Find r(t) · u(t). Is the result a vector-valued function? Explain. r(t) = (3t - 1)i + ¼t³j + 4k, u(t) = t²i - 8j + t³k

A candy of this type is selected at random from each of two newly opened bags. What is the probability that the two candies have the given color(s)? The first is not red, and the second is not orange.

Find the GCF and LCM of each pair of integers. 15 and 20

Write the area A of a circle as a function of the circumference C.

r(t) = cos ti + 2 sin tj Evaluate (if possible) the vector-valued function at each given value of t. (d)r(π/6 + Δt) - r(π/6)

A family is planning a vacation and is willing to spend no more than $2000 for 4 airplane tickets and 5 nights at a hotel. Write and graph an inequality that describes the combinations of prices x (in dollars) of an airplane ticket and prices y (in dollars) of a night at a hotel. If the family spends$275 per airplane ticket, is the family willing to spend $200 per night at a hotel? Explain your answer using the graph.

Represent the line segment from P to Q by a vector-valued function and by a set of parametric equations. $P(1,-6,8), Q(-3,-2,5)$

Answer true or false. If the statement is false, explain why and give an example that proves it false. Every integer is a whole number.

Read the newspaper article and answer the following questions:

What is the research question the study addresses?

Sketch the graph of r = 6 cos θ over each interval. Describe the part of the graph obtained in each case. π/2 ≤ θ ≤ π

Represent the line segment from P to Q by a vector-valued function and by a set of parametric equations. $P(0,0,0), Q(5,2,2)$

Is the first number divisible by the second? Explain.

$$78 \text { by } 9$$

Choose the letter of the best answer. A scientist mixes an unknown solid in water. He notices that the particles of the solid solute do not completely dissolve in the solvent and he could easily separate them out using filtration. Which of the following best describes this type of mixture? A. a solution B. a colloid C. a suspension D. a pure substance

Sunlight strikes the surface of a lake. A diver sees the Sun at an angle of $42.0 ^ { \circ }$ with respect to the vertical. What angle do the Sun's rays in air make with the vertical?