Suppose a surface S is parameterized by r(u,v) =< 3u + 2v,5u^3,v^2 >,0 ≤ u ≤ 8, 0 ≤ v ≤ 6
a. Find the equation of the tangent plane to S at (7,5,4).
b. Set up the double integral that represents the surface area of S.

Answers

Answer 1

To find the equation of the tangent plane to surface S at point (7,5,4), we first need to find the partial derivatives of the parameterization function r(u,v).
∂r/∂u = <3, 15u^2, 0>
∂r/∂v = <2, 0, 2v>
Evaluating these partial derivatives at (7,5,4), we get
∂r/∂u (7,5) = <3, 1875, 0>
∂r/∂v (7,5) = <2, 0, 8>
Next, we can find the normal vector to the tangent plane by taking the cross product of these partial derivatives:
N = ∂r/∂u x ∂r/∂v = <-15000, 6, -5625>
The equation of the tangent plane can then be written as:
-15000(x-7) + 6(y-5) - 5625(z-4) = 0
To set up the double integral that represents the surface area of S, we can use the formula:
Surface area = ∫∫ ||∂r/∂u x ∂r/∂v|| dA
where dA = ||∂r/∂u x ∂r/∂v|| du dv
Plugging in our parameterization function and taking the cross product of the partial derivatives as before, we get:
||∂r/∂u x ∂r/∂v|| = sqrt(2250000u^2 + 4v^2 + 42187500u^4)
So the surface area of S can be found by integrating this expression over the given ranges of u and v:
∫∫ sqrt(2250000u^2 + 4v^2 + 42187500u^4) du dv, 0 ≤ u ≤ 8, 0 ≤ v ≤ 6.

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Related Questions

.
Simplify the radical expression.



−4x2

2x2

−2x2

4x2

Answers

2x^2 ( the second one ) :-)

You get scores of 72 and 88 on 2 science tests. You have to have an average of at least 85 to not be grounded by your parents. What score do you need to make on your next test to not be grounded?

Answers

Answer:

95

Step-by-step explanation:

72+88+95=255:3= 85

Answer: 95
1. Add both test scores (72 & 88) together. You get 160
2. Then you divide 160 by 2. You get an average of 80.
3. When you add 72, 88, and 95 together you get 255.
4. You then divide 255 by 3
5. You get an average of 85

Write your question here (Keep it simple and clear to get the best answer) simplify (3x-4y)(5x+2y)-(x+y)

Answers

Answer:

15x^2−14xy−8y^2−x−y

Step-by-step explanation:

Combine like units.

Answer:

hope it helped

have a good day

1. Which of the following equations would NOT contain the point (4,12)?
A. y=-1/2x+14
B. y=1/2x+8
C.y=-2x+20
D.y=3/4x+9

Answers

Answer:

the answer is b hope this helps :)

Find the volume of the cylinder.
Either enter an exact answer in terms of it or use 3.14 for

Answers

Ans: 1205.76 units^3

Explanation:

Volume of cylinder

= base area x height

= 3.14 x 8² x 6

= 3.14 x 64 x 6

= 1205.76 units^3


In this question, I used 3.14 instead of π.

Base area = πr²

Hope it helps :), mark me brainliest please!

Vincent had 97 rocks in his collection. He found 48 more at the beach. How many did he have in all ?

Answers

Answer:

145

Step-by-step explanation:

97+48

7+8=15

9+4+1=14

145

PLEASE HELP!!
The cost to rent a chain saw for two days and a brush chipper for two days is $272. The cost to rent a
chain saw for two days and a brush chipper for one day is $195. Write a system of equation to solve to
find the cost of renting a chain saw for one day.

Answers

$272-$195= $77
So that means $77 is the price of the renting chain saw for one day

I NEED HELP ASAP WILL GIVE BRAINLYEST

Answers

Answer:

-8

Step-by-step explanation:

First simplify the expression to -(2^5)^3/5. Then you get -2^3, which is simplified again to -8.

What is the solution to the equation 3^x = 10?

Answers

Answer:

log3 (10) = x

the 3 is a tiny 3

Step-by-step explanation:

remember the saying, left right left.

so, 3 goes to the left, x goes to the right, and 10 goes to the left side of the equal sign which in turn comes out to log3(10) =x

Micah invests $5,280 in an account that earns 4.2% interest, compounded monthly.

Part A
Write a function for the amount that will be in the account after t years.

Part B
What is the value of the account after 8 years?

Answers

a) The function is given as follows: [tex]A(t) = 5280\left(1 + \frac{0.042}{12}\right)^{12t}[/tex]

b) The value of the account after 8 years is given as follows: $7,384.

What is compound interest?

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.

The parameter values for this problem are given as follows:

P = 5280, r = 0.042, n = 12.

Hence the equation is given as follows:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(t) = 5280\left(1 + \frac{0.042}{12}\right)^{12t}[/tex]

The value of the account after 8 years is obtained as follows:

[tex]A(8) = 5280\left(1 + \frac{0.042}{12}\right)^{12 \times 8}[/tex]

A(8) = $7,384.

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Dont be shy- drop the answer :)

Answers

Answer:

-11x = -55

x = 5

Step-by-step explanation:

Hope that helps!

CAN SOMEONE HELP LIKE RN I NEED IT QUICK

Answers

I’m pretty sure it’s 60

59:
Evaluate the function requested. Write your answer as a fraction in lowest terms.
B
39
15
36
Find tan A
a
5
tan A =
13
C.
5
tan A -
12
b.
13
d.
12
tan A =
tan A -
5

Answers

Answer:

Step-by-step explanation:

Plz help me with 18 is not -0.95

Answers

Answer:

Please refer to the attachment.......

Distance between (-1,-2) and (8,0)

Answers

Answer:

9.219544

Step-by-step explanation:

(8 - -1)^2 + (0 - -2)^2 = 85, sqrt 85 = 9.219544

Answer:

Step-by-step explanation:

Distance formula : d=√((x_2-x_1)²+(y_2-y_1)²)

d=√((8-(-1))²+(0-(-2))²)

d=√((9)²+(2)²)

d=√(81+4)

d=√(85)

d = 9.21954445729

Si 2X -7 = 3, luego 3X + 1 =

(1) 4
(2)5
(3)7
(4)12
(5)16

Answers

Answer:

2x-7=3

2x=3+7

{2x=10}÷2

x=5

꧁꧁꧂꧂

3x+1=

{3x=1}÷3

x=1/3

Jack made 9 identical bags using 5 yards of fabric. How much fabric did Jack use for each bag? Solve on paper and check your work on Zearn.

Answers

Answer: 5/9 yards

Step-by-step explanation:

From the question, we are informed that Jack made 9 identical bags using 5 yards of fabric.

To calculate the amount of fabric that Jack use for each bag, we have to divide 5 by 9. Thus will be:

= 5 / 9

Therefore, it means that Jack used 5/9 yards for each bag

Express the function F in the form f ∘ g. (Enter your answers as a comma-separated list. Use non-identity functions for f(x) and g(x).) F(x) = x + 2

Answers

Answer:

[tex]F(x) = f \circ g[/tex]

[tex]f(x) = x + 2[/tex] and [tex]g(x) = x[/tex]

Step-by-step explanation:

Given

[tex]F(x) = x + 2[/tex]

Required

Express as

[tex]F(x) = f \circ g(x)[/tex]

In functions:

[tex]f \circ\ g(x) = f(g(x))[/tex]

So, we have:

[tex]f(g(x)) = x + 2[/tex]

g(x) can be set to x and f(x) to x + 2

Hence:

[tex]F(x) = f \circ g[/tex]

When: [tex]f(x) = x + 2[/tex] and [tex]g(x) = x[/tex]

how muck is in kilograms?

Answers

Answer:

1000grams= 1 kilogram

Step-by-step explanation:

Answer:

1000 grams = 1 Kilo

HELP ASAP! EXPONENTIAL FUNCTIONS

Answers

it is the yellow one

PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer: 8463160

Step-by-step explanation:

Answer:

8463160

Step-by-step explanation:

                https://byjus.com/rounding-to-the-nearest-tenth-calculator/

graph the linear equation y = -6x - 5

Answers

here’s my answer from desmos!

this was my answer from demos

A leisure aircraft is owned by the Broadland Flying Group which has 10 members. The costs of keeping the aircraft comprise maintenance costs (including insurance) and the running cost which is mainly fuel. Average fuel consumption is 9 miles per gallon. If the 10 members of the Group are to share costs equally, write down a formula to enable Gordon the treasurer to calculate the annual cost for each member if the aircraft travels n miles in a year, incurs maintenance costs of £M and fuel costs £3 a gallon.

Answers

Answer:

£(M + n/3) / 10

Step-by-step explanation:

Given that :

Number of members = 10

Fuel consumption = 9 miles per gallon

Consumption for n miles = n/9 GALLONS

Cost of fuel = n/ 9 * £3 = 3n / 9 = £n / 3

Maintainace cost = £M

Annual cost per member :

£(M + n/3) / 10

the sum of two consecutive multiples of 4 is 36 . find the multiples ???
PLZZZZZZZZZ help me now ​

Answers

Answer:

The numbers are 16 and 20

Step-by-step explanation:

Let the multiples be: x+4 and x+8

Sum is 36, so we can make an equation:

x+4+x+8=36

2x=36-12

x=12

The numbers are 12+4=16, 12+8=20.

Hope this answer helped you! If so, please leave a rating and let me know if I was correct. (Hopefully Brainliest, but totally up to you.) Have a great day!

coat is 20% off. If the regular price of the coat is $225, what is the sale price of the coat?

Answers

Answer:

$180

Step-by-step explanation:

$225 times .20 = 45 .   225-45=180

Answer:

$180

Step-by-step explanation:

Find 1% of the price.

100% = 225

1% = 225 ÷ 100 = 2.25

100 - 20 = 80% (Percentage of sale price)

80% = 2.25 x 80 = 180

Find the measure......

Answers

Answer:

the answer would be S/ 2= 140/ 2 = 70°

find the m and b of the table

Answers

9514 1404 393

Answer:

  m = 1/2

  b = -7

Step-by-step explanation:

The formulas for these can be used.

  m = (y2 -y1)/(x2 -x1) . . . . . . . . . formula for slope given 2 points

  m = (-9 -(-11))/(-4-(-8)) = 2/4

  m = 1/2

__

  b = y1 -m·x1 . . . . . . . . . . . . formula for y-intercept given slope and point

  b = -11 -(1/2)(-8) = -11 +4

  b = -7

A newspaper invited readers to call a telephone number and record their comments. The next day they reported that readers overwhelmingly prefer two-way traffic flow to one-way streets. This is an example of: A. A convenience sample B. A self-selected sample C. A systematic sample D. A random sample​ does anyone know the answer​

Answers

Answer: Self selected sample

Step-by-step explanation:

They people chose themselves

This is an example of:  B. A self-selected sample , Option B is the answer.

What is  a self-selected sample ?

A self selected sampling technique is one in which the researcher puts out a call or publicises so that individuals and organisations can take part in the survey on their own will which saves the time for searching for the appropriate people .

It is given that

A newspaper invited readers to call a telephone number and record their comments.

This is an example of:  B. A self-selected sample

Therefore Option B is the answer.

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Find the area of the circle 18in

Answers

1017.88in^2

You need to use pi

Answer:

1017.88inches^2

Step-by-step explanation:

Area of a circle=pi * radius^2

324*pi=1017.88

10 + 2.5x > 35 please help meeee

Answers

[tex]x > 10[/tex]

Step-by-step explanation:

1) Subtract 10 from both sides.

[tex]2.5x > 35 - 10[/tex]

2) Simplify 35 - 10 to 25.

[tex]2.5x > 25[/tex]

3) Divide both sides by 2.5.

[tex]x > \frac{25}{2.5} [/tex]

4) Simplify 25/2.5 to 10.

[tex]x > 10[/tex]

Therefor the answer is, x > 10.

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