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raketka [301]
1 year ago
13

What is the value of P in the equation x2 12y?

Mathematics
1 answer:
Pani-rosa [81]1 year ago
5 0

The value of P is 3

Given general formula for a parabola is x2 = 4py ………….(a)

Also given that x2 = 12y …………..(b)

Equating (a) and (b), we get

x2 = 4py ≅ x 2 = 12y

⇒ 4py = 12y

Canceling the 'y' on either sides, we get

⇒ 4p= 12 p= 3

When the general formula for a parabola is x2 = 4py. The value of p in the equation x2 = 12y is 3.

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One description of a parabola involves a point and a line

To learn more about parabola visit:brainly.com/question/21685473

#SPJ4

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  • <em>2.21 and 2.23 are proved by contrapositive</em>
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<u />

<u />

<u>2.21: If </u>n^3<u> is even, then n is even (By contrapositive)</u>

The contrapositive of the above statement is that:

<em>If n is odd, then  </em>n^3<em> is odd</em>

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Take the cube of both sides

n^3 = (2k + 1)^3

Expand

n^3 = 8k^3 + 6k^2 + 6k + 1

Group

n^3 =[ 8k^3 + 6k^2 + 6k] + 1

Factor out 2

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So, we have:

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The constant term (i.e. 1) means that n^3 is odd.

Hence, the statement has been proved by contrapositive.

<em>i.e. If n is odd, then  </em>n^3<em> is odd</em>

<u />

<u>2.22  </u>3n + 4<u> is even, if and only if n is even</u>

We have: 3n + 4<u />

<u />

Assume that: n = 2k + 2 for k \ge 0

So, we have:

3n + 4 = 3(2k + 2) + 4

Open bracket

3n + 4 = 6k + 6 + 4

3n + 4 = 6k + 10

Factorize

3n + 4 = 2(3k + 5)

The factor of 2 means that 3n + 4 is even.

<em>Hence, </em>3n + 4<em> is even, if and only if n is even </em>

<em />

<u />

<u>2.22: </u>s \ne -1<u> and </u>t \ne -1<u>, then </u>s + t + st \ne -1<u />

To do this, we prove by contrapositive.

The contrapositive of the above statement is:

If s = -1 and t=-1, then s + t + st = -1

We have:

s + t + st = -1

Substitute the values of s and t in: s + t + st = -1

-1 -1 -1 \times -1 = -1

-1 -1 + 1 = -1

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Hence, by contrapositive:

If s = -1 and t=-1, then s + t + st = -1

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