1. There is four ball in the flat plane and for all the ball must be connected or touch each other. If the radius of the ball have the same value, 2 cm. Determine the high of the pile ball!
Answer:
Given from the question four balls must be connected so we can graph like the picture above:





So for finding the high of the pile ball we can describe that the triangle that we can look actually is a pyramid if in the plane room. This is the description:
The distance between center points also has the same value, 2 cm + 2 cm + 4 cm.
So the pyramid has the same distance for every side is 4 cm. For example, between A and B there is E. So for finding the high of the pyramid we can calculate ABE triangle. But we must know the length of BE side before. Look at the procedure above;

(BC)2 = (BE)2 + (EC)2
(4 )2 = (BE)2 + (2)2
(BE)2 = 16 – 4
(BE)2 =12
BE =2 √3
So we can see that BCD triangle is an equilateral triangle. If AO side is the altitude for ABE triangle therefore O is bisector of BE side. So, the length of OB side and OE are the same too that is OB + OE = BE then OB = OE = √3.
Look the ABE triangle above, where O point is between A and E point.


A


B O E
AB2 = AO2 + OB2
16 = AO2 + (√3)2
AO2 =16 – 3
AO = √13
Now, we can know the high of the pile ball (4 + √13) cm

2. The experiment holds on USAID, University in Australia. Research says that 70 % people believe that drug is not useful. According to the research, how much the probability at least three from five people who taken randomly say that drug is not useful.
Answer:
Using binomial leaflet the theory says that: if ‘p’ as a succeed so there is a ‘q’ as a failure. Then because p + q =1, q = 1 – p.
If we bring the question above to the binomial leaflet we can stimulate into:
70 % is the probability for p so p = 70 % = 0,7
Then q = 1 – p = 1 – 0,7 = 0,3
If at least three from five taken randomly, we can calculate the probability of person that says drug is not useful with binomial leaflet. B ( x, n, p ) = C53 (0.07)3 (0.03)2
And the result is 0,3087

3. Find the solution of the differential equation above
dy / dx = - (3x2y + y2 ) / ( 2x3 +3xy )
“Cannot be solved”



4. What is the plane equation for z = x2 + y2 in (1, 1, 2)?
Answer:
We can substitute z with f (x,y) because z is the function in x and y. To know what are the plane equation we must calculate the derivative based x and the derivative based y from the function.
F (x,y) = x2 + y2
∂f (x,y) / ∂x = 2x
∂f (x,y) / ∂y = 2y then write the vector coordinate ◊f(x,y) = 2xi + 2yj
From the question given that the plane equation in (1, 1, 2)
So ◊f(1,1) = 2i + 2j
There is the formula z –zo = ◊f (xo,yo) (x-xo, y-yo)
Z = f(1,1) + ◊f(1,1) (x-1,y-1)
Z = 2x + 2y +2


5. Find the minimum or maximum value from the function a(x) = l x – 1 l ; I = [0,3]
Answer:
For knowing the maximum and minimum value of a(x) = l x – 1 l in I = [0,3]
We must know the function has the stationer point, singular point and the end point.
1. Find the dot point from the interval. The interval [0,3] indicate 0≤ x ≥ 3, then substitute 0 and 3 into a(x) = l x – 1 l becomes a(0) = 1, a(3) = 2.
2. Find the first derivative or stationer point and we get a’(x) = 1, then substitute to the function will get a(1) = 0
3. Find the singular point but in this sample a(x) didn’t have singular point.
After that we can conclude that o as the minimum value and 2 as a maximum value and (1, 0) is the minimum point (3,2) is the maximum point for the [0,3] as interval of that function.


The Question is come from WIDHATUL MILLLA ( 08305141012 ), and will be finished by ANDINI SETIARI ( 08305141017 )