Find a point on the ellipsoid x2+y2+4z2=36x2+y2+4z2=36 where the tangent plane is perpendicular to the line with parametric equations

Answers

Answer 1

Answer:

A point on the ellipsoid is (-4,2,2) or (4,-2,-2)

Step-by-step explanation:

Given equation of ellipsoid f(x,y,z) :[tex]x^2+y^2+4z^2=36[/tex]

Parametric equations:

x=-4t-1

y=2t+1

z=8t+3

Finding the gradient of function

[tex]\nabla f(x,y,z)=<\frac{\partial{f}}{\partial{x}},\frac{\partial{f}}{\partial{y}},\frac{\partial{f}}{\partial{z}}>\\\nabla f(x,y,z)=<2x,-2y,8x>[/tex]

So, The directions vectors=(-4,2,8)

Now the line is perpendicular to plane when direction vector is parallel to the normal vector of line

[tex]\nablaf(x,y,z)=(2x,2y,8z)=\lambda(-4,2,8)[/tex]

So, [tex]2x=-4\lambda[/tex]

[tex]\Rightarrow x=-2\lambda[/tex]

[tex]2y=2\lambda\\\Rightarrow y=\lambda\\8z=8\lambda\\\Rightarrow z=\lambda[/tex]

Substitute the value of x , y and z in the ellipsoid equation

[tex](2\lambda)^2+(\lambda)^2+4(\lambda)^2=36\\9(\lambda)^2=36\\\lambda^2=4\\\lambda=\pm 2[/tex]

With [tex]\lambda = 2[/tex]

x=-2(2)=-4

y=2

z=2

With[tex]\lambda =- 2[/tex]

x=-2(-2)=4

y=-2

z=-2

Hence a point on the ellipsoid is (-4,2,2) or (4,-2,-2)


Related Questions

PLEASE HELP ME What is the amount of rain fall for the 1M 6 months of the year in Kennedale Texas
Arlington Texas Rainfall Amounts
Month
January
February
March
April
May
June
Rainfall Amount
+0.5 inches
-1.26 inches
+0.32 inches
+3.71 inches
- 1.27 inches
-2.40 Inches
A 2 inches
B. -0.4 inches
C 0.8 inches
D. -1.3 inches
Loo

Answers

Answer:

.5

Step-by-step explanation:

Ok so If and anchor descends -17.5 meters down in the ocean in 5 seconds, how much does it descend in 1 second?

Answers

-3.5 meters

explanation:
Divide -17.5 by 5 to get the distance the anchor travels in one second
-3.5 meters
Pls give the top person branly

You need to purchase supplies for building a backyard deck. Your boss gives you the supply list and asks that you get the best deal by buying from either True Builder or Quality Supplies. You call both stores, and they provide the price information that you put into the table below. Which store provides the lowest total cost, and what is the cost without sales tax?

Answers

Answer:

a) The store which provides the lowest total costs is:

True Builders

b) The cost without sales tax is:

$407.48

Step-by-step explanation:

Data and Calculations:

Product                Quantity       True Builders               Quality Suppliers

                                               Price          Costs             Price          Costs

Bricks                      120        $2.20       $264.00         $2.25      $270.00

2 x 4 boards            40 ft     $0.75            30.00         $0.70           28.00

1 x 6 boards           120 ft     $0.60            72.00         $0.65           78.00

2 x 6 boards           30 ft     $0.80            24.00         $0.80           24.00

Paint                        2 gal.    $15.50           31.00         $11.25          22.50

Paint Brushes         2           $7.50            15.00          $9.75           19.50

Total costs                                           $436.00                          $442.00

Imputed Sales Tax of 7%                        28.52                              28.92

Without Sales Tax                              $407.48                           $413.08

Answer:

Quality Supplies 442.00

Step-by-step explanation:

In the figure, mZ2 = 3(x+15) and m23 = 24°. Find x.
3
5
6
8

Answers

Answer:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    3*(x+15)*23-(24)=0  

Step by step solution :

STEP

1

:

Equation at the end of step 1

 (3 • (x + 15) • 23) -  24  = 0  

STEP

2

:

Equation at the end of step 2

 69 • (x + 15) -  24  = 0  

STEP

3

:

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  69x + 1011  =   3 • (23x + 337)  

Equation at the end of step

4

:

 3 • (23x + 337)  = 0  

STEP

5

:

Equations which are never true

5.1      Solve :    3   =  0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

5.2      Solve  :    23x+337 = 0  

Subtract  337  from both sides of the equation :  

                     23x = -337

Divide both sides of the equation by 23:

                    x = -337/23 = -14.652

Step-by-step explanation:

Let z = 1 + 3i and w = -3 - 4i.
Use the drop down menus to complete the statements.
The sum z + w is equal to - -i
The sum w + z is equal to - 2 - i
The result supports that complex number addition is

Answers

Step-by-step explanation:

z+w= 1+3i-3-4i = -2-i

w+z=-3-4i+1+3i = -2-i

So, z+w = w+z

So, complex number addition is commutative

If z = 1 + 3i and w = -3 - 4i, then z + w = - 2 - i and w + z = - 2 - i, which supports that complex number addition is commutative.

What is commutativity property of addition?

We are aware that the addition's commutative property states that altering the addends' order will not affect the sum.

How to solve it ?

Here z = 1 + 3i and w = -3 - 4i.

Now, z + w = 1 + 3i - 3 - 4i = 1 - 3 + 3i - 4i = - 2 - i

and w + z = - 3 - 4i + 1 + 3i = - 3 + 1 - 4i + 3i = - 2 - i

i.e. z + w = w + z

Clearly, the addition obeys the commutative property.

Therefore we can conclude that If z = 1 + 3i and w = -3 - 4i, then z + w = - 2 - i and w + z = - 2 - i, which supports that complex number addition is commutative.

Learn more about the commutative property here -

https://brainly.com/question/23736946

#SPJ2

Does anyone know this answer

Answers

2. Square root of 112

1/4(-16x+8)? simplify or expand the expression​

Answers

Answer:

-4x+2

Step-by-step explanation:

Help, please I need it. I am horrible at math.

Answers

B is the answer!!!!!!!!

Answer ASAP: What is the smallest positive number that can be added to 55 so that the resulting number and 45 have 9 as their greatest common factor?

Answers

Answer:

55 + 45 = 90

90 divided by  45 = 2

90 divided by 9 = 10

Step-by-step explanation:

A human head weighs 160 ounces. What is that weight in kilograms? Analyze the work below what is the students error?

Answers

Answer:

Well the weight is

Step-by-step explanation:

4.53592 kilos

Answer:

  4.535924 kilograms

Step-by-step explanation:

1 ounce = 0.02834952 kilogram

160 * 0.02834952  = 4.535924

Please find the area

Answers

Answer:

the answer is 6cm like its really obvious

5. A Ferrari gets 14 miles per gallon of gas. Gas costs $3.18 per gallon. If the Ferrari's gas
tank holds nineteen gallons, and assuming the tank was empty, how much would it cost to fill
the tank and how far could the Ferrari go before it ran out of fuel?

Answers

Answer:

44.52

Step-by-step explanation

find the perimeter of a circle whose diameter is 12.6 cm please help and show working​

Answers

Do you mean the circumference? You can’t find the perimeter of a circle. The circumstance of the circle is 39.584 to 3dp.

Answer:

39.584034 cm

Step-by-step explanation:

Firstly find the radius, 6.3 cm. Then plug into the formula, 2πr.

I used 3.14159 as pi.

work:

2 * 3.14159 * 6.3

6.28318 * 6.3

39.584034

Eight individuals are candidates for positions of president, vice president, and treasurer of an organization. How many possibilities of selections exist

Answers

Answer:

336

Step-by-step explanation:

It is given that,

Total number of individuals are 8

They are candidates for positions of president, vice president, and treasurer of an organization.

It is a based on permutations. We need to find P(8,3). It can be calculated as follows :

[tex]P(n,r)=\dfrac{n!}{(n-r)!}[/tex]

So,

[tex]P(8,3)=\dfrac{8!}{(8-3)!}\\\\=\dfrac{8!}{5!}\\\\=\dfrac{8\times 7\times 6\times 5!}{5!}\ [\because n!=n(n-1)!]\\\\=8\times 7\times 6\\\\=336[/tex]

Hence, there are 336 possibilities of selections.

Is 60N Cold or hot

Answers

Answer:

It is warm.

Step-by-step explanation:

If Jan is 3 years older now than Dale was 2 years ago, then Jan is how many older than Dale is right now.
A) 1 year
B) 2 years
C) 3 years
D) 5 years​

Answers

the answer is a (1 year)

Chris has 12 sweets. He has 3 red, 6 blue, 1 yellow and 2 green sweets what fraction of his sweets is red

Answers

Answer:

He has had a quarter of the red one

Step-by-step explanation:

3/12 is 1/4 when simplified

1/4 you just need to simplify 3/12

HELP MEE ;-;

2/3a - 7= 1/3 Round your answer to the nearest tenth.

Answers

Answer:

a=11

Step-by-step explanation:

Answer:

a = 11

Step-by-step explanation:

José correctly answered 80% of the
questions on a language arts quiz. If he
answered 16 questions correctly, how ma
questions were on the language arts quiz

Answers

Answer:

20

Step-by-step explanation:

80% needs 20% more to be 100%  so we devide 16 by 4 to get the awnser for 20% witch is 4 so 16+4 is equal to 80% + 20% so 20

Answer:

20

Step-by-step explanation: 16 you need to 2  more question to get 100 so if you use your brain and imagine doing a test and you get an 80 percent and answered 16 correct go back to the test to see what you have

PLEASE HELP WITH THIS WILL GET EXTRA POINTS

Answers

Answer:

1.2

2.4

3.6

4.8

5.9

6.4

7.3

8.6

Step-by-step explanation:

what is th nth term of 4 1 -2 -5 -8​

Answers

Answer:

-3

Step-by-step explanation:

Answer:

here:- a=4; d:- (1-4)=(-2-1)=>-3

so, nth term= a+(n-1)d

=> 4+(n-1)-3=>4-3n+3=>7-3n

Step-by-step explanation:

nth term=(7-3n)

The school band is in charge of a new set of uniforms made with a new logo. A local

business charges $140 to set up the logo with the design and $0.25 in materials per

logo printed. The function C(x) = 140+0.25x / x

represents the average cost per logo if x

uniforms are printed by this business.

a. What is the average cost per uniform to get the logo printed on 25 uniforms?

b. What is the average cost per uniform to get the logo printed on 100 uniforms?

C. How many uniforms should be printed to have an average cost of $1 per logo?

d. What will happen to the price as the number of uniforms printed increases?

Answers

Answer:

a. [tex]C(25) = 146.25[/tex]

b. [tex]C(100) = 165[/tex]

c. [tex]x = 187[/tex]

d. Increment in number of uniform causes an increment in price

Step-by-step explanation:

Given

[tex]C(x) = 140 + 0.25x[/tex]

Solving (a)

[tex]x = 25[/tex]

This gives:

[tex]C(x) = 140 + 0.25x[/tex]

[tex]C(25) = 140 + 0.25 * 25[/tex]

[tex]C(25) = 140 + 6.25[/tex]

[tex]C(25) = 146.25[/tex]

Solving (b):

[tex]x = 100[/tex]

This gives:

[tex]C(x) = 140 + 0.25x[/tex]

[tex]C(100) = 140 + 0.25 * 100[/tex]

[tex]C(100) = 140 + 25[/tex]

[tex]C(100) = 165[/tex]

Solving (c):

Average cost = $1 per logo

For x logos,

Average cost = $1 * x

Average cost = $x

So, we have:

[tex]C(x) = 140 + 0.25x[/tex]

[tex]x = 140 + 0.25x[/tex]

Collect Like Terms

[tex]x - 0.25x = 140[/tex]

[tex]0.75x = 140[/tex]

Solve for x

[tex]x = 140/0.75[/tex]

[tex]x = 187[/tex] ---- Approximated

Solving (d): What happens when number uniform increases.

Notice that in (a) & (b).

x increases from 25 to 100

Price also increases from $146.25 to $165.

Hence:

Increment in number of uniform causes an increment in price

Please answer this correctly without making mistakes

Answers

Answer:

This is what internet says. Maybe this helps.

Write the decimal represented by each shaded square.

Answers

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

The decimal would be .70 because there's 70 squares that are shaded.

You come from a large, dysfunctional family. You learn of this year’s upcoming reunion, and dread the very thought of being around those people for any length of time. However, you’ve been intrigued by your introductory statistics course, and decide you will have some fun with the reunion by using it as an opportunity to study your family. As a preliminary project, you want to keep track of how many times each family member verbally assaults another person throughout the first 24 hours.
After 24 hours, you review your notes:
Family Member # Verbal Assaults
Stew (Dad) 5
Marge (Mom) 7
Betsy 18
Fred 11
Gracie 4
Jorge 10
Kim 5
Ferdinand 15
Hal 6
You 19
Find the mean, median, and mode of your distribution:
1. Mean
2. Median
3. Mode
4. Which measure of central tendency do you think is most appropriate for this dataser? Why?
5. What is the range of your dataset? Show how you figured it out.
6. Define, as specifically as necessary, the population in which you are interested for this research. In other words, how do you decide whether a person would be appropriate to include in your study?
7-9. Find the standard deviation for the data in the table on the first page. Showing your work is how you earn points for this part
10. What is the standard deviation of your dataset?

Answers

Answer:

Explained below.

Step-by-step explanation:

The data provided is for the number of times each family member verbally assaults another person throughout the first 24 hours.

Use Minitab to compute the descriptive statistics.

Go to Stat → Basic Statistics → Display Basic Statistics

A dialog box will open.

Select the variable.

Select 'Statistics'.  

Another dialog box will open.

Select the statistics required.

Press OK.

Select "Graphs'.

Select Histogram.

Press OK

The output is attached below.

(1)

The mean of the data is, Mean = 10.

(2)

The median of the data is, Median = 8.50.

(3)

The mode of the data is, Mode = 5.

(4)

The inequality statement for the mean, median and mode is:

Mean > Median > Mode

A distribution is known as to be skewed to the right, or positively skewed, when maximum of the data are collected on the left of the histogram of the distribution.

Also if the Mean > Median > Mode then the distribution is skewed to the right.

For a skewed distribution the best of central tendency is the median.

So, the measure of central tendency that is most appropriate for this dataset is, Median = 8.50.

(5)

The range of the data set is:

Range = Maximum - Minimum

           = 19 - 4

           = 15

Thus, the range is 15.

(6)

The population of interest is the number of times the family members verbally assaults another person throughout the first 24 hours.

(7)

Consider the Minitab output.

The standard deviation of the data set is, SD = 5.60.

The rule (x, y)→(x−1, y-3) represents a translation 1 unit ____ and 3 units ____

Answers

Answer: left, down

Hope this helps.

Who likes sushi?!?!?!

Answers

Answer:

I do :)

Step-by-step explanation:

Lol I usually get the crunchy roll

Factorise fully
-14x - 8

ease do quick, will mark brainiest!​

Answers

Answer:

-2( 7x+4)

Step-by-step explanation:

-14x - 8

Factor out -2

-2*7x -2*4

-2( 7x+4)

Answer:

2(-7x -4)

Step-by-step explanation:

[tex] - 14x - 8[/tex]

Write -8 as -4×2

[tex] - 14x + 2 \times 4[/tex]

Factor out common term : 2

[tex]2( - 7x - 4)[/tex]

Simplify this radical.
Square root 84

Answers

Answer:  9.16515139

Answer 2:  2√21

Find the selling price of each item original plate price of gold fish at $7.65 discount 10%

Answers

Answer:

6.88 is what I think you're looking for

Step-by-step explanation:

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