Answer: 2r(0)/3.
Step-by-step explanation:
So, we are given one Important data or o or parameter in the question above and that is the function of the form which is given below(that is);
S(r) = (r0 - r) ar^2 -----------------------------(1).
We will now have to differentiate S(r) with respect to r, so, check below for the differentiation:
dS/dr = 2ar (r0 - r ) + ar^2 (-1 ) ---------;(2).
dS/dr = 2ar(r0) - 2ar^2 - ar^2.
dS/dr = - 3ar^2 + 2ar(r0) ------------------(3).
Note that dS/dr = 0.
Hence, - 3ar^2 + 2ar(r0) = 0.
Making ra the subject of the formula we have;
ra[ - 3r + 2r(0) ] = 0. -------------------------(4).
Hence, r = 0 and r = 2r(0) / 3.
If we take the second derivative of S(r) too, we will have;
d^2S/dr = -6ar + 2ar(0). -------------------(5).
+ 2ar(0) > 0 for r = 0; and r = 2r(0)/3 which is the greatest.
The least common multiple means that the least multiple that the numbers have in common. So you can make a little chart with each of the numbers multiples like so..
3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,69,
(Just added 3 each time)
5,10,15,20,25,30,35,40,45,50,55,60,65,70,
(Just added 5 each time)
7,14,21,28,35,42,49,56,63,70,77
(Just added 7 each time)
No we can go and look through the multiples and see what number they all have that's the same! You might have to keep added on multiples until you find some that are alike! You'll eventually reach 105 for each of the numbers and see that that's the first one that they have that's the same!! So 105 would be your least common multiple!
We know that
if the dilated circle <span>passes through the point (4, 0)
so
the new radius is the distance from the origin to point (4,0)
d=</span>√[(4-0)²+0²]-----> d=√16------> d=4 units
the new radius is 4 units
original radius is 1 units
[new radius]=[scale]*[original radius]
scale=new radius/original radius-----> scale=4/1-----> 4
the answer is
<span>the scale factor of dilation is 4</span>