Answer:
12.5
Step-by-step explanation:
150 / 12 = 12.5
(I'm not the best at explaining-)
Let . The tangent plane to the surface at (0, 0, 8) is
The gradient is
so the tangent plane's equation is
The normal vector to the plane at (0, 0, 8) is the same as the gradient of the surface at this point, (1, 1, 1). We can get all points along the line containing this vector by scaling the vector by , then ensure it passes through (0, 0, 8) by translating the line so that it does. Then the line has parametric equation
or , , and .
(See the attached plot; the given surface is orange, (0, 0, 8) is the black point, the tangent plane is blue, and the red line is the normal at this point)
Answer:
Order from Least to Greatest
-4/7 < -1/19 < 7/4
Showing Work
Rewriting as fractions or any negatives if necessary:
-1/19, 7/4, -4/7
The least common denominator (LCD) is: 532.
Rewriting as equivalent fractions with the LCD:
-28/532, 931/532, -304/532
Ordering these fractions by the numerator:
-304/532 < -28/532 < 931/532
Therefore, the order of your input is:
-4/7 < -1/19 < 7/4
Answer: yes you are correct 2 /1/2 is greater
Step-by-step explanation:
To factor, you can first treat it like a single bracket and find the common factor. In this case, the common factor is 3x, so you get
3x(x² + 7x + 12)
Now you can factor the bracket normally, by finding factors of 12 that add up to make 7. The factors would be 3 and 4, so the bracket becomes (x + 3)(x + 4).
This leaves your final answer as
3x(x + 3)(x + 4)
I hope this helps!