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-Dominant- [34]
2 years ago
11

Is it positive negative or none?

Mathematics
1 answer:
podryga [215]2 years ago
7 0

Answer:

positive

Step-by-step explanation:

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Suppose f(x,y)=xy, P=(−4,−4) and v=2i+3j. A. Find the gradient of f. ∇f= i+ j Note: Your answers should be expressions of x and
mart [117]

Answer:

a) The gradient of a function is the vector of partial derivatives. Then

\nabla f=(\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y})=(y,x)=y\hat{i} + x\hat{j}

b) It's enough evaluate P in the gradient.

\nabla f(P)=(-4,-4)=-4\hat{i} - 4 \hat{j}

c) The directional derivative of f at P in direction of V is the dot produtc of \nabla f(P) and v.

\nabla f(P) v=(-4,-4)\left[\begin{array}{ccc}2\\3\end{array}\right] =(-4)2+(-4)3=-20

d) The maximum rate of change of f at P is the magnitude of the gradient vector at P.

||\nabla f(P)||=\sqrt{(-4)^2+(-4)^2}=\sqrt{32}=4\sqrt{2}

e) The maximum rate of change occurs in the direction of the gradient. Then

v=\frac{1}{4\sqrt{2}}(-4,-4)=(\frac{-1}{\sqrt{2}},\frac{-1}{\sqrt{2}})= \frac{-1}{\sqrt{2}}\hat{i}-\frac{1}{\sqrt{2}}\hat{j}

is the direction vector in which the maximum rate of change occurs at P.

6 0
3 years ago
Identify whether each value of x is a discontinuity of the function by typing asymptote, hole, or neither. 5x/ x3 + 5x2 + 6x
tatiyna

Answer: hole at x = 0, asymptotes at x = -2 and x = -3

<u>Step-by-step explanation:</u>

  \frac{5x}{x^{3} + 5x^{2} + 6x}

= \frac{5x}{x(x^{2}+5x + 6)}

= \frac{5x}{x(x+2)(x+3)}

x ≠ 0 ---> the x cancels out so this is a hole  

x + 2 ≠ 0   ---> x ≠ -2   ---> asymptote at x = -2

x + 3 ≠ 0   ---> x ≠ -3   ---> asymptote at x = -3

3 0
2 years ago
Read 2 more answers
If ∠MHT measures 126°, what is the measure of ∠THN?
Sunny_sXe [5.5K]
THN forms a strait line with MHT so they would equal 180 when added. 

180-126 = 54

The answer is C
6 0
3 years ago
Read 2 more answers
Simplify this exponential expression:<br><br> (-49) 2/5<br><br> I give Brainliest
Aliun [14]

Answer:

I thank it is 12 4/5

Step-by-step explanation:

hope this helps if not please let me now and dont worry about  brainliest my main focus is just helping people.

5 0
1 year ago
An oil tanker is leaking at a constant rate per minute. After 11 minutes, 931 gallons of oil remain in the tanker. After 18 minu
bekas [8.4K]

The  function f(t) that describes this scenario will be A = -42.57t + 1399.28

  • Let the amount of oil remaining after time t be A
  • Let the time taken be "t"

This required linear expression will be given as A= mt + b

Writing the gallons of oil and the time taken as a coordinate point (A, t), these are given as (11, 931) and (18, 633)

m is the rate of change = 633-931/18-11

m = -298/7

m = -42.57

Get the intercept;

633 = -42.57(18) + b

633 = -766.29 + b

b = 1,399.28

Heence the  function f(t) that describes this scenario will be A = -42.57t + 1399.28

Learn more on functions here; brainly.com/question/17431959

5 0
2 years ago
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