1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Agata [3.3K]
3 years ago
8

Which related equations are in the same fact family as the following equation?

Mathematics
1 answer:
mafiozo [28]3 years ago
7 0

Answer:

A, B and D

Step-by-step explanation:

Because all of these are true

You might be interested in
Find the absolute maximum and absolute minimum values of the function f(x, y) = x 2 + y 2 − x 2 y + 7 on the set d = {(x, y) : |
dsp73

Looks like f(x,y)=x^2+y^2-x^2y+7.

f_x=2x-2xy=0\implies2x(1-y)=0\implies x=0\text{ or }y=1

f_y=2y-x^2=0\implies2y=x^2

  • If x=0, then y=0 - critical point at (0, 0).
  • If y=1, then x=\pm\sqrt2 - two critical points at (-\sqrt2,1) and (\sqrt2,1)

The latter two critical points occur outside of D since |\pm\sqrt2|>1 so we ignore those points.

The Hessian matrix for this function is

H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2-2y&-2x\\-2x&2\end{bmatrix}

The value of its determinant at (0, 0) is \det H(0,0)=4>0, which means a minimum occurs at the point, and we have f(0,0)=7.

Now consider each boundary:

  • If x=1, then

f(1,y)=8-y+y^2=\left(y-\dfrac12\right)^2+\dfrac{31}4

which has 3 extreme values over the interval -1\le y\le1 of 31/4 = 7.75 at the point (1, 1/2); 8 at (1, 1); and 10 at (1, -1).

  • If x=-1, then

f(-1,y)=8-y+y^2

and we get the same extrema as in the previous case: 8 at (-1, 1), and 10 at (-1, -1).

  • If y=1, then

f(x,1)=8

which doesn't tell us about anything we don't already know (namely that 8 is an extreme value).

  • If y=-1, then

f(x,-1)=2x^2+8

which has 3 extreme values, but the previous cases already include them.

Hence f(x,y) has absolute maxima of 10 at the points (1, -1) and (-1, -1) and an absolute minimum of 0 at (0, 0).

3 0
3 years ago
84×3=3×84 is what property
Katarina [22]
My property ..............................
6 0
3 years ago
16 is 4670 of what number ?<br><br><br> Helppp
maxonik [38]

Answer:

16

Step-by-step explanation:

Hope this helps sorry if I'm wrong

8 0
3 years ago
Read 2 more answers
How many 3/4 foot pieces of string can be cut from a piece of string 4 1/2 feet long
Gnom [1K]
3/4 foot is 9 inches, and 4 1/2 feet is 54 inches, so, 54/9 makes exactly 6 pieces of string. 
8 0
3 years ago
Work out the balance for £240 invested for 20 years at 7% per annum
Luda [366]

Step-by-step explanation:

It depends in the type on interest

Simple Interest

PxRxT

£240 x 0.07x 3 = £50.4

£240 + £50.4 = £290.4

Compound Interest

Px(1+R)^T

£290.4 x (1 + 0.07)³ = £355.7524872= €355.76

5 0
3 years ago
Other questions:
  • PLS HELP ME ASAP FOR ALL 6!! (MUST SHOW WORK!!) + LOTS OF POINTS AND BRAINLIEST!!
    10·1 answer
  • Pat collected 54 cans of food for a food drive. This is 6 times as many cans as Anne collected. How many cans did Anne collect?
    14·2 answers
  • Let’s assume that human body temperatures are normally distributed with a mean of 98.20° F and a standard deviation of 0.62° F.
    9·1 answer
  • How do you determine if two triangles are similar?
    15·2 answers
  • Part A: Solve the following system of authentically showing your work: 3x + 2y = 4 4x + 3y = 7.
    7·1 answer
  • PLEASE PLEASE HELP I HAVE OTHER WORK TO DO AND I NEED THIS ANSWER ASAP
    9·2 answers
  • What is the scale factor of 2/3
    5·1 answer
  • Solve the equation:<br><br> 9x - 5 = 5x + 7
    6·2 answers
  • Wich one is a better buy? Show your work.
    13·2 answers
  • Answer with explanation please
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!