Equation of any circle with (a,b) as its center, and on (x,y) coordinate, with radius r, is:
![(x-a)^2+(y-b)^2=r^2](https://tex.z-dn.net/?f=%28x-a%29%5E2%2B%28y-b%29%5E2%3Dr%5E2)
so here the center is at (4,5) with radius of 2, so,
The equation of this circle is:![(x-4)^2+(y-5)^2=4](https://tex.z-dn.net/?f=%28x-4%29%5E2%2B%28y-5%29%5E2%3D4)
Hope this helps.
Answer:yes
Step-by-step explanation:
Well, by definition, the tangent vector is the vector that is the result of differentiating every component of the function. Hence, the tangent vector is T=(3,-5sint,5cost). This has a magnitude of
![|r|^2=3^2+(-5sint)^2+(5cost)^2](https://tex.z-dn.net/?f=%7Cr%7C%5E2%3D3%5E2%2B%28-5sint%29%5E2%2B%285cost%29%5E2)
which yields |r|=
![\sqrt{34}](https://tex.z-dn.net/?f=%20%5Csqrt%7B34%7D%20)
(by using the known trigonometric formula
![cost^2+sint^2=1](https://tex.z-dn.net/?f=cost%5E2%2Bsint%5E2%3D1%20)
that holds for all t). Thus, the unit tangent vector t is given by: t=
![\frac{T}{\sqrt{34}}](https://tex.z-dn.net/?f=%20%5Cfrac%7BT%7D%7B%5Csqrt%7B34%7D%7D%20)
. Now, to find a normal unit vector, we just need to find a normal vector N and scale it appropriately. To find a normal unit vector, we can just find vector that satisfies V*T=0 (dot product of vectors). By inspection, we see that the vector N=(0, cost, sint) satisfies this requirement and that it is also a unit vector (due to the aforementioned trigonometric identity). Hence, a normal unit vector to our vector function is N.
Every triangle measures 180 degrees, if you add every expression and set it equal to 180 you will find the value of x.
Therefore, C is your answer.
Investment of $3000 at 16% simple interest for 2 years
Investment of $3000 at 5% simple interest for 20 years
Investment of $1000 at 16% simple interest for 20 years
Solution:
(1) Investment of $3000 at 5% simple interest for 20 years
![$\text{Simple interest}=\frac{PRT}{100}](https://tex.z-dn.net/?f=%24%5Ctext%7BSimple%20interest%7D%3D%5Cfrac%7BPRT%7D%7B100%7D)
![$=\frac{3000\times5\times20}{100}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B3000%5Ctimes5%5Ctimes20%7D%7B100%7D)
![$=3000](https://tex.z-dn.net/?f=%24%3D3000)
Simple interest 1 = $3000
(2) Investment of $3000 at 16% simple interest for 2 years
![$\text{Simple interest}=\frac{PRT}{100}](https://tex.z-dn.net/?f=%24%5Ctext%7BSimple%20interest%7D%3D%5Cfrac%7BPRT%7D%7B100%7D)
![$=\frac{3000\times16\times2}{100}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B3000%5Ctimes16%5Ctimes2%7D%7B100%7D)
![$=960](https://tex.z-dn.net/?f=%24%3D960)
Simple interest 1 = $960
(3) Investment of $1000 at 16% simple interest for 20 years
![$\text{Simple interest}=\frac{PRT}{100}](https://tex.z-dn.net/?f=%24%5Ctext%7BSimple%20interest%7D%3D%5Cfrac%7BPRT%7D%7B100%7D)
![$=\frac{1000\times16\times20}{100}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B1000%5Ctimes16%5Ctimes20%7D%7B100%7D)
![$=3200](https://tex.z-dn.net/?f=%24%3D3200)
Simple interest 1 = $3200
Order from least interest amount to greatest interest amount:
$960 < $3000 < $3200
Investment of $3000 at 16% simple interest for 2 years
Investment of $3000 at 5% simple interest for 20 years
Investment of $1000 at 16% simple interest for 20 years