Exam 7: Vectors, the Complex Plane, and Polar Coordinates

A force of 890 pounds is needed to pull a speedboat and its trailer up a ramp that has an incline of 13.0°. What is the weight of the boat and its trailer? Round to the nearest pound.

Convert the point to exact polar coordinates. Assume 0 $\le$ $\theta$ $\le$ 2 $\pi$ .

Express the complex number in polar form.

A force of 582 pounds is needed to pull a speedboat and its trailer up a ramp that has an incline of 8.5°. What is the weight of the boat and its trailer? Round to the nearest pound.

Find the dot product. < 20.8, -4.9 > · < 4.9, -9 >

Convert the point to exact polar coordinates. Assume 0 $\le$ $\theta$ $\le$ 2 $\pi$ .

Find the result of the expression using De Moivre's theorem. Write the answer in rectangular form.

Many microphones advertise that their exceptional pickup capabilities hat isolate the sound source and minimize background noise. The name of these microphones comes from the pattern formed by the range of the pickup. Graph the cardioid curve to see what the range looks like.

Find the dot product.

Perform the indicated vector operation given u = < 1, -11 > and v = < -9, -2 >.

Perform the indicated vector operation given u = < 9, -3 > and v = < 14, 0 >.

Find all complex solutions to the equation.Write answers in rectangular form.

A force with a magnitude of 1332 pounds and another with a magnitude of 276 pounds are acting on an object. The two forces have an angle of 75 degrees between them. What is the direction of the resultant force with respect to the force with a magnitude of 1332 pounds? Round to one decimal place.

Find all complex solutions to the equation.Write answers in rectangular form.

Find the product, z₁z₂ in rectangular form. and

Find all nth roots of z. Write answers in polar form and plot roots in complex plane.

Find a unit vector in the direction of the vector v. v = <5, -12>

Find all nth roots of z. Write answers in polar form and plot roots in complex plane.

Use a calculator to express the complex number in polar form. Round angle to one decimal place and in degrees.

Find the difference quotient of the vector-valued function.