Using Lagrange multipliers, we have the Lagrangian
with partial derivatives (set equal to 0)
Substituting the first three equations into the fourth allows us to solve for
:
For each possible value of
, we get two corresponding critical points at
.
At these points, respectively, we get a maximum value of
and a minimum value of
.
Answer:
1 999 000
Step-by-step explanation:
Formula:
………………………………………
Then
Answer:
1. sum of term = 465
2. nth term of the AP = 30n - 10
Step-by-step explanation:
1. The sum of all natural number from 1 to 30 can be computed as follows. The first term a = 1 and the common difference d = 1 . Therefore
sum of term = n/2(a + l)
where
a = 1
l = last term = 30
n = number of term
sum of term = 30/2(1 + 30)
sum of term = 15(31)
sum of term = 465
2.The nth term of the sequence can be gotten below. The sequence is 20, 50, 80 ......
The first term which is a is equals to 20. The common difference is 50 - 20 or 80 - 50 = 30. Therefore;
a = 20
d = 30
nth term of an AP = a + (n - 1)d
nth term of an AP = 20 + (n - 1)30
nth term of an AP = 20 + 30n - 30
nth term of the AP = 30n - 10
The nth term formula can be used to find the next term progressively. where n = number of term
The sequence will be 20, 50, 80, 110, 140, 170, 200..............
<em>Only y= x - 2 intercepts x-axis at 2 and y-axis at -2. Thus meaning that they intercept oppositely.</em>
<em>Find if both graphs are parallel, that means the equation must be false.</em>
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<em>Multiply whole equation by 2 to get rid of the fractional 2.</em>
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<em>Well, that doesn't seem to be parallel. This is called one solution answer. Both graphs intercept at (2,0). There are no linear graphs that intercept at (2,-2) except for y = x-2 so there are no graphs with (2,-2) that are parallel to the equation y = -5x/2+5 </em>
The answer is b
(-1,3,5)
Hope this helps!
