1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ELEN [110]
3 years ago
7

1 pt) If a parametric surface given by r1(u,v)=f(u,v)i+g(u,v)j+h(u,v)k and −4≤u≤4,−4≤v≤4, has surface area equal to 1, what is t

he surface area of the parametric surface given by r2(u,v)=5r1(u,v) with −4≤u≤4,−4≤v≤4?
Mathematics
1 answer:
natta225 [31]3 years ago
8 0

The area of the surface given by \vec r_1(u,v) is 1. In terms of a surface integral, we have

1=\displaystyle\int_{-4}^4\int_{-4}^4\left\|\frac{\partial\vec r_1(u,v)}{\partial u}\times\frac{\partial\vec r_1(u,v)}{\partial v}\right\|\,\mathrm du\,\mathrm dv

By multiplying each component in \vec r_1 by 5, we have

\dfrac{\partial\vec r_2(u,v)}{\partial u}=5\dfrac{\partial\vec r_1(u,v)}{\partial u}

and the same goes for the derivative with respect to v. Then the area of the surface given by \vec r_2(u,v) is

\displaystyle\int_{-4}^4\int_{-4}^425\left\|\frac{\partial\vec r_1(u,v)}{\partial u}\times\frac{\partial\vec r_1(u,v)}{\partial v}\right\|\,\mathrm du\,\mathrm dv=\boxed{25}

You might be interested in
Please help fan and medal whatever you want.<br> What are the factors of x2 − 81?
Bas_tet [7]
x^2-81=(x-9)(x+9)
3 0
3 years ago
Read 2 more answers
A gas station sells a coffee mug filled with coffee for $3. For each refill, using the same mug, the gas station charges $1.25 f
avanturin [10]
Since the price of the coffee itself is $1.25, the gradient of the function will be 1.25 and will give a straight line. However, since the first cup of coffee costs $3, when extrapolated to x = 0, the price is 3 - 1.25 = $1.75 which indicates the cost of using the cup. Therefore this is the y-intercept. This can be expressed as a linear function of y = mx + c where y is the price, m is the gradient, x is the number of times the cup has been filled with coffee, and c is the price of using the cup, giving:
y = 1.25x + 1.75
3 0
3 years ago
Simplify: 299.081+59.26-95.32-365.195
Lilit [14]
-102.174. Just plugged into a calculator
5 0
3 years ago
Hellen has 10 sweets,shelly has 30 sweets.Faith has 4 fewer sweets than the average number of sweets that hellen,shelly and fait
allsm [11]

Answer:

The sum of all the sweets is 54 sweets

Step-by-step explanation:

Here, we want to calculate the number of sweets the three have altogether.

Let the number of sweet Faith has be x

Mathematically;

Faith has 4 sweets fewer than the average number of sweets

The average is the sum of all the sweets divided by 3

The average will be (10 + 30 + x)/3

Thus;

(10 + 30 + x)/3 - 4 = x

(40 + x)/3 = x + 4

40 + x = 3(x + 4)

40 + x = 3x + 12

40-12 = 3x -x

28 = 2x

x = 28/2

x = 14 sweets

So the sum of all the sweets would be 10 + 30 + 14 = 54 sweets

7 0
3 years ago
I need help asap:) thanks
Len [333]

Answer:

More than one triangle can be formed by three angles measuring 75°, 45° and 60°. Solution : We know that, The sum of the measures of all angles of a triangle should be equal to 180

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Which of the following is a rational number? Square root= sq <br><br> Sq 22 sq 23 sq 24 sq 25
    11·1 answer
  • David writes down the sequence 2,6,10,14 he says the sequence is n+4 is he correct
    6·2 answers
  • A candle is 17 in. tall after burning for 3 hours. After 5 hours, it is 15 in. tall. Write a linear equation to model the relati
    13·1 answer
  • Um....help me with this question​
    11·1 answer
  • V= πr^2h explain with words step by step how you solve for “h” in the previous exercise
    8·1 answer
  • Which linear function has the steepest slope? On a coordinate plane, a line goes through points (0, 1) and (1, negative 2). A 2-
    10·2 answers
  • What is 1 half plus 2 fifths?
    7·1 answer
  • Can you reduced 87/100?
    8·1 answer
  • Which expression is equivalent to (3−22)+5?
    14·1 answer
  • X + 8 = -15<br> What does x= ???
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!