How can you solve p2 - 12 =p ?

2 answers:

4 0

$- {p}^{2} - 12 = p \\ {p}^{2} - 12 - p = 0 \\ {p}^{2} - p - 12 = 0$

Now, use the mid term splitting technique

${p}^{2} - 4p + 3p - 12 \\ = p(p - 4) + 3(p - 4) \\ = (p + 3)(p - 4) \\ \\ \\ \\$

From here
we'll do the same thing we do to find the zeroes,

p+3=0 or p -4 =0

p = -3 or p = 4

Therefore
p = -3 and 4

Licemer1 [7]3 years ago

3 0

P= 4 and -3
Move all the terms to the left side and set equal to zero. Then set each factor to zero.

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36.4725 rounded to the nearest hundredths

Vadim26 [7]

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Step-by-step explanation:

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The function g has an inverse. The function g − 1 determines the number of folds needed to give the folded paper a thickness of

Amanda [17]

Answer:

$\mathbf{g^{-1} (t) = log _2 \ 20 \ t}$

Step-by-step explanation:

Here is the full question

A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times. We'll assume we can make "perfect folds," where each fold makes the folded paper exactly twice as thick as before - and we can make as many folds as we want.

Write a function g that determines the thickness of the folded paper (in mm) in terms of the number folds made, n. (Notice that g(0) 0.05,)

$g(n )= (05)2^n$

The function g has an inverse. The function g⁻¹ determines the number of folds needed to give the folded paper a thickness of t mm. Write a function formula for g⁻¹).

SOLUTION:

If we represent g(n) with t;

Then

$\mathbf{t = (0.05)2^n} \\ \\ \mathbf{\dfrac{t}{0.05} = 2^n} \\ \\ \mathbf{\dfrac {100 \ t }{ 5} = 2^n} \\ \\ \mathbf{20 t = 2^n}$

Taking logarithm of both sides; we have :

$\mathbf{log (20 t) = n log 2} \ \ \ \mathbf{(since \ , log \ a^b = b \ log \ a) } \\ \\ \mathbf{n = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = log _2 \ 20 \ t}$