Answer:
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I assume the cone has equation (i.e. the upper half of the infinite cone given by ). Take
The volume of the described region (call it ) is
The limits on and should be obvious. The lower limit on is obtained by first determining the intersection of the cone and sphere lies in the cylinder . The distance between the central axis of the cone and this intersection is 1. The sphere has radius . Then satisfies
(I've added a picture to better demonstrate this)
Computing the integral is trivial. We have
Answer:
3, 5, 2, 1, 4
Step-by-step explanation:
In step 2, parentheses are eliminated: distributive property.
In step 3, x is subtracted: subtraction property.
In step 4, 12 is added: addition property.
In step 5, the equation is divided by 17: division property.
__
The properties are listed in the order of statements ...
3, 5, 2, 1, 4
The correct answer is C) 800,000 cubic meters.
The scale given is for the length, width or height of the model. In order to find the scale for the volume, we would cube this scale, since volume is a cubic measurement:
(1/200)³ = 1/8,000,000
Since the volume of the model is 0.1, we multiply this by 8,000,000 to find the volume of the actual dam:
0.1(8000000) = 800,000
Using algebra...
n and n+2 are the integers
n*(n+2)=288
n^2+2n=288
n^2+2n-288=0
288=2*2*2*2*2*3*3=(2*2*2*2)*(2*3*3)=16*18 and 18-16=2
factor
(n+18)(n-16)=0
n+18=0
n=-18
n+2=-16
this is one solution
n-16=0
n=16
n+2=18
this is another solution
as you can see, it's just a matter of factoring
288
using arithmetic...
√288=16.97≈17
16 and 18 are the integers (as well as -16 and -18)