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# The restorative power of sleep is graphically approximated by the func

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Math Expert
Joined: 02 Sep 2009
Posts: 58390
The restorative power of sleep is graphically approximated by the func  [#permalink]

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30 Nov 2016, 03:04
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Difficulty:

65% (hard)

Question Stats:

59% (01:53) correct 41% (01:57) wrong based on 251 sessions

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The restorative power of sleep is graphically approximated by the function −x^2 + 16x + 36, where the x-axis measures sleeping hours and the y-axis measures the restoration value. After how many hours does sleep no longer perform restorative duties according to the function?

A. −2
B. 4
C. 8
D. 13
E. 18

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Re: The restorative power of sleep is graphically approximated by the func  [#permalink]

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30 Nov 2016, 04:50
2
Bunuel wrote:
The restorative power of sleep is graphically approximated by the function −x^2 + 16x + 36, where the x-axis measures sleeping hours and the y-axis measures the restoration value. After how many hours does sleep no longer perform restorative duties according to the function?

A. −2
B. 4
C. 8
D. 13
E. 18

The restorative power is given by $$-x^2 + 16x + 36$$.

We want the value of x (number of hours) for which it will become 0.

-x^2 + 16x + 36 = 0
x = 18, -2

After 18 hours, the graph will be negative so there will be no positive restoration value.
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Re: The restorative power of sleep is graphically approximated by the func  [#permalink]

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30 Nov 2016, 07:19
The restorative power is given by the equation -x^{2}+16x+36, which is equal to x^2-16x-36. We are told that the restoration value is in the y-axis, and we want to find out after how much sleep we would not get any restoration for our sleep.
So if y becomes 0, we have x^2-16x-36=0.
or
(x-18)(x+2)=0
Which means that x=18 or x=-2
Since we are counting hours of sleep, the answer cannot be negative, thus x=18 and the answer is E.
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Re: The restorative power of sleep is graphically approximated by the func  [#permalink]

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16 Jun 2017, 23:50
1
Bunuel wrote:
The restorative power of sleep is graphically approximated by the function −x^2 + 16x + 36, where the x-axis measures sleeping hours and the y-axis measures the restoration value. After how many hours does sleep no longer perform restorative duties according to the function?

A. −2
B. 4
C. 8
D. 13
E. 18

This question is simple yet has a very subtle trap answer- in order to find the values of x we must factor the equation- if you simply plug in values and solve for 0 you would also find that -2 and 18 equal 0. However, theoretically, you cannot have a negative amount of sleep therefore the answer is simply 18. This is just a matter of reading the question

Thus
"E"
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Re: The restorative power of sleep is graphically approximated by the func  [#permalink]

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13 Jul 2019, 03:07
Bunuel wrote:
The restorative power of sleep is graphically approximated by the function −x^2 + 16x + 36, where the x-axis measures sleeping hours and the y-axis measures the restoration value. After how many hours does sleep no longer perform restorative duties according to the function?

A. −2
B. 4
C. 8
D. 13
E. 18

The restorative power is given by $$-x^2 + 16x + 36$$.

We want the value of x (number of hours) for which it will become 0.

-x^2 + 16x + 36 = 0
x = 18, -2

After 18 hours, the graph will be negative so there will be no positive restoration value.

The quadratic function here opens downwards. After the maxima point the effect of sleep is negative. I think point of maxima is the correct answer. As the question asks when does the restorative duties end and not when does the effect of sleep becomes zero.
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The restorative power of sleep is graphically approximated by the func  [#permalink]

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15 Jul 2019, 09:59
1
Every equation can be represented as a graph on X-Y coordinate plot.
For this problem we do not actually need to plot a graph, but having understanding of where a graph lies on coordinate system help in better understanding.
So before reading the explanation I would suggest to google some simple graph of $$x^2$$, $$-x^2$$, $$x^2$$+1 , and $$x^2$$+x+1 etc
(You can also copy paste same equation on Google ; see attached graph)

Now from figure i.e. understanding of equation, this is an equation of downwards open parabola. As its parabola it can cut x-axis at two point
When it cuts x-axis its y coordinate will be 0.
So putting value in Y=0
0 = -$$x^2$$ + 16x + 36
x = -2 or 18

After both this point 'restorative power' i.e. Y coordinate gets negative. So -2 or 18 is Ans
But Sleep hours practically could not be -2. So correct ans is 18
Option E

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2019-07-15 21_55_28--x^2 + 16x + 36 - Google Search.jpg [ 25.74 KiB | Viewed 149 times ]

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The restorative power of sleep is graphically approximated by the func   [#permalink] 15 Jul 2019, 09:59
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