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]
$70
.25(56) = 14
14 + 56= $70
If they are parallel they will have the same slope , m
So in y = mx + c, if there are two equations which both have the same m value they will be parallel.
If the lines are perpendicular they'll have slopes like this: 1/2 to -2/1 - where they flip and a negative gets added.
In the equations: 10x + 5y = -5 , and y = -2x + 6
We can rearrange 10x + 5y = -5 to be in the form y = mx + c
10x + 5y = -5
5y = -5 - 10x
y = -1 - 2x
y = -2x - 1
Since y = -2x - 1 and y = -2x + 6 both have the same slope of -2 they are parallel!
Correct answer:
5/64
Step-by-step explanation:
- Multiply the numerators: 10 × 2 = 20
- 16 × 16 = 256
- Put them together: 20/256
- Simplify: 20/256 = 5/64
I hope this helps!
Answer:
x=-8.5.
Step-by-step explanation:
First, write an equation. Twice x (2x) plus 7 (+7) is the same as (=) negative ten (-10), or 2x+7=-10. To solve, first subtract 7 from both sides to get 2x=-17. Then, divide both sides by 2 (x=-8.5).
