find and sketch the domain of the function. f(x, y, z) = ln(144 − 9x2 − 16y2 − z2)
Answers
The domain of the function f(x, y, z) = ln(144 − 9x² − 16y² − z²) is x ∈ (-4, 4), y ∈ (-3, 3) and z ∈ (-12, 12). It forms an ellipsoid.
Domain of a function is the set of all values possible for the input parameters for real output parameter or output parameter in given range.
f(x, y, z) = ln(144 − 9x² − 16y² − z²)
For f(x, y, z) to be real, 144 − 9x² − 16y² − z² should be greater than 0. So,
144 − 9x² − 16y² − z² > 0
9x² + 16y² + z² < 144
x²/ 4² + y²/ 3² + z²/ 12² < 1
So the domain is an ellipsoid.
Therefore x ∈ (-4, 4)
y ∈ (-3, 3)
z ∈ (-12, 12)
To know more on domain
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Related Questions
Please Help ASAP!!!!!!!!
Answers
Answer:
A
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 6x - 4 ← is in slope- intercept form
with y- intercept c = - 4 → A
Michelle is making a scale model of her favorite car. The actual car is 8 feet long and 4 feet wide. Michelle wants her model to be 12 inches in length. Which could be used to find the width of her model if she used the same ratio?
Answers
Answer:
6 inches
Step-by-step explanation:
It is given that :
Length of the actual car = 8 feet
Width of the actual car is = 4 feet
Michelle is making a model of her car.
The length of her model car = 12 inches
Therefore, the ration is 3 : 2
So the width of the model car = 4 x 3/2
= 6 inches
timothy is planting a garden. Tulips cost $125 per bub. The total cost c of his gardening supplies is $1.25 per bub b plus $10 for a bag of mulch. What is the independent and dependent variables and the equation and solution!
Answers
Answer:
Independent variable = number of bub (b)
Dependent variable = total cost (c)
Equation: c = $1.25b + $10
Timothy would spend: $20
Step-by-step explanation:
Total cost = c
Number of bub = b
✔️Total cost, c, is dependent on the number of bub, b.
Therefore:
Independent variable = number of bub (b)
Dependent variable = total cost (c)
✔️Equation that describes this situation can be written as:
c = $1.25b + $10
✔️If Timorhy buys 8 bubs, he would spend the following:
Substitute b = 8 into c = $1.25b + $10, and solve for c.
c = $1.25(8) + $10
c = $10 + $10
c = $20
Ms. Cathy bought a package of pens. Out of every 10 pens, 6 are black. If there are 20 pens in the pack, what fraction of the pens in the pack are black? What percent of the pens in the pack are black?
Answers
Answer:
12/20 or 60%
Step-by-step explanation:
Given the table below, determine if the data represents a linear or an exponential function and find a possible formula for the function. x 0 1 2 3 4 f(x) 0 2 4 6 8 a. Exponential; y = 1 (1.2) Superscript x c. Exponential; y = 2 (1.1) Superscript x b. Linear; y = 2x d. Linear; y = x
Answers
Answer:
Its B
Step-by-step explanation:
If you look at how the chart is flowing, the y values are 2 times the x value.
for example,
1x2=2
2x2=4
3x2=6
and
4x2=8
Therefore, the equation is linear and y=2x
Answer:
b. Linear; y = 2x
Step-by-step explanation:
Ms. Ruiz has a piece of fabric that is 3 3/4 yards long. She waves to cut it into 12 equal pieces. How many yards will each piece of fabric be
Answers
Answer:
the number of yards be 0.3125
Step-by-step explanation:
The computation of the number of yards will each piece of fabric be is shown below:
Given that
There is [tex]3 \frac{3}{4}[/tex] yards long i.e. 15 ÷ 4
And, it should be cut into 12 equal pieces
So, the number of yards will each piece of fabric be is
= 15 ÷ 4 ÷ 12 ÷ 1
= 15 ÷ 48
= 0.3125
Hence, the number of yards be 0.3125
Answer:
5/16
Step-by-step explanation:
3 3/4= 13/4
13/4 ÷ 12= 0.3125
0.3125 = 5/16
Complete the following table using the equation: y = x squared
x
-3
-1
0
1
3
y
Plot the points on a graph and determine which graph best represents the equation.
Graph A
On a coordinate plane, a parabola opens up and goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4).
Graph B
On a coordinate plane, a parabola opens down and goes through (negative 2, negative 4), has a vertex at (0, 0), and goes through (2, negative 4).
a.
-9, -1, 0, -1, -9; Graph B
b.
9, 1, 0, 1, 9; Graph B
c.
9, 1, 0, 1, 9; Graph A
d.
-9, -1, 0, -1, -9; Graph A
Answers
Answer:
Step-by-step explanation:
ITS A
Answer:
The answer is C , Graph A
Step-by-step explanation:
Pls find B asap.....
Answers
Answer:
Point B is at coordinate point (7,9)
Which of the following describes the function of the nervous system?
A. to regulate internal temperature
B. to carry blood through the body
C. to rid the body of cellular waste
D. to respond to external stimuli
Answers
I think lol
The best description of the function of the nervous system among all the options is to respond to external stimuli.
Your nervous system is your body’s command center. Originating from your brain, it controls your motions, studies, and instinctive reactions to the humankind around you. It too controls distinct body systems and processes, similar to digestion, breathing, and sexual growth( puberty). conditions, accidents, poisons, and the natural aging course can compromise your nervous system.
Thus, option D is correct in that the nervous system is responsible to respond to external stimuli.
Learn more about Nervous System here:
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Find the value of x (7TH GRADE MATH)
Answers
Answer:
the answer is 5
Step-by-step explanation:
a right angle has a total of 90 degrees
so you subtract 65 from 90 and get 25
that is the total degrees in the rest of the angle
then you would have to divide 25 by 5
leaving you with 5
2, en un curso de 37 estudiantes se proponen a elaborar un cohete con material reciclado, para poder hacer los cohetes, en el curso se cuenta con 151 tubos de cartón que se recolectaron en una jornada de reciclable. A: si para hacer un cohete se necesitan 4 tubos de cartón, ¿Hay suficientes tubos para que cada estudiante elabore su cohete?
Answers
Answer:
Yes, there enough tubes for each student to make their rocket.
Step-by-step explanation:
Given - In a course of 37 students they propose to make a rocket with recycled material, in order to make the rockets, in the course there are 151 cardboard tubes that were collected in a recyclable day.
To find - If 4 cardboard tubes are needed to make a rocket, are there enough tubes for each student to make their rocket ?
Proof -
Given that,
1 rocket is made with 4 cardboard tubes
Total cardboard tubes = 151
Now,
1 student will make 1 rocket
Total students = 37
⇒Total rockets made by the course = 37
Now,
1 rocket used 4 cardboard tubes
⇒37 rocket used 37×4 cardboard tubes
⇒37 rocket used 148 cardboard tubes.
As
148 < 151
⇒There are enough tubes for each student to make their rocket.
What is the value of x?
Enter your answer in the box.
x =
Answers
Answer:
x = 4
Step-by-step explanation:
Let's find the length of JL as a first step. Knowing the result, we can easily find x.
|JL| 1
sin 30 degrees = ----------------- = --------
8√2 2
Then 2 |JL| = 8√2, or |JL| = 4√2
Next, find x: sin 45 degrees = x / |JL| = x / [4√2], and since sin 45 degrees is 1 / [√2],
1
x / [4√2] = -------- which results in x = 4
√2
Find the value of the variable.
8
4
6
y =
Answers
9514 1404 393
Answer:
y = 12
Step-by-step explanation:
The angle bisector divides the sides proportionally.
y/6 = 8/4
y = 6·8/4
y = 12
Answer:
Solution :-At first we know that
In a bisector
[tex] \sf \: a \times c = b \times d[/tex]
[tex] \bf \: 8 \times 6 = 4 \times y[/tex]
[tex] \bf \: 48 = 4y[/tex]
[tex] \bf \: y = \dfrac{48}{4} [/tex]
[tex] \bf \: y = 12[/tex]
find the slope of the line that passes through points (2,8) and (1,3)
Answers
Answer:
Slope is m = 5
Step-by-step explanation:
Find the value of x.
Answers
Answer:
x = -7
Step-by-step explanation:
All triangle angles add up to 180
84 + x + 59 + x + 51 = 180
2x + 194 = 180
2x = 180 - 194
2x = -14
x = -7
PLEASEEE HELP I JUST NEED TO KNOW WHICH ONES ARE TRUE AND FALSE
Answers
Answer:
Step-by-step explanation:
1-true
2-false
3-true
4-false
answer answer answer answer
Answers
Answer:
[tex]12 \leqslant x < 26[/tex]
answer question asap please
Answers
AnswThe answer would be 5 and 86
Step-by-step explanation:
sulitions are 5 and 86
Answer:
x = 1/5 , -3/5 ??
Step-by-step explanation:
Seth has some $1 bills and some $5 bills. In total he has 6 bills that are worth a total of $22. Write a system of equations and solve to find out how many $5 bills Seth has.
Answers
find value of x and y
Answers
Step-by-step explanation:
x = 144 ( corresponding angle)
y = 180- 144 ( linear pair)
y= 36°
I need help please I’ll give you 15 points
Answers
Answer:
3 x 5 x 5
Step-by-step explanation:
75 = 15 x 5
15 = 3 x 5
Write an expression that represents: 6 less than ⅓ times the sum of x and 4
Help please dont say I dont knoẁ and waste my points know or give something this is the second time I am asking this question
Answers
Answer:
(1/3-6) x (x+4)
Step-by-step explanation: Less than indicates you put the 1/3 first, giving you 1/3-6. Then you multiply that by x+4. Sum means additon! The X in the middle is a multiplacation symbol.
A square is cutting hair creating two equal triangles each triangle has an area of 0.32 cm what is the side length of the square in centimeters
Answers
Answer:
the lengt is 3.27cm
Step-by-step explanation:
its pretty hard to explain
Answer:
0.787400787
Step-by-step explanation:
Two equal triangles cut from a square are each .32cm so just multiply that by two and find the square root. Square root of .62 is 0.787400787
(っ◔◡◔)っ ♥ Hope It Helps ♥
there is 1 pint of liquid in this container if another pint was added how much liquid would ther be
Answers
Answer:
2 us liquid pints =
0.25 us liquid gallon
Step-by-step explanation:
2x+10=28
What is the solution to this equation
Answers
Answer:
x=9
Step-by-step explanation:
step 1. restate the equation
2x+10=28
step 2. subtract 10 from both sides of the equations
2x+10-10=28-10
2x=18
step 3. get x alone by dividing 2 from both sides
2x/2=18/2
step 4. the answer
x=9
y = 5x + 2
4x - y = 0
Is (2 , 12) a solution of the system?
Answers
Step-by-step explanation:
no , (2,12) only works for the 1st one
Answer:
Step-by-step explanation:
No
PLEASE HELP ANSWER CORRECTLY !!!!!!!!!!!!!! WILL MARK BRIANLIEST !!!!!!!!!!!!!!
Answers
Hello, hehelol12.
The length of PR is the same as TR.
Length of PR = 11.
The measure of angle PQR is the same as angle RST.
Measure of angle PQR = 39
I hope this helps you out!
PS. Brainliest would be appreciated. :)
helpppppppp pleaseeeeeeeeeeeee
Answers
Answer:
area of the triangle is
[tex] \frac{1}{2} \times 4.4 \times (6.1 + 3.3)[/tex][tex] 2.2 \times 9.4[/tex][tex]20.68 \: {in}^{2} [/tex]What is the horizontal difference between (2, 4) and (-1, 0)?
Answers
Answer:
3
Step-by-step explanation:
Which of these is a trinomial?
A. 2x^3 – 7y^3
В. 5xy
C. 2x - 7
D. x + 2y^2-7
Answers
Answer:
D. x + 2y² - 7
Step-by-step explanation:
it because it has 3 terms