Determine the points (if any) on the curve C at which the vector field F is tangent to C and normal to C. Sketch C and a few representative vectors of F.

F = < 6x, 6y >, where C = { (x, y): x^2 + y^2 = 64 }

Where is F tangent to C?

Where is F normal to C?

Sketch C on a graph and a few representative vectors of F.

Use the distributive property to factor the expression. 15x + 6 a) 2 5 b) − 2 5 c) 3(5x + 2) d) 5(3x + 6)

Tom is making a punch that contains 80% cranberry juice and the rest ginger ale. the punch has 2 liters of ginger ale. part a: write an equation using one variable that can be used to find the total number of liters of cranberry juice and ginger ale in the punch. define the variable used in the equation and solve the equation. hint: 0.8x represents the number of liters of cranberry juice in the punch. (5 points) part b: how many liters of cranberry juice are present in the punch? show your work.

At a pizza shop 70% of the customers order a pizza 25% of the customers order a salad and 15% of the customers order both a pizza and a salad if s customer is chosen at random what is the probability that he or she orders either a pizza or a salad