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3 years ago

Samantha conjectures that for x < -1, it is true that x5 - 2 > x. Is her conjecture correct? Why or why not?

Mathematics

1 answer:

Ronch [10]3 years ago

4 0

Answer:

The conjecture cannot work for any negative numbers, It works for x > 1.3.

Step-by-step explanation:

An odd power preserves the sign. For |x| > 1, the power increases the magnitude. For x < 0, adding -2 only increases the magnitude more. A negative number of larger magnitude will not be "greater than" the reference. It will be "less than."

It only takes a counterexample to show the conjecture is incorrect.

x^5 -2 ?? x

(-2)^5 -2 ?? (-2)

-32 -2 ?? -2

-34 < -2 . . . . . . not greater than

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Consider the function f(x)=-3x^2 +7x -k. [3 Marks] a) For what values of k will the function have no zeros? b) For what values o

Anna35 [415]

Answer: a) k >4.08

b) k = 4.08

c) k<4.08

Step-by-step explanation:

Since we have given that

$f(x)=-3x^2+7x-k$

a) For what values of k will the function have no zeros?

It mean it has no real zeroes i.e. Discriminant < 0

As we know that

$D=b^2-4ac$

Here, a =-3

b = 7

c = -k

So, it becomes,

$D$

b) For what values of k will the function have one zero?

It means it has one real root i.e equal roots.

So, in this case, D = 0

So, it becomes,

$D=b^2-4ac=0\\\\D=7^2-4\times -3\times -k=0\\\\49-12k=0\\\\49=12k\\\\k=\dfrac{49}{12}\\\\k=4.08$

c) For what values of k will the function have two zeros?

It means it has two real roots.

In this case, D>0

So, it becomes,

$D=7^2-4\times -3\times -k>0\\\\49-12k>0\\\\-12k>-49\\\\12k$

Hence, a) k >4.08

b) k = 4.08

c) k<4.08

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Answer:

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Step-by-step explanation:

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Read 2 more answers

Mrs. Cerra planted 4 ⅞ acres of wheat and 1 ⅝ acres of corn. How much more wheat did she plant than corn?

alukav5142 [94]

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2 years ago