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

A force of 1181 pounds is acting on an object at an angle of 39 degrees from the horizontal. Another force of 507 pounds is acting at an angle -49 degrees from the horizontal. What is the magnitude of the resultant force? Round to the nearest pound.

A baseball player throws a ball with an initial velocity of 66 feet per second at an angle 43 degrees with the horizontal. What are the vertical and horizontal components of the velocity? Round to one decimal place.

A car that weighs 11000 lbs is parked on a hill in San Francisco with a slant of 28° from the horizontal. How much force will keep it from rolling down the hill? Round to the nearest integer.

A ship's caption sets a course due south at 11 mph. The water is moving at 7 mph due east. What is the actual velocity of the ship, and in what direction is it traveling?

A semi trailer truck that weighs 40000 lbs. is parked on a hill in San Francisco with a slant of 27° from the horizontal. A tow truck has to remove the truck from its parking spot and move it 75 feet up the hill. How much work is required? Round to the nearest integer.

Express the complex number in rectangular form. -12(cos 210° + i sin 210°)

The lemniscate motion occurs naturally in the flapping of birds' wings. The bird's vertical lift and wing sweep create the distinctive figure-eight pattern. The patterns vary with the different wing profiles. Compare the two possbile lemniscate patterns by graphing them on the same polar graph: r² = cos 2 $\theta$ and r² = cos (2 $\theta$ + 2).

Plot the point in a polar coordinate system.

Graph the complex number in the complex plane. -4i

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

Graph the equation.

Express the complex number in rectangular form.

A baseball player throws a ball with an initial velocity of 102 feet per second at an angle 56 degrees with the horizontal. What are the vertical and horizontal components of the velocity? Round to one decimal place.

Convert the point to exact rectangular coordinates.

Perform the indicated vector operation given u = < 23, -20 > and v = < -5, 21 >. 5 u - 8 v

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

Determine if the vectors are orthogonal. < -20, -2 > and < -3, 40 >

Express the complex number in polar form.

Force A, at 170 pounds, and force B, at 605 pounds, make an angle of 115° with each other. Represent their respective vectors as complex numbers written in trigonometric form and solve for the resultant angle to one decimal place.

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