Number 3 ### Educational Exercise Problems1. **Find the equation of the ellipse:** - Eccentricity: \(\frac{3}{5}\) - Endpoints of the minor axis: \((-3, -5)\) and \((-3, 3)\)2. **Solve the following:** - (a) Solve: \(x + \ln x \leq \ln x + 1\) - (b) Solve algebraically for \(x\) (exact answers only): \[ \frac{e^x - e^{-x}}{2} = 2 \]3. **Convert and analyze equations:** - (a) Change \(\theta = \tan^{-1} \frac{3}{2}\) to an equivalent rectangular equation. - (b) By changing to rectangular coordinates, show that \(r = 4 \sec^2 (\theta/2)\) is a parabola. Find the focus and equation of the directrix of the parabola.4. **Dissolution of a solid:** - If a solid is placed in water, the amount undissolved after \(t\) seconds is \(A(t) = A_0 e^{-kt}\). If 30 grams of the solid are placed in the water and it takes 10 seconds for half to dissolve, how long will it take for 3 grams to be left undissolved?5. **Find the equation of the parabola:** - A parabola has a horizontal axis of symmetry, passing through the points \((0, 3)\), \((-2, 1)\), and \((6, -3)\).6. **Repeat for emphasis**: - If a solid is placed in water, the amount undissolved after \(t\) seconds is \(A(t) = A_0 e^{-kt}\). If 30 grams of the solid are placed in the water and it takes 10 seconds for half to dissolve, how long will it take for 3 grams to be left undissolved?---**Note**: Problems may contain complex concepts requiring a strong understanding of calculus and algebra. Each task involves analyzing specific conditions, converting between different forms of equations, or solving for unknown variables.

Name: Number 3 ### Educational Exercise Problems1. **Find the equation of th
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: Number 3 ### Educational Exercise Problems1. **Find the equation of the ellipse:** - Eccentricity: \(\frac{3}{5}\) - Endpoints of the minor axis: \((-3, -5)\) and \((-3, 3)\)2. **Solve the following:** - (a) Solve: \(x + \ln x \leq \ln x + 1\)