Identify the errors made in finding the inverse of

Mathematics

1 answer:

andrezito [222]2 years ago

4 0

Answer:

x = y² + 12x

y² = x - 12

y² = -11x.

Step-by-step explanation:

We need to find the inverse of the given function , which is ,

$\rm\implies y = x^2 + 12x$

Step 1 : Interchange x and y :-

$\rm\implies x = y^2 + 12y$

But according to the steps given in the Question , in very first step in 12x , x is not replaced by y . After which , the steps go wrong in the question .

The 3 errors :-

x = y² + 12x
y² = x - 12
y² = -11x.

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Suppose we want to choose 4 colors, without replacement, from 18 distinct colors.

amm1812

Answers:

(a) 73440
(b) 3060

=====================================================

Explanation for part (a)

Consider four slots labeled A,B,C,D.

We have

18 choices for slot A
17 choices for slot B
16 choices for slot C
15 choices for slot D

We started at 18 and counted down until we filled the four slots. The countdown is because we cannot repeat a color. Multiply out those values to get the answer: 18*17*16*15 = 73440

You can use the nPr permutation formula as an alternative method

$_nP_r = \frac{n!}{(n-r)!}$

in this case n = 18 and r = 4. The exclamation marks indicate factorial.

-----------------------------------

Explanation for part (b)

Let's say we had color labels A,B,C,... all the way up to R which is the 18th letter in the English alphabet. From those 18 letters, we can only pick four. Let's say we pick D,E,F,G.

Focusing solely on the set {D,E,F,G}, we only have one set and the order doesn't matter. So {D,E,F,G} is the same as {D,E,G,F}.

There are 4*3*2*1 = 24 ways to arrange those four items meaning that we'll need to divide the result of part (a) by 24 to get the result of part (b)

73440/24 = 3060

You could use the nCr combination formula to get the same result

$_nC_r = \frac{n!}{r!(n-r)!}$