Answer:
Step-by-step explanation:
Consider that F(x,y,z) = (x + y, y + z, z + z)
![r(t)=(cos t,4sint,\sqt{5}cost)\\r'(t)=(-sint,4cost,-\sqrt{5}sint)\\F(r(t))=[tex]\int\limits^{2\pi}_0 {F(r(t))r'(t)} \, dt \\\\=\int\limits^{2\pi}_0(cost+4sint,4sint+\sqrt{5}cost+cost)(-sint,4cost,-\sqt{5}sint)dt\\\\=\int\limits^{2\pi}_0(-sintcost-4sin^2t+16costsint+4\sqrt{5}cos^2t-5sintcost-\sqrt{5}sintcost)dt\\\\=\int\limits^{2\pi}_0(10sintcost-4sin^2t+4\sqrt{5}cos^2t-\sqrt{5}sintcost)dt\\\\=\int\limits^{2\pi}_0((10-\sqrt{5})sintcost-(4+4+\sqrt{5})sin^2t+4\sqrt{5})dt\\\\(10-\qrt{5})(0)-(4+4+\sqrt{5}(\pi)+4\sqrt{5}(2\pi)\\\\(\sqrt{5}-1)4\pi)](https://tex.z-dn.net/?f=r%28t%29%3D%28cos%20t%2C4sint%2C%5Csqt%7B5%7Dcost%29%5C%5Cr%27%28t%29%3D%28-sint%2C4cost%2C-%5Csqrt%7B5%7Dsint%29%5C%5CF%28r%28t%29%29%3D%5Btex%5D%5Cint%5Climits%5E%7B2%5Cpi%7D_0%20%7BF%28r%28t%29%29r%27%28t%29%7D%20%5C%2C%20dt%20%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7B2%5Cpi%7D_0%28cost%2B4sint%2C4sint%2B%5Csqrt%7B5%7Dcost%2Bcost%29%28-sint%2C4cost%2C-%5Csqt%7B5%7Dsint%29dt%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7B2%5Cpi%7D_0%28-sintcost-4sin%5E2t%2B16costsint%2B4%5Csqrt%7B5%7Dcos%5E2t-5sintcost-%5Csqrt%7B5%7Dsintcost%29dt%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7B2%5Cpi%7D_0%2810sintcost-4sin%5E2t%2B4%5Csqrt%7B5%7Dcos%5E2t-%5Csqrt%7B5%7Dsintcost%29dt%5C%5C%5C%5C%3D%5Cint%5Climits%5E%7B2%5Cpi%7D_0%28%2810-%5Csqrt%7B5%7D%29sintcost-%284%2B4%2B%5Csqrt%7B5%7D%29sin%5E2t%2B4%5Csqrt%7B5%7D%29dt%5C%5C%5C%5C%2810-%5Cqrt%7B5%7D%29%280%29-%284%2B4%2B%5Csqrt%7B5%7D%28%5Cpi%29%2B4%5Csqrt%7B5%7D%282%5Cpi%29%5C%5C%5C%5C%28%5Csqrt%7B5%7D-1%294%5Cpi%29)
[/tex]
Answer:
if breadth is y feet long
let length be y+4
Step-by-step explanation:
therefore,
area=(4+y)*y
area=4y+y2
Answer:
£390
Step-by-step explanation:
The ratio of money in bank:
Terry : Faye
3 : 7
Terry put £220 in his account
Faye withdrew £300 from her account
Unknown:
Initial amount Terry had = ?
Solution:
Let the real amount terry has = 3x
Faye will have = 7x
Now;
3x + 220 = 7x -300
Solving this equation:
3x + 220 = 7x -300
3x - 7x = -300 - 220
-4x = - 520
4x = 520
x = 130
Originally, Terry has 3x = 3 x 130 = £390
There are exactly 0.499999 quarts in 1 <span>pint.</span>
60 degrees, because it's an equilateral triangle, as you can tell because the sides are all the same length.
