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]
8 nickels, because 8 (nickels) × 5 (worth) = 40
24 dimes, because 8 × 3 = 24 24 × 10 = 240
240 + 40 = 280
Negative 4 or -4 is the answer
Answer:
412 is the quotient
Step-by-step explanation:
14 goes into 5768 412 times.
Answer:
You would usually use 3.14
Step-by-step explanation:
It kind of depends on where you are using it. In an equation, pi would be used as 3.14 and the answer would be approximated. To write it anywhere else (I dont know where else you would though), you would do the pi symbol. I hope this helps.
