Answer:
x=2.125
y=0
C=19.125
Step-by-step explanation:
To solve this problem we can use a graphical method, we start first noticing the restrictions 
and 
, which restricts the solution to be in the positive quadrant. Then we plot the first restriction 
shown in purple, then we can plot the second one 
shown in the second plot in green.
The intersection of all three restrictions is plotted in white on the third plot. The intersection points are also marked.
So restrictions intersect on (0,0), (0,1.7) and (2.215,0). Replacing these coordinates on the objective function we get C=0, C=11.9, and C=19.125 respectively. So The function is maximized at (2.215,0) with C=19.125.
Answer:
84
Step-by-step explanation:
7 × 12 = 84
84 × 1000 = 84000
84000 mililetre
Just substitute x = 2 and y = 5 into the equation wherever you see x and y.
2 + (12 - 5x) · 2y
2 + (12 - 5(2)) · 2(5)
2 + (2) · 10
4 · 10
40, is the answer which should be the first box.
Proof by induction
Base case:
n=1: 1*2*3=6 is obviously divisible by six.
Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.
For n+1:
(n+1)(n+2)(n+3)=
(n(n+1)(n+2)+3(n+1)(n+2))
We have assumed that n(n+1)(n+2) is divisble by 6.
We now only need to prove that 3(n+1)(n+2) is divisible by 6.
If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.
The "cool" part about this proof.
Since n is a natural number greater than 1 we can say the following:
If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.
Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.
Answer:
The total population of the school is 300 students.
Step-by-step explanation:
Considering, we are working with percentage we can use the equation:
y = %x.
To fill in the equation you can use what you already know, 60% = 180
180 = 0.60x
To solve this, you can then divide both sides of the equation by 0.60. This will then give you your answer, 300 = x.
For checking, you can do 180 = 0.60(300) which will result in 180 = 180.
