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Consider the sequence of numbers a1, a2, a3, ..... to infinity where a1 = 81.33 and a2 = -19 and aj = aj-1 -aj-2 for j ≥ 3. What is the sum of the first 6002 terms of this sequence?

CAT,

Let C be a circle with centre P0 and AB be a diameter of C. Suppose P1 is the mid point of the line segment P0B, P2 is the mid point of the line segment P1B and so on. Let C1, C2, C3, ...... be circles with diameters P0P1, P1P2, P2P3 ... respectively. Suppose the circles C1 C2, C3, .... are all shaded. The ratio of the area of the unshaded portion of C to that of the original circle C is

CAT,

Answers / { jagdeep }

We have 2 poles 5 m and 7 m height ropes are connected from

top of one to tthe bottem of another find the intersection

height of those poles.

Answer

of one to bottom of other. at what heightthe two wires will

cross

We will use algebra and an x-y coordinate axis to solve this

problem. Let the pole of 5 m be located at the origin, so

the two ends of that pole are at (0,0) and (0,5). Let the

pole of 7 m be located on the x-axis at a distance of a to

the right of the first pole, so the two ends of that pole

are at (a, 0) and (a,7). The problem does not state the

distance between the poles, so we let that equal an unknown

constant "a" for now. We will find out later that the value

of "a" is irrelevant.

So we want to draw two lines, one from the base of one to

the top of the other and vice versa.

Line 1: Points (0,0) and (a,7)

Slope of line 1: m = 7/a

Intercept of line 1: b = 0

Equation of line 1: y = (7/a) x

Line 2: Points (0,5) and (a,0)

Slope of line 2: m=-5/a

Intercept of line 2: b = 5

Equation of line 2: y = (-5/a)x + 5

The point where these lines meet is the place where the

wires cross!

Solve equation 1 for x:

x = (a/7) y

Substitute this into equation 2:

y = (-5/a) (a/7) y + 5

Notice that a cancels out!

y = (-5/7)y + 5

(12/7) y = 5

12y = 35

y = 35/12 = 2.912

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