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3 years ago

A fraction is less than 1. Choose a counterexample that will prove this conjecture false

Mathematics

1 answer:

Vesnalui [34]3 years ago

7 0

Answer:

1st option

Step-by-step explanation:

Here we are trying to prove that not all fractions are less than 1. So we have to choose an example in which the fraction is more than 1.

1) $\frac{8}{7} = 1 \frac{1}{7}$

This fraction is greater than 1 hence it can prove that the conjecture is false.

2) ½ is lesser than 1 and will not prove that the conjecture is false.

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3 years ago

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3 years ago

Read 2 more answers

One more time!

CaHeK987 [17]

Since q(x) is inside p(x), find the x-value that results in q(x) = 1/4

$\frac{1}{4} = 5 - x^2\ \Rightarrow\ x^2 = 5 - \frac{1}{4}\ \Rightarrow\ x^2 = \frac{19}{4}\ \Rightarrow \\
x = \frac{\sqrt{19} }{2}$

so we conclude that
$q(\frac{\sqrt{19} }{2} ) = 1/4$

therefore

$p(1/4) = p\left( q\left(\frac{ \sqrt{19} }{2} \right) \right)$

plug $x=\sqrt{19}/2$ into p( q(x) ) to get answer

$p(1/4) = p\left( q\left( \frac{ \sqrt{19} }{2} \right) \right)\ \Rightarrow\ \dfrac{4 - \left( \frac{\sqrt{19} }{2}\right)^2 }{ \left( \frac{\sqrt{19} }{2}\right)^3 } \Rightarrow \\ \\ \dfrac{4 - \frac{19}{4} }{ \frac{19\sqrt{19} }{8}} \Rightarrow \dfrac{8\left(4 - \frac{19}{4}\right) }{ 8 \cdot \frac{19\sqrt{19} }{8}} \Rightarrow \dfrac{32 - 38}{19\sqrt{19}} \Rightarrow \dfrac{-6}{19\sqrt{19}} \cdot \frac{\sqrt{19}}{\sqrt{19}}\Rightarrow$

$\dfrac{-6\sqrt{19} }{19 \cdot 19} \\ \\ \Rightarrow -\dfrac{6\sqrt{19} }{361}$

$p(1/4) = -\dfrac{6\sqrt{19} }{361}$

3 0

3 years ago

What is bigger 5/6 or 11/12?

Maurinko [17]

First you find the common deoninator.
Step 1: Reduce (simplify) entered fractions to lowest terms, if the case:Fraction: 5 / 6 it's already reduced to lowest terms
Fraction: 11 / 12 it's already reduced to lowest terms
Step 2: Calculate LCM (lowest common multiple) of the reduced fractions' denominators, it will be the common denominator of the compared fractions:Denominator 6, factored = 2 * 3
Denominator 12, factored = 22 * 3
LCM (6, 12) = 22 * 3 = 12Step 3: Calculate each fraction's expanding number (LCM divided by each fraction's denominator):For fraction: 5 / 6 is 12 : 6 = (22 * 3) : 6 = 2
For fraction: 11 / 12 is 12 : 12 = (22 * 3) : 12 = 1
Step 4: Expand fractions to bring them to the common denominator (LCM):5 / 6 = (2 * 5) / (2 * 6) = 10 / 12
11 / 12 = (1 * 11) / (1 * 12) = 11 / 12

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3 years ago

What is 14/4y + 4/2=3y-3

OverLord2011 [107]

Answer:

-10

Step-by-step explanation:

Solve for y by simplifying both sides of the equation, then isolating the variable

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3 years ago

A fraction is less than 1. Choose a counterexample that will prove this conjecture false​

A fraction is less than 1. Choose a counterexample that will prove this conjecture false