find a function r(t) that describess the curve where the following surfaces intersect. answere are not unique x^2 y^2

Answers

Answer 1

Complete Question

find a vector function that represents the curve of intersection of the two surfaces. The cylinder  [tex]x^2+y^2= 36[/tex] an the surface [tex]z=xy[/tex]

Answer:

The function is  [tex]r(t) =  6cos(t) \ i + 6sin (t) \ j +  36costsint \ k[/tex]

Step-by-step explanation:

From the question we are told that

   The equation of the cylinder is  [tex]x^2+y^2= 36[/tex]

   The equation of the surface is  z = xy

Generally the general form of this  function is  

      [tex]r(t) =  x(t)i + y(t)j +  z(t) k[/tex]

Generally to confirm the RHS and the LHS of the equation for the cylinder

Let take x (t) =  6cos(t)

and        y(t) = 6sin (t)

So

        [tex]x^2  +  y^2  = [ 6cos(t)]^2 + [6 sin (t)]^2[/tex]

=>     [tex]x^2  +  y^2  = 6^2 cos^2t + 6^2 sin ^2t[/tex]

=>      [tex]x^2  +  y^2  = 6^2 [cos^2t +  sin ^2t] [/tex]    

Generally  [tex]cos^2t +  sin ^2t = 1[/tex]

So

        [tex]x^2  +  y^2  = 36[/tex]  

So at  x (t) =  6cos(t) and  y(t) = 6sin (t) the RHS is equal to LHS

  So

   [tex]z(t) = x(t) *  y(t)[/tex]

    [tex]z(t) = (6 cos(t)) *  (6 sin(t))[/tex]

=>     [tex]z(t) =36costsint[/tex]

So the function is  

     [tex]r(t) =  6cos(t) i + 6sin (t) j +  36costsint k[/tex]

   


Related Questions

How do i turn 80% 0f 86- i know the answer but i don't know how to do it

Can someone please teach me

Answers

We know that of refers to multiplication (from BODMAS)

% means per hundred, i.e., 1/100

So, 80% of 86 is:

(80/100) × 86

or (4/5) × 86

or 4 × 17.2

or 68.8

Hope you understand

Answer:

68.8

Step-by-step explanation:

Let x be 80% of 86.

To find 80% of 86

[tex] \frac{80}{100} = \frac{x}{86} [/tex]

[tex]80 \times 86 = 100x[/tex]

[tex]6880 = 100x[/tex]

[tex]68.8 = x[/tex]

Or you can simply do it as:

[tex]86 \times 80\%[/tex]

[tex]86 \times \frac{80}{100} [/tex]

[tex] \frac{86 \times 80}{100} [/tex]

[tex] \frac{6880}{100} [/tex]

[tex]68.8[/tex]

A box contains three types of fruits:
apples, bananas, and pears. There are
20 pieces of fruit in all. Of these, 3 are
apples and 11 are bananas. What is the
ratio of pears to bananas?
А
6 3 11
B 11 26
C 3: 11
D
11: 3
Ο Α
o
D

Answers

Answer:

d

Step-by-step explanation:

The Distance between the school and the park 6km there 1.6km in 1 mile how many miles are between the school and the park

Answers

Answer : 3.75 miles

Answer:

3.75

Step-by-step explanation:

6 km     =     1.6 km

1 km      =      x

6 / by 1.6 = 3.75

HOPE ITS HELPFUL!

Find Mx, My, and (x, y) for the lamina of uniform density rho bounded by the graphs of the equations. y = x2/3, y = 0, x = 1

Answers

The required value for the lamina of uniform density [tex]\bar x\\[/tex] and  [tex]\bar y[/tex] are written below,

[tex]\bar x = \dfrac{5}{8}\\[/tex]

[tex]\bar y = \dfrac{5}{14}[/tex]

Given that:

The density of lamina: ρThe graph for the lamina: [tex]y = x^{\frac{2}{3}}[/tex], y = 0, and x = 1

Calculus's core idea of integration entails determining a function's integral. It is a reverse process of differentiation that enables us to compute cumulative numbers, find the area under a curve, solve differential equations, and more.

The function can be written as,

[tex]m = \rho\int_0^1x^{\frac{2}{3}}dx\\= \rho\left[\dfrac{x^{\frac{5}{3}}}{\frac{5}{3}}}\right]\\=\dfrac{3}{5}\rho[/tex]

The value of Mx can be calculated as,

[tex]M_x = \rho\int_0^1\dfrac{x^{\frac{2}{3}}}{2}}\times x^{\frac{2}{3}}dx\\=\dfrac{\rho}{2}\left[\dfrac{x^{(\frac{2}{7})}}{\frac{7}{3}}\right]_0^1\\=\dfrac{3}{14}\rho[/tex]

Calculate the value of My,

[tex]M_y =\rho \int_0^1 x\times x^{\frac{2}{3}}dx\\=\rho \left[\frac{x^\frac{8}{3}}{\dfrac{8}{3}}\right]\\=\dfrac{3}{8}{\rho[/tex]

The value of [tex]\bar x\\[/tex] will be calculated as,

[tex]\bar x = \dfrac{M_x }{m}\\=\dfrac{ \dfrac{3}{8}\rho}{\dfrac{3}{5}\rho}\\=\dfrac{5}{8}[/tex]

The value of [tex]\bar y\\[/tex] is calculated as,

[tex]\bar y= \dfrac{M_y }{m}\\=\dfrac{ \dfrac{3}{14}\rho}{\dfrac{3}{5}\rho}\\=\dfrac{5}{14}[/tex]

Therefore, the required values are [tex]\bar x = \dfrac{5}{8}\\[/tex] and  [tex]\bar y = \dfrac{5}{14}[/tex].

To know more about the area of the region follow

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Nate and his brother are saving money to buy a gaming system. The system they want cost $349. The store is having a sale and the system is 30% off. State sales tax 6%.

Answers

Answer:

258.96

Step-by-step explanation:

%30 = 0.3

%6   = 0.06

so..

349 - (349 × 0.3)

349 - 104.7

244.3

then do the tax which is %6 or 0.06

244.3 + (244.3 × 0.06)

244.3 + 14.66

258.96

Good Job! Pls Brailniest! it would mean a lot ;) !

If a crew of loggers cleared 1
acre of lumber in 4 days, how
long will it take the same crew to
clear 5 acres of lumber?

Answers

Answer:

1 acre of lumber takes 4 days so we have to do acres times days here so              4 x 1 = 1 that's for the first day. For 5 acres we would do 5 x 4 = (20 Days) Hope this helped! :))

Step-by-step explanation: 5 times 4 = 20  

Please help me solve this, I will give you brainliest.

Answers

Answer:

5h+10=50

Step-by-step explanation:

4h + 3f + 3c + f + 2c + h + 2c pls help

Answers

Answer:

5h + 4f + 7c

Step-by-step explanation:

Combine like terms!

4h + h = 5h

3f + f = 4f

3c + 2c + 2c = 7c

And you can't put numbers together that have different variables.

5 7/12 + 4 6/12 = 9 13/12 = 1 1/12 what's the error analysis? ​

Answers

Answer:boo

Step-by-step explanation:booooo

Answer:

5 7/12 + 4 6/12 = 9 13/12 is correct but 9 13/12 is equal to 10 1/12 not 1 1/12  because 13/12 is 1 1/12 and you have to add 1 1/12 to 9. So the error analysis is simplifying  9 13/12 to 1 1/12.

Someone plz help me with this I will mark you as brainlyest

Answers

(-2, -7), (-1,-4), (0,-1) (1,2)

All the Xs are the inputs and all the Ys are the outputs. (X,Y)

So I basically just used the Xs it gave us and then I put it in the function equation to solve for the outputs

What is the value of the expression -7+-4

Answers

-11 cuz 7+4 is 11 and since they both negative, 11 will be negative

Answer:

-11

Step-by-step explanation:

This is the answer because:

1) First, multiply the negative sign with the positive sign.

Negative x Positive = Negative

Equation: -7 - 4

2) Now, multiply the negative sign with the negative sign.

Negative x Negative =  Positive  

Equation: 7 + 4 = 11

3) Finally, add the greater number's sign (-7) in front of the number.

-11

Hope this helps! :D

Please help!! Will give brainliest if correct!

If triangle RST is an equilateral triangle, find x and y.

A. x = 70, y = 35
B. x = 80, y = 40
C. x = 120, y = 30
D. x = 120, y = 40

Answers

Answer:

C.

Step-by-step explanation:


There are 16 boys and 20 girls in a class. What part of the class is boys? What part girls?

Answers

Answer:

girls 4/9 or (Decimal: 0.444444) percent is 44.4%

boys 5/9 or (Decimal: 0.555556) percent is 55.5%

Can anyone solve this for me. Thanks

Answers

Answer:

y=-1/3x+3

Step-by-step explanation:

Pls help me I will pick brainliest

Answers

Answer:

What do you need help with?

Step-by-step explanation:

Answer:

??

Step-by-step explanation:

.

Chloe runs the after-school cookery club.
The group will be baking 36 scones using the following recipe.
Recipe for 12 scones:
• 250 g self-raising flour
• 60 g butter
• 30 g caster sugar
• 175 ml milk
How much milk will be used?
ml​

Answers

Answer:

525 ml

Step-by-step explanation:

12 : 175 ml

36 : x

= 175 × 36

= 6300

x = 6300/12

= 525 ml

The amount of milk that is used while baking 36 scones will be 525 mL.

What are ratio and proportion?

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

Chloe runs the after-school cookery club. The group will be baking 36 scones using the following recipe.

Recipe for 12 scones:

250 g self-raising flour60 g butter30 g caster sugar175 mL milk

The amount of milk that is used while baking 36 scones will be given as,

⇒ 175 x 36 / 12

Simplify the expression, then we have

⇒ 175 x 36 / 12

⇒ 175 x 3

⇒ 525 mL

The amount of milk that is used while baking 36 scones will be 525 mL.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

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Dean walked from the library to the mall. For the
first 12 minutes, he walked at a speed of 80
m/min, but then he slowed his speed to 68
m/min for next 7 minutes. If he was still 130 m
away from the mall, what was the distance
between the library and the mall?

Answers

905 mph because of the 7 minutes

The last school year enrollment of Genoa Middle school was 465 students. This year the enrollment is 525.

Answers

Answer:

465 to 525

Step-by-step explanation:

60 difference

Scarlett stopped at a campground along the Appalachian trail. The campground had a 1
2
acre area for tents, divided into 6 equal campsites. Scarlett picked one of the sections to pitch her tent.

Which expression would give you the size of Scarlett’s campsite? Check all that apply.
One-half divided by 6
StartFraction 6 Over 7 EndFraction divided by 6
6 divided by one-half
StartFraction 6 Over 12 EndFraction divided by 6
6 divided by StartFraction 3 Over 6 EndFraction

Answers

Answer:

1/2 divided by 6

6/12 divided by 6

Step-by-step explanation:

Answer:

a - d

Step-by-step explanation:

8s + 6 + 2s - 4 + 4s

Answers

Answer:

14s + 2

Step-by-step explanation:

add the s values up and you’ll get 14s (8s + 2s + 4s) and then add the regular ones and you’ll have 2 (6 + -4)

Find the measure of an angle such that the sum of its supplement and four times its
complement is 13° less than twice the angle.
Show work

Answers

Answer:

Angle=79°

Step-by-step explanation:

Hope it helps!

grrrrrr please help i’ll give u a cookie :)

Answers

im only in 6th grade

Step-by-step explanation:

PLEASE HELP! I NEED ANSWERS! 8-11 FIND THE RELATIONSHIP

Answers

Answer:

8. complementary 9. linear pair 10. adjacent 11.  vertical

Step-by-step explanation:

The sum of two numbers is 49 and the difference between these two numbers is 9.
What are these two numbers?​

Answers

Answer:

the answer is 39 and 14.

The solution is, the numbers are 20 and 29.

What is Subtraction?

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

Here, we have,

given that,

The sum of two numbers is 49

and the difference between these two numbers is 9.

let, the numbers are x & y

so, we get,

according to question:

x+y = 49 ...1

x-y = 9 ....2

so, simplifying we get,

2x = 58

or, x = 29

so, we get,

y = 20

Hence, The solution is, the numbers are 20 and 29.

To learn more on subtraction click:

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PLS HELP!! According to the following diagram, which two options form a pair of opposite rays?

Answers

Ello there mate hows it going? I have done geometry and parlinguals along with alegbra! I am certified as a college professor and am willing to help ya!

PLEASE THANK ME RATE MY QUESTION 5 STARS AND MARK ME BRAINLIEST for my extrodinary and overly qualified help!

A,C

yours,

a soon to be brainliest

>_< I need some help pls,

Answers

Answer: 80 = 20 + 5v

Step-by-step explanation:

This equation allows you to find out how many visits would create an even rate for both gyms.

a car traveled 23 miles in 15 minutes. how many miles per hour was it traveling?

Answers

Answer:

1.53333... mph

Step-by-step explanation:

Well, if you want to figure out the speed (miles per hour), all you need to do is divide the distance by the time. In this case, the distance is 23 miles, and the time is 15 minutes. 23/15= 1.53333...

Hope this helps!! Have an amazing day c:

The speed of the car with given distance and time is 92 miles per hour.

Given that, a car traveled 23 miles in 15 minutes.

What is the speed?

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

We know that, speed = Distance/Time

Here 15 minutes = 15/60

= 1/4 hours

Now, speed = 23 ÷ 1/4

= 23 ×4

= 92 miles per hour

Therefore, the speed of the car with given distance and time is 92 miles per hour.

To learn more about the speed, distance, and time visit:

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1. Refer to the equation 3x − 5y = 15. (a) Create a table of values for at least 4 points. Show your work on how you found the values for each coordinate pair, and validated the points were on the line. Work for Point 1 Work for Point 2 Work for Point 3 Work for Point 4

Answers

Answer:

We have the equation:

3x - 5y = 15

a) We want to create a table with at least 4 points.

To do this, first, let's write the equation as a function: We must isolate one of the variables. Let's isolate y.

5y = 3x - 15

y = (3/5)*x - 3.

Then we have a linear equation.

Now, we can input different values of x, and see what value takes y in each case, then in this way we can be sure that the points will be on the line.

x = 0.

y = (3/5)*0 - 3

y = -3

Then we have the point (0, -3).

x = 1.

y = (3/5)*1 - 3 = 3/5 - 15/5 = -12/5

y = -12/5

Then we have the point (1, -12/5)

x = 5

y = (3/5)*5 - 3 = 3 - 3 = 0

y = 0

then we have the point (5, 0)

x = 10

y = (3/5)*10 - 3 = 6 - 3 = 3

y = 3

Then we have the point (10, 3).

Now we can create the table

[tex]\left[\begin{array}{ccc}x&y\\0&-3\\1&-12/5\\5&0\\10&3\end{array}\right][/tex]

Below you can see a graph, where the blue dots are our 4 points, and the green line is the line that represents the equation.

Question 2
Explain the difference between the graphs y = x3 and y = 3(x – 4)3 + 7.

Answers

Answer:

The first graph , y=x³ is a cubic function graph and that of the second graph, y = 3(x – 4)3 + 7 is a linear graph.

Step-by-step explanation:

The graph of y=x³ is a cubic function graph where the x term has the highest power of x as 3. As attached in the first graph.

The second graph for y = 3(x – 4)3 + 7. is a linear graph that can be written as;

y=(3x-12)3 +7

y=9x-36 + 7

y=9x - 29

which is a linear graph with a slope of 9 and cuts the y-axis at -29 as shown in the second attached graph.

How many kilograms of potatoes will each person get if 5 people share 1/3 of a kilogram of potatoes equally?

Answers

Answer:

1/15 kg

Step-by-step explanation:

Divide by 5 can be written as multiply by 1/5

1/3 * 1/5 = 1/15

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