Question

Find the value of p=9:P :: 27:45
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Answer 1

Answer:

MATHS

Find the value of p for which the curves x2=9p(9−y) and x2=p(y+1) cut each other at right angles.

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VIDEO EXPLANATION



ANSWER

The given curves are x2=9p(9−y) .... (1)

x2=p(y+1) ...... (2)

Solving (1) and (2) simultaneously, we get

9p(9−y)=p(y+1)⇒81−9y=y+1

⇒10y=80⇒y=8

x2=9p(9−8)⇒x2=9p⇒x=±3p

Therefore, given curves intersect at points (±3p,8) i.e., at points P(3p,8) and Q(−3p,8)

Differentiating (1) and (2) w.r.t x, we get

2x=−9pdxdy⇒dxdy=9p−2x ...... (3) and 

2x=p

Answer 2

Answer:

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Step-by-step explanation:

Think of the numbers before the equal signs as the numbers associated with terms in a series. Thus, term 2 1s 6, term 3 is 12, term 4 is 20, term 5 is 30, and term 6 is 42. Notice that the differences between successive terms is a sequence of steadily increasing even numbers, i.e. term 3 = term 2 + 6, term 4 = term 3 + 8, term 5 = term 4 + 10, term 6 = term 5 +12. If this is really the pattern producing these numbers, we can proceed as follows:

term 7 = term 6 + 14 = 42 + 14 = 56; term 8 = term 7 + 16 = 56 + 16 = 72, and to answer your question

term 9 + term 8 + 18 = 72 + 18 = 90, and you are correct.

Notice that we could also work backwards to find term 1 = 2, and term 0 = 0, and these terms fit the same pattern. Finally, notice that there are several other ways to represent the terms in this pattern, including the following:

term n = n(n + 1); term n = n + n^2; term n = 2 (0 + 1 + 2 + 3 + … + n), etc.