4. A candle burned at a steady rate of 2 cm per hour for 4 hours Now it is only 6 cm long. How long was the candle at first? Equation:

a. The temperature at \( 8: 00 \mathrm{PM} \). is \( 35^{\circ} \mathrm{C} \). If it drops \( 1^{\circ} \mathrm{C} \) per minute, what will the temperature be at 8.30 P.M .? The temperature will be \( 5^{\circ} \mathrm{C} \) at \( 8: 30 \mathrm{P.M} \). b. The temperature at \( 8: 20 \mathrm{P.M} \). is \( 3^{\circ} \mathrm{C} \). If it has dropped \( 2^{\circ} \mathrm{C} \) per minute, what was the temperature at \( 7: 55 \) P.M.? The temperature was \( \square^{\circ} \mathrm{C} \) at \( 7: 55 \mathrm{P.M} \).

Verify the identity. \[ \cos (x+y) \cos (x-y)=\cos ^{2} x-\sin ^{2} y \]

For the given function, find (a) \( f(-2)(b) f(-1) \). (a) \( f(-2)=\square \) (a) \( f(-1)=\square \)

Find the length of the line segment connecting points \( C \) and \( D \) located at \( (2,4) \) and \( (4,8) \), respectively.

Determine if the given value is a solution to the equation. \( 2 \sin x+\frac{\sqrt{3}}{2}=\sin x \) (a) \( \frac{4 \pi}{3} \) (b) \( -\frac{\pi}{3} \) Part 1 of 2 (a) \( \frac{4 \pi}{3} \) (Choose one) \( \nabla \) a solution. Part 2 of 2 (b) \( -\frac{\pi}{3} \) (Choose one) \( \nabla \) a solution.