What is the coefficient of the term 12p in the expression 12p+9q
2 answers:
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Answer:
129
Step-by-step explanation:
Let a and b be two numbers.
We have been given that the greatest common divisor of two positive integers less than 100 is equal to 3. We can represent this information as .
Their least common multiple is twelve times one of the integers. We can represent this information as .
Now, we will use property .
Upon substituting our given values, we will get:
Switch sides:
Now, we need to find a number less than 100, which is co-prime with 12 after dividing by 3.
The greatest multiple of 3 less than 100 is 99, but it is not co-prime with 12 after dividing by 3.
Similarly 96 is also not co-prime with 12 after dividing by 3.
We know that greatest multiple of 3 (less than 100), which is co-prime with 12, is 93.
Let us add 36 and 93 to find the largest possible sum of the required two integers as:
Therefore, the required largest possible sum of the two integers is 129.
Solution:
There is no saddle point (DNE). However, there is local maximum at (1, 1/2) for the given function.
Explanation:
we have function of two variables f(x,y)= 9-2x+4y-x^2-4y^2
we will find the values by partial derivative with respect to x,y,xy
= -2 -2x
= 4 -8y
to find the saddle point we should first find the critical points so equate
-2 -2x=0 and 4 -8y=0
we get x= 1 and y =1/2 so, critical points are (1,1/2)
to find local maximum or minimum we have to find ,
and
formula is *
-
=0
= -2
= -8
=0
putting values in formula
(-2)*(-8) -0 =16 > 0, and < 0 and
<0
so, here we have local maximum
we have no saddle point for this function by using the same formula we used to find extrema.
