Answer:
-0.555
Step-by-step explanation:
The terminal point of the vector in this problem is
(-2,-3)
So, it is in the 3rd quadrant.
We want to find the angle
that gives the direction of this vector.
We can write the components of the vector along the x- and y- direction as:
![v_x = -2\\v_y = -3](https://tex.z-dn.net/?f=v_x%20%3D%20-2%5C%5Cv_y%20%3D%20-3)
The tangent of the angle will be equal to the ratio between the y-component and the x-component, so:
![tan \theta = \frac{v_y}{v_x}=\frac{-3}{-2}=1.5\\\theta=tan^{-1}(1.5)=56.3^{\circ}](https://tex.z-dn.net/?f=tan%20%5Ctheta%20%3D%20%5Cfrac%7Bv_y%7D%7Bv_x%7D%3D%5Cfrac%7B-3%7D%7B-2%7D%3D1.5%5C%5C%5Ctheta%3Dtan%5E%7B-1%7D%281.5%29%3D56.3%5E%7B%5Ccirc%7D)
However, since we are in the 3rd quadrant, the actual angle is:
![\theta=180^{\circ} + 56.3^{\circ} = 236.3^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%3D180%5E%7B%5Ccirc%7D%20%2B%2056.3%5E%7B%5Ccirc%7D%20%3D%20236.3%5E%7B%5Ccirc%7D)
So now we can find the cosine of the angle, which will be negative:
![cos \theta = cos(236.3^{\circ})=-0.555](https://tex.z-dn.net/?f=cos%20%5Ctheta%20%3D%20cos%28236.3%5E%7B%5Ccirc%7D%29%3D-0.555)
Answer:
Elena invested $ 1,700 at 5%, $ 700 at 4%, and $ 600 at 3%.
Step-by-step explanation:
Given that Elena receives $ 131 per year in simple interest from three investments totaling $ 3000, and part is invested at 3%, part at 4% and part at 5%, and there is $ 1000 more invested at 5% than at 4%, to find the amount invested at each rate, the following calculations must be performed:
1500 x 0.05 + 500 x 0.04 + 1000 x 0.03 = 75 + 20 + 30 = 125
1600 x 0.05 + 600 x 0.04 + 800 x 0.03 = 80 + 24 + 24 = 128
1700 x 0.05 + 700 x 0.04 + 600 x 0.03 = 85 + 28 + 18 = 131
Therefore, Elena invested $ 1,700 at 5%, $ 700 at 4%, and $ 600 at 3%
If it is a triangle h is height and b is base.
Answer:
109.0125 dollars, rounded is 109.01$
Step-by-step explanation:
The denominator of the raised fraction is what goes on the outside of the square root. So if you had 2 raised to 1/3, you'd put the 3 raised outside to the left of the radical and the 2 inside. They give the same answer, so if you know one, you can always play with the other until you get the same answer. My teacher told us in Calculus a funny/weird way to remember it is the "bottom (of the raised fraction) goes in the crack (of the radical)." Does this help??