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IRINA_888 [86]
2 years ago
5

(1 point) Consider the paraboloid z=x2+y2. The plane 2x−2y+z−8=0 cuts the paraboloid, its intersection being a curve. Find "the

natural" parametrization of this curve. Hint: The curve which is cut lies above a circle in the xy-plane which you should parametrize as a function of the variable t so that the circle is traversed counterclockwise exactly once as t goes from 0 to 2*pi, and the paramterization starts at the point on the circle with largest x coordinate. Using that as your starting point, give the parametrization of the curve on the surface.

Mathematics
1 answer:
skad [1K]2 years ago
8 0

Answer:

\left \{ {{x(t)=-1+\sqrt{10}Sin(t) } \atop {y(t)=1+\sqrt{10}Sin(t)}} \right.

Step-by-step explanation:

We have the plane 2x-2y+z-8=0 and the paraboloid z=x²+y².

We match the equations:

z=8-2x+2y

z=x²+y²

x²+y²=8-2x+2y

Then, we get the equation of the curve:

x²+2x+y²-2y=8 (adding +2x and -2y in both members of the equation)

(x²+2x+1)+(y²-2y+1)=8+1+1

Trinomials can be reduced as squared binomials

(x+1)²+(y-1)²=10

This is a circle with center in (-1,1) and radius √10

The generic

The parametric expression of the circle is:

\left \{ {{x(t)=-1+\sqrt{10}Sin(t) } \atop {y(t)=1+\sqrt{10}Sin(t)}} \right.

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Evgesh-ka [11]

Answer:

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4 0
1 year ago
Harriet earns the same amount of money each day. Her gross pay at the end of 7 workdays is 35h+56 dollars.which expression repre
statuscvo [17]

The expression 5h+8 represents Harriet's gross pay each day.

Step-by-step explanation:

Given,

Gross pay of Harriet = 35h + 56

This expression represent Harriet's pay for 7 day.

Harriet's gross pay per day = \frac{Gross\ pay}{Number\ of\ days}

Harriet's gross pay per day = \frac{35h+56}{7}

Harriet's gross pay per day = \frac{35h}{7}+\frac{56}{7}

Harriet's gross pay per day = 5h+8

The expression 5h+8 represents Harriet's gross pay each day.

Keywords: division, addition

Learn more about division at:

  • brainly.com/question/106975
  • brainly.com/question/10712420

#LearnwithBrainly

4 0
2 years ago
A pile of coins, consisting of quarters and half dollars, it worth $11.75. If there are 2 more quarters than half dollars, how m
lord [1]
Let the number of half dollars be x,

number of quarters = x + 2
amount of half dollars = 0.5x
amount of quarters = 0.25(x + 2)
= 0.25x + 0.5
total amount = 0.5x + 0.25x + 0.5
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0.75x + 0.5 = 11.75
0.75x = 11.25
x = 15
number of quarters = x + 2
= 15 + 2
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There are 17 quarters and 15 half dollars.
3 0
2 years ago
after taking nine test Carols average grade in her Italian classes 90 her teacher drops the lowest of the nine test scores to de
Ostrovityanka [42]

Answer:

82

Step-by-step explanation:

The sum of scores for the 9 tests must be 90 * 9 = 810. The sum of scores for the 8 tests is 8 * 91 = 728 so the lowest score is 810 - 728 = 82.

5 0
2 years ago
Larji bought a dozen ears of corn. She prefers yellow corn, which costs 40 cents an ear, and her siblings prefer the peaches and
Murrr4er [49]

Answer:  x+y =12

0.40x+0.50y =5.70

Step-by-step explanation:

Let x = Number of ears of yellow corn

y - Number of ears of peaches and cream variety.

AS per given,

x+y = 1 dozen

⇒ x+y =12     [1 dozen =12]

Cost per ear of yellow corn = 40 cents = $0.40    [1 dollar = 100 cents, 1 cent = 0.01 dollar]

Cost per ear of peaches and cream variety = 50 cents = $ 0.50

Total cost ( in$): 0.40x+0.50y =5.70

Required system of equations represents the number of ears of corn of each type that Larji purchased:

x+y =12

0.40x+0.50y =5.70

8 0
2 years ago
Read 2 more answers
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