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
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
Using the linearity of the integral and Barrow's Theorem we have
As a result, the value of the double integral is -48-
Answer:
1: 11982.79
2: 12136.31
4: 12216.09
12: 12270.46
365: 12297.10
Step-by-step explanation:
The compound interest formula is A=P*(1+r/n)^nt
P=principal amount
r=rate
n=number of compounds per period
t=number of periods
In this situation, the principal amount is 5,000=P. The rate is 6%, so r=0.06. n is equal to the top number in the table. And this is 15 years, so t=15.
For 1, it would be A=5,000*(1+.06/1)^1*15, or A=5,000(1.06^15), or 11982.79.
For 2, it would be 5,000*(1+.06/2)^2*15, or 5,000*(1.03^30), or 12136.31.
And so forth. Good luck
Answer:
n=12.5
Step-by-step explanation:
10/8=n/10
multiply the denominator and numerators 10 ad 10=100 divide by 8=12.5
Look at the coefficient of x², ignore the positive or negative sign. The larger the coefficient, the narrower the graph.
in this case, the coefficients are -2, -1/2, -4, and 1/7
ignore the positive or negative sign, 4 is the largest number, so y=-4x² is the narrowest.
Note: the positive/negative sign tells you whether the graph opens upward or downward. It doesn't determine the width of the graph.
