Ellie's bird feeder:
We're trying to find a cylinder that has exactly the same volume as a certain cone. The first thing we need is the formulas for the volumes of cones and cylinders.
Volume of a cone = (1/3) (pi) (radius)² (height)
Volume of a cylinder = (pi) (radius)² (height)
We know all the measurements of the cone. We also know the radius of the cylinder. We want their volumes to be equal, and we need to find the height of the cylinder that will make them equal.
Here's the easiest way to do it:
Write an equation that <u>says</u> the volumes are equal. In that equation, the height of the cylinder will be the only thing we don't know, and we can use the equation to find what it is.
Cone volume = Cylinder volume
(1/3) (pi) (cone-R)² (cone-hight) = (pi) (cyl-R)² (Cyl-height)
Divide each side by (pi):
(1/3) (cone-R)² (cone-hight) = (cyl-R)² (Cyl-height)
Put in all the numbers we do know:
(1/3) ( 3 )² ( 25 ) = ( 5 )² (Cyl-height)
( 1/3 x 9 ) x ( 25 ) = ( 25 ) x (Cylinder height)
Divide each side by 25: (1/3 x 9) = Cylinder height.
<em> 3 inches = Cylinder height</em>
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Jade scooping sand:
I'm sorry. Maybe I don't understand the question, but I have to say
that none of the answers on the list is possible.
-- She has a cylinder that's completely full of sand, and she's using a
cone-shaped scooper to scoop sand out of the cylinder.
-- That means she has to slip the cone-shaped scooper down and
bury it in the sand, and then turn it right-side-up,and lift it out of the
cylinder along with the sand that's in it.
-- She can't get the scooper into the cylinder if the scooper's diameter
is bigger than the cylinder's diameter. It won't fit.
-- The cylinder's diameter is 12 . Its radius is 6. The scooper's radius
can't be more than 6, or it won't fit.
In choices 'A', 'B', and 'C', the radius of the scooper is more than 6,
so none of those can even fit into the cylinder.
In choice 'D', the radius and diameter of the scooper is the same as
the cylinder, but its height (15) is three times the height of the cylinder !
I can't imagine how you could even scoop with it at all.
Answer:
C=$30.00+.10m
Step-by-step explanation:
The total cost per mile is 10 cents or $0.10. If he drives 5 miles, that will cost him an extra 50 cents on top of the base total of 30.
<span>
<u><em>The correct answers are: </em></u>1) f(x)=1/2x;
2) f(x)=2x+1;
3) f(x)=x^3;
4) f(x)=6x.
<u><em>Explanation</em></u><span>
<u><em>: </em></u>Let x be the input. In function notation, the output is denoted by f(x).
For #1, since the output is half of the input, we want to take half of x; this would give us
f (x)=</span></span>
<span><span>x.
For #2, twice the input is 2x; one more than this is 2x+1, which gives us
f (x)=2x+1.
For #3, the cube of the input is x</span></span>³<span><span>, which gives us
f (x)=x</span></span>³<span><span>.
For #4, six times the input is 6x, which gives us
f (x)=6x.</span></span>
Answer:
Starting position of mine shaft is = 10m above ground
but,
it moves in opposite direction so it travels the distance (-350 m ) below the ground.
Total distance covered by mine shaft = 10m - (-350m)
= 10 + 350
= 360m
Now, taken to cover a distance of 6m by it = 1 minute
Time taken to cover a distance of 1m by it = \frac{1}{6\ }\min
Therefore, tie taken to a cover a distance of 360m = \frac{1}{6}\times\ 360\ =\ 60\ \min\ \
60 minutes = 1 hour
thus, in one hour the mine shraft reaches = 350 below the ground
Step-by-step explanation:
(1 5/3) / (16 3/2)
(8/3) / (35/2)
(8*2) / (3*35)
16 / 105