Reason abstractly, Evaluate each expression: |13 - 6| = ____

Mathematics

2 answers:

horrorfan [7]3 years ago

7 0

Answer:

Step-by-step explanation:

»Solve inside the absolute value sign | |

|13 - 6| = |7|

The absolute value of 7 is just 7:

|7| = 7

<u>Answer:</u> 7

Reil [10]3 years ago

6 0

Answer:

Step-by-step explanation:

13-6=7 the other line doesn't affect the answer because it isn't negative

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Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x, y) = 4y sqrt (x) , (4, 5) max

liubo4ka [24]

Answer:

Remember that the maximum rate of change of f at a point u is the length of the of the gradient vector evaluate in u, and the direction in which it occurs is in direction of the gradient vector evaluate in u.

The gradient vector of f is

$\triangledown f(x,y)=(\frac{\partial f}{\partial x},\frac{\partial f}{\partial y})=(2yx^{-\frac{1}{2}}, 4\sqrt x)$

Then, the maximum rate of change is $|\triangledown f(4,5)|=|(2*5*4^{-\frac{1}{2}}, 4\sqrt 4)|=|(5,8)|=\sqrt{5^2+8^2}=\sqrt89$ in the direction of (5,8).