For the derivative tests method, assume that the sphere is centered at the origin, and consider the
circular projection of the sphere onto the xy-plane. An inscribed rectangular box is uniquely determined
1
by the xy-coordinate of its corner in the first octant, so we can compute the z coordinate of this corner
by
x2+y2+z2=r2 =⇒z= r2−(x2+y2).
Then the volume of a box with this coordinate for the corner is given by
V = (2x)(2y)(2z) = 8xy r2 − (x2 + y2),
and we need only maximize this on the domain x2 + y2 ≤ r2. Notice that the volume is zero on the
boundary of this domain, so we need only consider critical points contained inside the domain in order
to carry this optimization out.
For the method of Lagrange multipliers, we optimize V(x,y,z) = 8xyz subject to the constraint
x2 + y2 + z2 = r2<span>. </span>
Answer:
he grows by 5 cm every year between 1999 and 2006
Step-by-step explanation:
This is a arithmetic progression problem with the formula;
T_n = a + (n - 1)d
We are told that In 1999 Daniel was 146 cm tall. He grew to be 176 cm by the year 2006.
Thus;
a = 146
d = 2006 - 1999 = 7
Thus;
176 = 146 + (7 - 1)d
176 - 146 = 6d
30 = 6d
d = 30/6
d = 5 cm
Thus, he grows by 5 cm every year between 1999 and 2006
It is not straight and does not always pass through 0,0
so A, C, and D are incorrect.
Look up nonlinear function, and it shows a curved line.
The answer is B. It can be curved.
Slope = m
Equation to find slope is:
m = (y2 - y1) / (x2 - x1)
2 points:
(4,-2) 4 = x1 and -2 = y1
(8,5) 8 = x2 and 5 = y2
So...
m = (y2 - y1) / (x2 - x1)
m = (5 - (-2)) / (8 - 4)
m = 7 / 4 or 1.75
Therefore, the slope of the line is 7/4 OR 1.75.
