Answer:
Step-by-step explanation:
See the attached image
Answer:
If sine theta = .3090 then arc sine theta =
18 degrees
Then we look up csc 18 degrees which = 3.2361
Step-by-step explanation:
Answer:
the first one and the second one not the third one
Answer:
= 12π
Step-by-step explanation:
The field F is given by:
(1)
The curve C is the ellipse:

In order to calculate the circulation of F around the curve C, you first find the parametric equation for the given ellipse.
The general form of an ellipse equation is:

The parametric equation is:
(2)
The Stokes's theorem is given by the following identity:
The path integral is also:
(3)
For F(r(t)) and dr(t) you obtain:

Next, in the equation (3) you obtain:
![\int_0^{2\pi} (-48sin^2t+64cos^2t)dt=\int_0^{2\pi}(-\frac{48}{2}(1-cos2t)+\frac{64}{2}(1+cos2t))dt\\\\=\int_0^{2\pi}(-24+24cos2t+32+32cos2t)dt\\\\=\int_0^{2\pi}(6+56cos2t)dt\\\\=[6t+56sin2t]_0^{2\pi}=[6(2\pi)-0]=12\pi](https://tex.z-dn.net/?f=%5Cint_0%5E%7B2%5Cpi%7D%20%28-48sin%5E2t%2B64cos%5E2t%29dt%3D%5Cint_0%5E%7B2%5Cpi%7D%28-%5Cfrac%7B48%7D%7B2%7D%281-cos2t%29%2B%5Cfrac%7B64%7D%7B2%7D%281%2Bcos2t%29%29dt%5C%5C%5C%5C%3D%5Cint_0%5E%7B2%5Cpi%7D%28-24%2B24cos2t%2B32%2B32cos2t%29dt%5C%5C%5C%5C%3D%5Cint_0%5E%7B2%5Cpi%7D%286%2B56cos2t%29dt%5C%5C%5C%5C%3D%5B6t%2B56sin2t%5D_0%5E%7B2%5Cpi%7D%3D%5B6%282%5Cpi%29-0%5D%3D12%5Cpi)
The circulation of the field around C is 12π
Answer:
SA = 18.2+10.4h
59.8yd²
Step-by-step explanation:
Surface area of a 3D shape is the sum of the areas of its faces. A rectangular prism is made of 2 rectangles that make the top and bottom, plus four equal, larger rectangles.
surface area = 2(small rectangles)+4(large rectangles)
surface area = 2(3.5*2.6)+4(2.6h)
SA = 18.2+10.4h
SA = 18.2+10.4h
SA = 18.2+10.4(4)
SA = 18.2+41.6
SA = 59.8yd²