<span>Let r(x,y) = (x, y, 9 - x^2 - y^2)
So, dr/dx x dr/dy = (2x, 2y, 1)
So, integral(S) F * dS
= integral(x in [0,1], y in [0,1]) (xy, y(9 - x^2 - y^2), x(9 - x^2 - y^2)) * (2x, 2y, 1) dy dx
= integral(x in [0,1], y in [0,1]) (2x^2y + 18y^2 - 2x^2y^2 - 2y^4 + 9x - x^3 - xy^2) dy dx
= integral(x in [0,1]) (x^2 + 6 - 2x^2/3 - 2/5 + 9x - x^3 - x/3) dx
= integral(x in [0,1]) (28/5 + x^2/3 + 26x/3 - x^3) dx
= 28/5 + 40/9 - 1/4
= 1763/180 </span>
Answer:
The North and South poles on the bar magnets attract to one another when they are placed near each other. When the North and North or the south and south are placed near each other, they repel away from each other.
I hope this helps :)
Answer:
22.5° and 67.5°
Step-by-step explanation:
The sum of complementary angles equal 90°.
Given that one of the complementary angles is 3 times larger than the other, let "x" represent the other angle.
Thus, the following expression can be written to represent this case:
Solve for x
Divide both sides by 4
The measure of the complementary angles are:
x = 22.5°
3x = 3(22.5) = 67.5°
The rule would be : 3^x, where x starts at 0.
3^0 is 1,
3^1 is 3, because 3 one time is 3.
3^2 is 9, because 3x3 is 9.
3^3 is 27, because 3x3x3 is 27
Answer: 3^x
The formula to get the circumference is 2πr, π being pi and r being your radius.
Your r is 0.9 since the radius is half the diameter.
2πr = 2 x 3.142 x 0.9
= 5.6556cm
≈ 5.7cm
