Applying Vectors in the Plane — Cumulative exam Answers

Carissa is budgeting for her next semester at college. She spent $50 on gas this month. Economists are predicting gas prices to rise 8% per month for the next 6 months. How much should she budget for gas if classes start next month and are 4 months long?

Let w = where O(–5, 6) and R(4, –2). What is the component form of w?

Convert 9x2 + 4y2 – 54x – 8y – 59 = 0 into standard form.

Which of the following is another way of expressing ?

Which recursive formula describes the sequence below?5, 13, 29, 61, 125, ...

Air traffic controllers are watching two planes on radar to ensure there is enough distance between them. Plane A took off at 10:00 a.m., and plane B took off at the same runway 5 minutes later. Both planes are flying at the same direction angle and the same path. At 10:10 a.m., the airport’s radar system detected plane A at (24, 18) and plane B at (8, 6). The scale on the radar is 1 unit = 25 miles.Which vector represents the path from plane A to plane B, and what is the actual distance between them?

Which equation could be used to solve for the measure of side q in shown below, given s = 15, S = 45°, and Q = 105°? [Not drawn to scale]

What are the conjugate and modulus of –14 – 2i?

Review the proof of de Moivre’s theorem. Proof of de Moivre's Theorem [cos(θ) + i sin(θ)]k + 1A= [cos(θ) + i sin(θ)]k ∙ [cos(θ) + i sin(θ)]1B= [cos(kθ) + i sin(kθ)] ∙ [cos(θ) + i sin(θ)]C= cos(kθ)cos(θ) − sin(kθ)sin(θ) + i [sin(kθ)cos(θ) + cos(kθ) sin(θ)]D= cos(kθ + θ) + i sin(kθ + θ)E= cos[(k + 1)θ] + i sin[(k + 1)θ]

Tara deposits $1,000 in a retirement savings account at the beginning of each year. The account pays an interest rate of 5% compounded annually, and the interest is paid on the last day of the year. What is the balance in Tara’s account at the end of the fourth year?

Modern Electronics offers a one-year monthly installment plan for a big screen TV. The payment for the first month is $62, and then it increases by 4% each month for the rest of the year. Which expression can be used to find the total amount paid in the first 12 months?

Mya has a picture that measures 10 inches by 10 inches. She uses a photocopier to reduce the length and width of the picture to 75% their original size. What are the dimensions of the picture after five reductions (reducing to 75% each time)? Round any decimals to the nearest tenth.

Rectangular coordinates and polar coordinates both represent the same complex number z.Which set of equations demonstrates why both sets of coordinates represent the same number?

Which is the equation of an asymptote of the hyperbola whose equation is = 1?

Given vectors u = ⟨–2, 1⟩ and v = ⟨4, –2⟩, which statement is true concerning u and v?

Review the graph.

Review the graph of complex number z.

Which property of multiplication is shown below? If x = 3 + 4i and y = 5 + 6i, x × y = y × x.

Consider z = 3 + 3i. What happens to the modulus and argument when z is raised to the 4th power?

What is ?