Jolene invests her savings in two bank accounts, one paying 6 percent and the other paying 10 percent simple interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual interest is 5412 dollars. How much did she invest at each rate? Amount invested at 6 percent interest is Amount invested at 10 percent interest is

QUESTION 6 (a) Given the equation of the circle \( x^{2}+y^{2}-4 x+6 y-3=0 \), Determine (i) The radius (ii) The co-ordinates of the centre of the circle (b) The equation \( 4 x^{2}+9 y^{2}=36 \) is an eclipse. Determine (i) The foci (ii) The major notices (iii) The co-notices (iv) Sketch the graph

Find an algebraic expression equal to \( \sec \left(\cot ^{-1}(5 x)\right) \). (You may assume that \( -\frac{\pi}{2}<\cot ^{-1}(5 x)<\frac{\pi}{2} \).)

7. Sea \( C \) la curva dada por \( r(t)=\left(t, t^{2}, t\right) \) y el plano \( 4 x-y+6 z-16=0 \), hallar la longitud de la curva de la porción \( C \), comprendida entre las intersecciones con el plano.

1. \( 365-142= \)

9. \( \square^{2}-50=-1 \)