The answer is 7x so I this helps you please thank me plz bye
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.
Answer:
B: About 50 grams of the material was left in the container after 140 days.
Step-by-step explanation:
Radioactive materials decay at a rate called "half-lives." After a certain amount of time, the grams of radioactive material will be reduced to half. After that same amount of time again, the material will be reduced to half of the half.
1/4 is equal to 1/2 times 1/2. So, when 1/4 of the material remains, two half-lives have elapsed.
The question states that after 280 days, 25 grams of the material was left in the container. 25 grams is 1/4 of the original 100 grams that the scientist started with at time = 0 days.
When 25 grams of material remain, two half-lives have elapsed. 280 days equals two half-lives for this material. So 140 days (half of 280 days) equals one half-life for this material.
After 280 days (two half-lives), one fourth of the material (25 grams) will remain.
After 140 days (one half-life), half of the material (50 grams) will remain.
