Given
To obtain the minimum value of y, we first take the derivative of y
The derivative of y is:
Equating
gives the minimum value we require.
Doing that, we have:
So that
Therefore, the minimum value is x = 3
Answer:
The number of teachers who teach physics n(P) = 12
Step-by-step explanation:
<u><em>Step(i):</em></u>-
Given that the number of teachers who teach mathematics or physics
n(MUP) = 20
Given that the number of teachers who teach mathematics
n(M) = 12
Given that the number of teachers who teach both mathematics and physics
n(M∩P) = 4
<u><em>Step(ii):-</em></u>
By using n(A∪B) = n(A) + n(B) - n(A∩B)
n(M∪P) = n(M) +n(P) - n(M∩P)
20 = 12 + n(P) - 4
20 -12 +4 = n(P)
n(P) = 12
<u><em>Final answer:-</em></u>
The number of teachers who teach physics n(P) = 12
Find if all the ratios are proportional to 1:8. 2:16 is, so is 3:24, and 4:32. 4.5*8=36, and 5:40 is proportional. 6:48 is, and 6.5*8=52. The table is proportional, just divide the pay by the hours and you should be getting 8.
3/12 + 10/12 = 13/12 because the points lie in-between the 1/6 and 2/6 marks and the 6/6 and 7/6 marks.
