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) which forms an ellipsoid.
What is the domain?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.
Given the function as f(x, y, z) = ln(144 − 9x² − 16y² − z²)
For f(x, y, z) to be real, the function 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
Therefore, the domain is an ellipsoid.
Therefore x ∈ (-4, 4)
y ∈ (-3, 3)
z ∈ (-12, 12)
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Related Questions
Please help!!! I don’t know this answer ?
Answers
They will walk 6 laps and run 10 laps for a total of 16 miles considering each lap is of 1 mile.
What is mile?The mile is a customary unit of measurement in both the United States and the United Kingdom that is based on the older English unit of length equal to 5,280 English feet, or 1,760 yards. It is also referred to as the international mile or statute mile to distinguish it from other miles.
In 1959, the statute mile was formally redefined with respect to SI units as exactly 1,609.344 metres, establishing a standard between the British Commonwealth and the United States.
With qualifications, mile is also used to describe or translate a wide range of units derived from or approximately comparable to the Roman mile, such as the nautical mile (now exactly 1.852 km), the Italian mile (roughly 1.852 km), and the Chinese mile (now 500 m exactly).
6 laps + 10 laps = 16 laps
1 mile each laps = 16 miles
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50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Answers
Answer:
8.2 m
Step-by-step explanation:
To solve the problem, we use pythagorean theorem, which is a^2 + b^2 = c^2. We are given both the legs, so we can substitute them in:
8^2 + 2^2 = c^2
And simplify to get:
c^2 = 64 + 4
c^2 = 68
Now, we find the square root of both sides to isolate c:
c = √68
√68 is approximately 8.24621125124
This rounded to the nearest tenth is 8.2 m
x^2=4+64
x^2=68
x=√ 68=2√ 17
Help ASAP no links I will report only answer if you know!!!!
Answers
Answer: 380.1
Step-by-step explanation:
v=h*pi*r^2
v=4*pi*5.5^2
v=380.1
A bakery made 100 donuts, in the display case, 40/100 were chocolate, 3/10 were glazed and cinnamon. which fraction of the donuts were cinnamon?
Answers
Explanation:
100-40 = 60 and 3 of those were glazed so that leaves us with 57
Answer:
57/100
Step-by-step explanation:
<
Quadrilateral A'B'C'D' is the image of quadrilateral ABCD under a translation.
←++
-7-6-5-4-3/2
A translation by
up/down
7-
6+
6543
У
5-
3-
24
2345
-3-
Determine the translation.
Use non-negative numbers.
-5+
-6-
D'
A
34 9/7
B
2
units to the right/left ✓
and
units
Answers
Answer:
1 unit to the left, 3 units down
Step-by-step explanation:
Take any point: I will take D. In order to get to D', you need to travel 1 unit along the x-axis towards the left, then 3 until along the y-axis downwards. The same applies for any other point.
How many solutions does 10+5x=5x+10 have?
Answers
10 + 5x = 5x + 10
Reorder the terms:
10 + 5x = 10 + 5x
Add '-10' to each side of the equation.
10 + -10 + 5x = 10 + -10 + 5x
Combine like terms: 10 + -10 = 0
0 + 5x = 10 + -10 + 5x
5x = 10 + -10 + 5x
Combine like terms: 10 + -10 = 0
5x = 0 + 5x
5x = 5x
Add '-5x' to each side of the equation.
5x + -5x = 5x + -5x
Combine like terms: 5x + -5x = 0
0 = 5x + -5x
Combine like terms: 5x + -5x = 0
0 = 0
Solving
0 = 0
Answer: 0 solutions
Given the following table, find the domain and range of the function.
A) domain: {2, 4, 5, 9}
B) range: {2, 4, 5, 9}
C) range: {-3, 1, 5, 7}
D) domain: {-3, 1, 5, 7}
Answers
The domain and range of the function on the table are the ones in options B and C.
Domain: {-3, 1, 5, 7}
Range: {2, 4, 5, 9}
How to find the domain and range of the function?For a function y = f(x), we define the domain as the set of the inputs, this is, the set of the possible values of x.
On the other hand, the range is the set of the outputs, this is, the set of the possible values of y.
Then the domain is just the set of the values of x on the table:
Domain: {-3, 1, 5, 7}
And the range is the set of the values of y on the table:
Range: {2, 4, 5, 9}
Then the correct options are C and B.
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Solve
15 - 6(x + 1) = 12
help pls
Answers
Answer:
x = -0.5
Step-by-step explanation:
15- 6(x+1) = 12
> 15- 6x -6 = 12
>15 - 6x = 18
>-6x = 3
>x = -0.5
Answer:
1/2
Step-by-step explanation:
15-6(x+1)=12
15-6x-6=12
-6x=12+6-15
-6x=3
x=-1/2
ive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic. Step 2 of 2: Suppose a sample of 2017 new car buyers is drawn. Of those sampled, 484 preferred foreign over domestic cars. Using the data, construct the 95% confidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars. Round your answers to three decimal places.
Answers
Answer:
0.2305 ; 0.2495)
Step-by-step explanation:
Sample size, n = 2017
Number who preferred foreign over domestic cars, x = 484
Phat = 484 / 2017 = 0.2399603 = 0.240
The confidence interval :
Phat ± Margin of error
Margin of Error = Zcritical * √(phat(1-phat)/n)
Zcritical at 95% = 1.96
1 - phat = 1 - 0. 240 = 0.76
Margin of Error = 1.96 * √((0.240*0.76)/2017) = 0.0095095
Confidence interval :
Lower boundary : 0.240 - 0.0095 = 0.2305
Upper boundary : 0.240 + 0.0095 = 0.2495
(0.2305 ; 0.2495)
Plz help me well mark brainliest if correct!!
Answers
Answer:
1 hour
Step-by-step explanation:
Each graph shown lasts for 1/2 hour / 30 minutes
Which is the graph of f(x) = 1/4(4)^x?
Answers
Answer:
The last graph with the point (2,4).
Step-by-step explanation:
Make a table of the values, then graph.
Example:
X: -2, -1, 0, 1, 2
Y: [tex]\frac{1}{64}[/tex], [tex]\frac{1}{16}[/tex], [tex]\frac{1}{4}[/tex], 1, 4
80% of x is 20. What is x?
FIRST TO ANSWER GETS BRAINLIEST
Answers
Answer:
16
Step-by-step explanation:
(80x20)/100 = 16
(this is wrong, i misunderstood the question)
Which graph represents the system of linear inequalities?
2x+y<1
y≥12x+2
Answers
The graph of the system of linear inequalities 2x + y < 1 and y ≥ 12x + 2 is attached.
What is an equation?An equation shows how two or more numbers and variables are related to each other.
The standard linear equation is:
y = mx + b
Where m is the rate of change and b is the y intercept
Inequalities is used for the non equal comparison of numbers and variables.
The graph of 2x + y < 1 and y ≥ 12x + 2 is attached.
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a figure has 2 pairs of pararell sides, 2 pairs of sides are equal length, and 4 right angles, what quadrilateral best describes this figure?
Answers
Answer:
a rectangle
Step-by-step explanation:
Answer:
Square
Step-by-step explanation:
Use the Venn diagram to determine if each statement is always true, sometimes true, or never true.
Answers
Answer:
1) Sometimes
2) Always
3) Never
4) Always
5) Sometimes
Step-by-step explanation:
1) Sometimes
2) Always
3) Never
4) Always
5) Sometimes
Make x the subject of h = 4(x + 3y) + 2
Answers
H = 4x + 12y + 2
H - 12y - 2 = 4x
(H - 12y - 2) / 4 = x or 1/4H - 3y - 1/2 = x
Determine the least common multiple (LCM) of 48 and 16.
A. 16
B. 24
C. 36
D. 48
Answers
Answer:
16
since it's the least that can be divided by both
Answer:
a) 16
Step-by-step explanation:
Determine the least common multiple (LCM) of 48 and 16.
A. 16
A cone consitst of these measure but need to find the volume and surface area. The diameter is 16m, height is 8m, and the slant height is 11.31m.
A.) V=769.17m³ SA=535.89m²
B.) V= 535.89m SA=769.17m
C.) V=535.89m³ SA= 769.17m²
D.) V=1607.68m³ SA=769.56m²
Answers
Volume = (1/3) * pi * radius^2 * height
Surface area = pi * radius * (radius + slant height)
In this case, the diameter is 16m, so the radius is 8m. The height is 8m and the slant height is 11.31m. Substituting these values into the formulas gives:
Volume = (1/3) * pi * 8m^2 * 8m = (1/3) * pi * 64m^3 = 21.333m^3 * 64m^3 = 1,365.33m^3
Surface area = pi * 8m * (8m + 11.31m) = pi * 8m * 19.31m = pi * 153.48m^2 = 483.04m^2
So, the volume of the cone is 1,365.33m^3 and the surface area is 483.04m^2. The correct answer is therefore C) V=535.89m³ SA= 769.17m².
What is the value of P for the following triangular prism? 19 yd 12 yd 6 yd 18 yd
Answers
Answer:
12 yds
Step-by-step explanation:
I just answered it. :)))
Answer:
option C
Step-by-step explanation:
The answer is 12 yd. All you muxt do is find the volume.
Lana wants to enclose a garden plot each side of the garden will be 9 feet what is the area of the garden
Answers
The area of garden will be 81 feet².
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Each side of the garden = 9 feet
We know that;
⇒ Area of square = Side²
Here, Each side of the garden = 9 feet
Hence, The area of garden = 9²
= 81 feet²
Thus, The area of garden = 81 feet²
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One answer, I’ll mark brainlist, NO LINKS!!!
Answers
Answer:
B
Step-by-step explanation:
You must multiply 1/4 to 2/8 so you can subtract
What is the value of x?
A. x = 94
B. x = 49
C. x = 86
D. x = 36
Answers
Answer: A
Step-by-step explanation: angle LJK says x subtract 8 degrees and since angle LJH is bigger than angle LJK the one over 90 degrees is the only logical one
Answer:
A. x = 94
Step-by-step explanation:
Add up angles to equal 180 because that is how much a line measures.
x + (x - 8) = 180
Simplify.
2x -8 = 180
Solve for x.
2x -8 = 180
+8 = +8
2x = 188
2 = 2
x = 94
The graph of a linear function contains the points (4,5), (6, 13). (a, 25). What is the value of a?
4
9
12
36
Answers
Answer:
12
Step-by-step explanation:
4,5
6,13
12,24
So I belive it C
A sports statistician claims that the mean winning times for Boston Marathon women's open division champions is 2.68 hours. A sample of 20 randomly is selected Boston Marathon women's open division champions reported a mean winning time of 2.6 hours. Based on the previous records, the standard deviation is 0.32 hour. At 5% level of significance, do you have enough evidence to show that the winning time is different than the claim?
Answers
Answer:
Please find the complete question and its solution in the below section.
Step-by-step explanation:
Follows are the null and alternative Hypothesis:
Null Hypothesis [tex]H_0: \mu = 2.68[/tex]
Alternative Hypothesis[tex]H_a: \mu < 2.68[/tex]
You buy 8.25 ounces of almonds and 7.5 ounces of cashews. You combine the nuts and divide them equally into 9 bags. How many ounces are in
Options are below
⬇️
1.75 ounces
9.5 ounces
15.5 ounces
17.5 ounces
PLS FOR 18 POINTS
Answers
4. Twelve nails have a mass of 423 grams. The number of grams per nail is between what 2
numbers?
a. 31 and 32
b. 33 and 34
C. 35 and 36
d. 37 and 38
Answers
Answer:
C
Step-by-step explanation:
you do twelve divided by 423 to get your answer.
Which radicals are already in the simplest form?
Answers
A can be broken down into 4 * 7
C can be broken down into 49 * 3
D can be broken down into 9 * 7
Ryan spots an airplane on radar that is currently approaching in a straight line, and
that will fly directly overhead. The plane maintains a constant altitude of 6300 feet.
Ryan initially measures an angle of elevation of 15 to the plane at point A. At some
later time, he measures an angle of elevation of 31 to the plane at point B. Find the
distance the plane traveled from point A to point B. Round your answer to the
nearest foot if necessary.
Answers
If Ryan spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The distance the plane traveled from point A to point B is: 13,027ft .
How to find the distance?Constant altitude =6300 feet
Angle of elevation =15 to the plane at point A
An angle of elevation =31 to the plane at point B.
So,
Tan 15° = 6300/ON
ON =23,511.92
Tan 31° =6300/OB
OB = 10,484.96
So,
AB =23,511.92 - 10,484.06
AB = 13,026.96
AB = 13,027ft (Approximately)
Therefore the distance is 13,027ft.
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Data for the estimated number of HIV cases worldwide between 1988 and 1996 suggests exponential growth in the number of cases over this time period. An appropriate transformation of the data (base-ten logarithms were used) produced a strongly linear scatterplot, and a regression analysis was performed on the transformed data.
Here is the computer output:
Predictor Constant Coef SE Coef T F
-151.281 2.038 -74.22 0.000
Year 0.076577 0.001023 74.84 0.000
S= 0.00792598 R-Sq= 99.9% R-Sg (adj ) =99.9%
Note that HIV cases are in millions.
Which of the following value is closest to the value that this model predicts for the number of HIV cases in 1998?
(a) 1.72 million cases
(b) 2.18 million cases
(c) 17.2 million cases
(d) 52.5 million cases
(e) The predicted value is negative because we are extrapolating beyond the range o f the explanatory variable
Answers
Answer:
d. 52.5 million cases
Step-by-step explanation:
from the data output in the question, we have the regression equation to be
log y = -151.281 + 0.076577x
y is the number of hiv cases which is in millions
x is the year of the hiv case
x = 1998
we put the value of x in the regression equation
log y = -151.281 + 0.076577(1998)
log y = -151.281 + 153.000846
log y = 1.719846
since the result is in log form,
[tex]y=10^{1.791846}[/tex]
y = 52.5 million cases
Single payment loan for $1200 repay in 120days interest rate is 7%, what is the maturity value of the loan?
Answers
The maturity value of the loan based on the calculation is $1227.72
How to illustrate the interest?From the information, single payment loan for $1200 repay in 120days interest rate is 7% and we want to calculate the maturity value of the loan.
It should be noted that the interest will be calculated as:
= Principal × Rate × Time
= 1200 × 7% × (120/360)
= 1200 × 0.07 × 0.33
= $27.72
Maturity amount = $1200 + $27.72
Maturity amount = $1227.72.
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