0.5}+π{1}+π{1.5}+...+π{6.5}

=π{0.5+1+1.5+...+6.5}

{sum of AP}

=π{0.5+6.5}/2
Similar questions