(a) Find and identify the traces of the quadric surface x2 + y2 − z2 = 81 given the plane. x = k Find the trace.

Answers

Answer 1

Answer:

Hyperbola

Step-by-step explanation:

Consider [tex]x=k.[/tex]

Substitute [tex]x=k[/tex] in given equation [tex]x^2+y^2-z^2=81[/tex]

[tex]k^2+y^2-z^2=81[/tex]

[tex]\Rightarrow y^2-z^2=9^2-k^2[/tex]

[tex]\Rightarrow y^2-z^2=(9-k)(9+k)[/tex]

Here, different orientation for [tex]-9<k<9[/tex] then [tex]-9<k[/tex] or [tex]k<9.[/tex]

Hence, the surface equation represents a trace of the hyperbola.


Related Questions

ezekiel has $250 in his bank account he deposts $35 from his birthday and then buys clothes for school for $75

Answers

Answer:

$140

Step-by-step explanation:

i assume ur asking for how much is left over

250-35= 215

215-75= 140

$140 left

Venus is an average distance of 108.2 million kilometers from the sun. Use the conversion factor

Answers

0.72 AU is the answer

4x +14+ 4x=38 solve equation

Answers

Answer:

3

Step-by-step explanation:

4x +14 +4x =38

8x =38 - 14

8x=24

x=24 :8

x=3

Choose the expression that completes the equation. 24 ÷ 6 + 20 =______

Answers

Hey there!

ANSWER: [tex]24[/tex]EXPLANATION:

[tex]\text {Choose the expression that completes the equation}\\24/6+20=?[/tex]

To complete the equation, we will need to use the order of operations(PEMDAS). Let's start with division since that's the highest in the order.

[tex]24/6=4[/tex]

Now let's addition since that's all that is left.

[tex]4+20=24\\24(ANSWER)[/tex]

So now let's complete the equation.

[tex]24/6+20=24(ANSWER)[/tex]

Hope this helps!

[tex]\text {-TestedHyperr}[/tex]

How do you solve this?

Answers

Answer:

Well one do the square root of 16

Answer:

1 and 9

Step-by-step explanation:

[tex]5-\sqrt{16}[/tex]

[tex]5+\sqrt{16\\[/tex]

(6 + √27) / 3 Sorry i wrote it wrong the first time.

Answers

3.73205081 i think it right hope it helps

Answer: [tex]2 + \sqrt{3}[/tex]

==============================================

Work Shown:

[tex]\frac{6 + \sqrt{27}}{3}\\\\\frac{6 + \sqrt{9*3}}{3}\\\\\frac{6 + \sqrt{9}*\sqrt{3}}{3}\\\\\frac{6 + 3\sqrt{3}}{3}\\\\\frac{3(2 + \sqrt{3})}{3}\\\\2 + \sqrt{3}\\\\[/tex]

The idea with simplifying the square root (steps 2 through 4) has us factoring 27 so that one factor is a perfect square. We want the largest perfect square factor possible.

That way when we use the rule sqrt(x*y) = sqrt(x)*sqrt(y), we pull out that perfect square to then use the rule sqrt(x^2) = x where x is nonnegative.

After simplifying the square root, we factor out the GCF and then cancel out the 3's.

6.1+
4.55+
1.09 +
15.9+
3.771

Answers

Answer:

31.411

Step-by-step explanation:

6.1+4.55+1.09+15.9+3.771= 31.411

Which one is from greatest to least?

A : -15, -8, 10, 12

B : 12, 10, -15, -8

C : 12, 10, -8, -15

D : -15, -8, 12, 10

HELPPP!! ASAP!!

Answers

Answer:

C is correct!

12,10,-8,-15

Which one is from greatest to least?
C: 12, 10, -8, -15

PLEASE HELP!

What percent of the circle is shaded?
Can you also explain how to get the answer?

Answers

Answer:

40%

Step-by-step explanation:

1/5 = 20%

then 2/5 would equal 40%

Answer:

40%

Step-by-step explanation:

It is 40 because if you move the two shaded then its two and if you fill in the rest you will need three more.

Each side of a regular pentagon is m+10 inches. The formula for finding the perimeter of the pentagon is shown below.

Answers

Answer:

5m+50

Step-by-step explanation:

since it's regular all sides are equal

it's have 5 sides of m+10

[tex]P=5(m+10)\\\\P=5m+50[/tex]


Austin removed 16 fish from his pond over a period of 2 days. He removed the same number of fish each day. What was the change in the number of fish in the pond each day?

Answers

Answer:

-8

Step-by-step explanation:

if he took out the same number of fish each day then it would be 8 a day resulting in a decrese of 8 fish a day.

SIMPLIFY THE EXPRESSION THEN MATCH TO ANSWER (USE ORDER OF OPERATIONS) PLS HELP I DONT UNDERSTAND TY I APPRECIATE IT

Answers

plz I need a link to solve that

vertices of parallelogram ABCD are A(2, 0), B(4, 3), C(3, 1). How many possibilities are there for the position of the fourth vertex?

Answers

Answer:

1 possibility is there for the the position of the fourth vertex.

Multiply (6x^3+8)(7x^2+8x+7)

Answers

that’s the answer for you
hope this helps if you have any more questions about this let me know!!

The sum of prime number
less than x is 58
find an integer value for x

Answers

Answer:

58

Step-by-step explanation:

Prime Numbers = 2+3+5+7+11+13+17

= 58

Can anyone help me with my algebra work for #14 and #15?

Answers

14.yes
15. EDF,FDE,ED,FD,DE and DF
(i think this is correct)

What is the solution to this equation?
–14x = 70
A.x = –5
B.x = 5
C.x = 84
D.x = –84

Answers

Answer:

x = − 5

Step-by-step explanation:

Divide each term by  − 14  and simplify.

Answer: x =5

Step-by-step explanation:

14x/14= 70/14

X = 5

what is one and three hundred twenty-four thousand in decimal

Answers

Answer:

1.324

Step-by-step explanation:

"and" is basically the decimal

Answer:

.32400

Step-by-step explanation: just cs

27 is nine more than six times
Hugo's age. What is Hugo's
age?

Answers

Hugo is three years old

Answer:

3

Step-by-step explanation:

First, subtract 9 from 27:

27 - 9 = 18

Next, divide 6 from 18:

18/6 = 3

3 is Hugo's age.

~

A grid that represents 1 whole , what would you shade for 0.4 and 0.04? 100 squares in rows of 10.

Answers

For .4 shade 4 squares, for .04 shade a bit less than half a square

Which type of transformation preserves the symmetry of an even function f(x) but does not preserve the symmetry of an odd function g(x)? vertical translation horizontal translation reflection over the x-axis reflection over the y-axis

Answers

Answer:

Vertical Translation.

Step-by-step explanation:

If you shift a parabole up, for example, it is still symmetric about the y-axis. If you shift it left or right, it loses its symmetry. Reflection maintains symmetry for both even and odd functions.

Answer:

vertical translation

Step-by-step explanation:

if x - 2y = 1 and 2x - y = -4, then x + y = ?

Answers

Answer:

x + y = -5

Step-by-step explanation:

x - 2y = 1

2x - y = - 4

then:

x = 1 + 2y

then:

2(1+2y) - y = -4

(2*1 + 2*2y) - y = -4

2 + 4y - y = -4

3y = -4 -2

3y = -6

y = -6/3

y = -2

x = 1 + 2y

x = 1 + 2*-2

x = 1 - 4

x = -3

Check:

x - 2y = 1

-3 -2*-2 = 1

-3 + 4 = 1

Answer:

x + y = -3 -2= -5

PLEASE HELP !! Which is the equation of a line that has a slope of 1/2 and passes through point (2,-3)

Answers

Answer:

y = 1/2x - 4

Step-by-step explanation:

You would use point slope to solve this. y-y = m(x-x) with your numbers it would look like this ---> y+3 = 1/2(x-2). (I changed it to +3 because y- -3 = y+3. Two negatives make a positive.)  Next you would use the distributive property and it would look like this ---> y+3 = 1/2x - 1 -----> -3 on both sides ------->

y = 1/2x - 4. Hope this helped!!!!

A garden table and
bench cost $897 combined. The garden table costs $47 more than the bench. What is the cost of the bench?

Answers

Answer:

472

Step-by-step explanation: First subtract the additional cost from the overall cost, than you find the value of the bench by dividing by 2, than add the additional cost to the price of the bench to find the total cost of the Garden Table.

897-47=850

850 divided by 2 = 425

425 + 47 = 472

Round 7696.41481885 to the nearest thousand

Answers

the answer is 7696.415 !

Round the number 7696.41481885 to the nearest thousandth will be 7696.415.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The decimal number is the sum of a whole number and part of the fraction number. The fraction number is greater than zero but less than one.

The decimal number is given below.

7696.41481885

Round the number 7696.41481885 to the nearest thousandth term, which will be done if the number is greater than 5 then the previous of that number is increased by 1. Then the number will be

7696.415

Round the number 7696.41481885 to the nearest thousandth will be 7696.415.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

Find the midpoint of points A(-3,9) and B(0, 1) graphically.


Answers

Answer:

[tex](-\frac{3}{2} , 5)[/tex]

Step-by-step explanation:

The graph is in the image

[tex]Midpoint =\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(-3,\:9\right),\:\left(x_2,\:y_2\right)=\left(0,\:1\right)\\\\\left(\frac{0-3}{2},\:\frac{1+9}{2}\right)\\\\Add\:or\:subtract\:the\:numbers\\\\(\frac{-3}{2} , \frac{10}{2}) \\\\Simplify\\\\(-\frac{3}{2} , 5)\\[/tex]

1. -x divided by 11
2. z multiplied by - 5
working pls

Answers

Answer:

1. [tex]-x \div 11 = \frac{-1}{11}x[/tex]

2. [tex]z \times -5 = -5x[/tex]

Hope this helped you!

I need this right now please

Answers

I think this is the fraction -4/9
Yes i agree it is the first option

Solve 1-4 to be mark brainiest and show your work!

Answers

Answer:

Hope you understand not to sure but that's what I got

Find the complement of the set given that U = {3, 4, 5, 6, 7, 8, 9, 10, 11). (Use the roster method to write the set. Enter EMPTY or for the empty set.)

{5, 7, 9, 10)

Answers

Answer:

(3, 4, 6, 8, 11)

Step-by-step explanation:

The complement of a set are elements of a universal set that isn't present in the given set.

The universal set is  U = {3, 4, 5, 6, 7, 8, 9, 10, 11)

[tex]\left \{ 3,4,6,8,11 \right \}[/tex]

A set is a well-defined collection of objects.

The collection of all items in a certain context or theory is known as a universal set.

The complement of a set is the set that contains all of the universal set's elements that aren't found in the provided set.

[tex]U=\left \{ 3,4,5,6,7,8,9,10,11 \right \}[/tex]

Let [tex]A=\left \{ 5,7,9,10 \right \}[/tex]

Complement of set is [tex]\left \{ 3,4,6,8,11 \right \}[/tex]

For more information:

https://brainly.com/question/2332158?referrer=searchResults

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