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scZoUnD [109]
3 years ago
5

A ray is a defined term because

Mathematics
1 answer:
Simora [160]3 years ago
4 0
Because it can be described using two undefined terms, point and line.
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Let ????C be the positively oriented square with vertices (0,0)(0,0), (2,0)(2,0), (2,2)(2,2), (0,2)(0,2). Use Green's Theorem to
bonufazy [111]

Answer:

-48

Step-by-step explanation:

Lets call L(x,y) = 10y²x, M(x,y) = 4x²y. Green's Theorem stays that the line integral over C can be calculed by computing the double integral over the inner square  of Mx - Ly. In other words

\int\limits_C {L(x,y)} \, dx + M(x,y) \, dy =  \int\limits_0^2\int\limits_0^2 (M_x - L_y ) \, dx \, dy

Where Mx and Ly are the partial derivates of M and L with respect to the x variable and the y variable respectively. In other words, Mx is obtained from M by derivating over the variable x treating y as constant, and Ly is obtaining derivating L over y by treateing x as constant. Hence,

  • M(x,y) = 4x²y
  • Mx(x,y) = 8xy
  • L(x,y) = 10y²x
  • Ly(x,y) = 20xy
  • Mx - Ly = -12xy

Therefore, the line integral can be computed as follows

\int\limits_C {10y^2x} \, dx + {4x^2y} \,dy = \int\limits_0^2\int\limits_0^2 -12xy \, dx \, dy

Using the linearity of the integral and Barrow's Theorem we have

\int\limits_0^2\int\limits_0^2 -12xy \, dx \, dy = -12 \int\limits_0^2\int\limits_0^2 xy \, dx \, dy = -12 \int\limits_0^2\frac{x^2y}{2} |_{x = 0}^{x=2} \, dy = -12 \int\limits_0^22y \, dy \\= -24 ( \frac{y^2}{2} |_0^2) = -24*2 = -48

As a result, the value of the double integral is -48-

3 0
3 years ago
A physical education class lasts for 7/8 -hour. How many minutes do they spend 1/2 of their playing time?
olchik [2.2K]
(7/8) of an hour is 52.5 minutes. If you are looking for half of that, it would be 26.25 minutes or 26 minutes and 15 seconds.
4 0
3 years ago
A blueprint of a house shows a dining room with
Gnom [1K]

Actual area = 42ft²

The actual area will simply be calculated as:

= 6 × 7

= 42 feet²

8 0
2 years ago
(140-x)/(7)+70 = 120. Please answer correctly.
slava [35]
From question,
(140-x)/7+70=120
Or, (140-x)/7=120-70
Or,140-x=50X7
Or, -x=350-140
Or, -x=210
:• x = -210 answers
6 0
3 years ago
Simplify completely:<br> 4V10 – V6 +3710<br> Show all work for full credit.
schepotkina [342]
The answer is 7√10−√6

5 0
3 years ago
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