Mathematics, 23.08.2019 18:50 peep372

Your bedroom is in the shape of a square that is 12 feet long on each side. will a circular rug with a circumference of 40.82 feet fit into your room? if not, by how many feet is the rug too wide?

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Answer from: shawny5

We know the area of the rug must be smaller than the area of the room, aye?
we simply need to find the area of the room and the rug, and then compare them :)

the room is easy, we know its a SQUARE, the area for a square is:
l x w = A

the length and width of a SQUARE are always the same
(12 x 12 = 144)

the area of the room is 144 (remember that, we will come back to it later)

now, the area of the CIRCLE
is $A= \pi r^2$
we are given the circumfrence..... awww dang Dx ughhh okok fine, we can work through this (-~-)

the circumfrence is the distance around a circle (like a perimeter)

$C= \pi (d)$

we know pi is 3.14, we know the circumfrence is 40.82,

40.82 = 3.14(d)

we now must solve for d by dividing both sides of the equation by 3.14
we get
d = 13

YAYYYYY ok, NOW we can find the area of the circle :)

as i was saying, the area is
A = π r²
where r is the radius (which is Half of the diameter we found earlier)

plugging in the things we know,

A = (3.14) (13/2)²
we get
A = 132.665

In conclusion, the area of the circle is less than the area of the square, HOWEVER!!!
remember how the diameter (of the rug) is 13? The length of the room is only 12 units ;) sneaky little question hahaha, anyways, the rug will NOT fit becuase it has a larger diameter than the rooms length :/

imagine fitting a circle into a square thats too small, the corners fit, but the middles dont :(

Answer from: Quest

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

Me if you can and if you finished this lesson on edg- comment you.

Answer from: Quest

$53.50

step-by-step explanation:

you have to subtract the amount of money chuck earned ($72.50) by the cost of the gas for the mower ($11.25) and the new string for the trimmer he bought ($7.75).

72.50-11.25=61.25

and then subtract $61.25 by the second thing he bought (the new string for the trimmer)

61.25-7.75=53.5

so in total it's $53.50 (53 dollars and 50 cents)