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3 years ago

Which of the following sets of ordered pairs represents a function

Mathematics

1 answer:

IgorC [24]3 years ago

3 0

Answer:

D is the correct answer.

Step-by-step explanation:

When given points, one way to tell if it is a function is to see if the x-coordinate changes. If all the x-coordinates are different, then it is a function. If there is a group of x-coordinates that are the same, then you need to check the y-coordinate. If the y-coordinate is the same with the same x-coordinate, then it is still a function [Example: (12, 15), (12, 15) is a function, but (12, 15), (12, 18) is not)

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Find the max and min values of f(x,y,z)=x+y-z on the sphere x^2+y^2+z^2=81

Anton [14]

Using Lagrange multipliers, we have the Lagrangian

$L(x,y,z,\lambda)=x+y-z+\lambda(x^2+y^2+z^2-81)$

with partial derivatives (set equal to 0)

$L_x=1+2\lambda x=0\implies x=-\dfrac1{2\lambda}$
$L_y=1+2\lambda y=0\implies y=-\dfrac1{2\lambda}$
$L_z=-1+2\lambda z=0\implies z=\dfrac1{2\lambda}$
$L_\lambda=x^2+y^2+z^2-81=0\implies x^2+y^2+z^2=81$

Substituting the first three equations into the fourth allows us to solve for $\lambda$ :

$x^2+y^2+z^2=\dfrac1{4\lambda^2}+\dfrac1{4\lambda^2}+\dfrac1{4\lambda^2}=81\implies\lambda=\pm\dfrac1{6\sqrt3}$

For each possible value of $\lambda$ , we get two corresponding critical points at $(\mp3\sqrt3,\mp3\sqrt3,\pm3\sqrt3)$ .

At these points, respectively, we get a maximum value of $f(3\sqrt3,3\sqrt3,-3\sqrt3)=9\sqrt3$ and a minimum value of $f(-3\sqrt3,-3\sqrt3,3\sqrt3)=-9\sqrt3$ .

5 0

3 years ago

Write the first 10 multiples of 3

Pavel [41]

3, 6, 9, 12, 15, 18, 21, 24, 27, 30.

4 0

3 years ago

Read 2 more answers

What is the volume of a cone with a radius of 4 centimeters and a height of 5 centimeters?

vovangra [49]

Answer:

83.79 cm²

Step-by-step explanation:

(please refer to attached)

recall that the volume of a cone is given by

V = (1/3) π r² h

where

r = radius = given as 4 cm

h = height = given as 5 cm

assume π = 3.142

substituting the values into the formula:

V = (1/3) π r² h

V = (1/3) (3.14) (4)² (5)

V = 83.79 cm²

8 0

3 years ago

HELP PLEASE

Stella [2.4K]

Answer:

The right answer is: 14,256 cubic inches

Step-by-step explanation:

First of all, let's identify the dimensions of the tank and convert them to inches

Knowing that 1 Feet = 12 inches

So, the dimensions of the tank, expresed in inches will be:

Height (H): 2 ft. x 12 = 24 inches

Width (W): 1.50 ft. x 12 = 18 inches

Lenght (L): 3 ft. x 12 = 36 inches

Before calculating the volume of water inside the thank, We must consider that <em>there are two inches of empty space at the top.</em>

So , We must substract 2 inches to the height to calculate the volume.

Then, the height used for calculating the volume will be:

H'= 24 inches - 2 inches = 22 inches

Then,

Volume (V)= W x L x H'

V= (18 inches) x (36 inches) x (22 inches)

V= 14,256 cubic inches

8 0

3 years ago

What is the graph of f(x) = (x+3)(x-2)?

valina [46]

Answer:

yoo

Step-by-step explanation:

8 0

4 years ago