has critical points wherever the partial derivatives vanish:
Then
- If , then ; critical point at (0, 0)
- If , then ; critical point at (1, 1)
- If , then ; critical point at (-1, -1)
has Hessian matrix
with determinant
- At (0, 0), the Hessian determinant is -16, which indicates a saddle point.
- At (1, 1), the determinant is 128, and , which indicates a local minimum.
- At (-1, -1), the determinant is again 128, and , which indicates another local minimum.
Answer:
A = 90°
B = 37°
C = 53°
Step-by-step explanation:
Given three sides of a triangle, the Law of Cosines can be used to find the angles.
__
For angle A (the largest), we can use ...
a² = b² +c² -2bc·cos(A)
Solving for A, we get ...
A = arccos((b² +c² -a²)/(2bc)) = arccos((3² +4² -5²)/(2·3·4)) = arccos(0)
A = 90°
We can use a similar equation for angle B:
B = arccos((a² +c² -b²)/(2ac)) = arccos((25 +16 -9)/(2·5.4)) = arccos(4/5)
B ≈ 37°
The sum of angles is 180°, so ...
C = 180° -90° -37°
C = 53°
15 minutes= 2 problems
75 / 15 = 5
2 x 5 = 10 problems
Answer: See explanation
Step-by-step explanation:
Liters → Milliliters
1 liter → 1000 milliliters
0.73 → 730
3.9 → 3900
10.65 → 10650
147.2 → 147200
Milliliters → Liters
1000 → 1
217 → 0.217
6570 → 6.57
14200 → 14.2
213920 → 213.92