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2 years ago

Determine if the conjecture is true or false. If true, explain your reasoning briefly. If false provide a counterexample.

Mathematics

1 answer:

Arisa [49]2 years ago

7 0

9514 1404 393

Answer:

false

Step-by-step explanation:

The conjecture shown in this problem statement does not follow from the examples offered. They support the notion that ...

1/x ≤ x . . . . for x ≥ 0 (<u>not x ≤ 0</u>)

There are several possible counterexamples showing the conjecture is FALSE.

1/0 is undefined
1/(-5) > -5 . . . . . . . . a case for x < 0

If the intended domain is x ≥ 0, then the conjecture can also be demonstrated to be false for 0 < x < 1:

1/(1/5) > 1/5

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3 years ago

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Point b has coordinates (-8,15) and lies on the circle whose equation is x^2+y^2=289. If an angles is drawn in standard position

Alenkinab [10]

Answer:

$\cos \theta=-\dfrac{8}{17}$

Step-by-step explanation:

Coordinates of Point b $=(-8,15)$

b lies on the circle whose equation is $x^2+y^2=289$

$x^2+y^2=17^2$

Comparing with the general form a circle with center at the origin: $x^2+y^2=r^2$

The radius of the circle =17 which is the length of the hypotenuse of the terminal ray through point b.

For an angle drawn in standard position through point b,

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Therefore, the angle is in Quadrant II.

$\cos \theta=\dfrac{Adjacent}{Hypotenuse} \\$Adjacent=-8\\Hypotenuse=17\\\cos \theta=\dfrac{-8}{17} \\\cos \theta=-\dfrac{8}{17}$

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3 years ago

A football team has $3,744 to spend on hats for their fans. Each hat costs $8. How many hats can the team buy?

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Answer:

468

Step-by-step explanation:

3,744/8=468

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Answer:

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Step-by-step explanation:

hope this helps!

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3 years ago