91Ó°ÊÓ

In Problems, opposite vertices of a rectangular box whose edges are parallel to the coordinate axes are given. List the coordinates of the other six vertices of the box.

$\left(-1,0,2\right);\left(4,2,5\right)$

Ramp Angle Billy and Timmy are using a ramp to load furniture into a truck. While rolling a 250-pound piano up the ramp, they discover that the truck is too full of other furniture for the piano to fit. Timmy holds the piano in place on the ramp while Billy repositions other items to make room for it in the truck. If the angle of inclination of the ramp is ${20}^{∘},$how many pounds of force must Timmy exert to hold the piano in position?

Find each quantity if v=3i-5j and w=-2i+3j then 2v+3w

In Problems 39–54, the polar coordinates of a point are given. Find the rectangular coordinates of each point.

$(7.5,{110}^{∘})$

Static EquilibriumA weight of $2000$pounds is suspended from two cables, as shown in the figure. What are the tensions in each cable?

Find the six complex sixth roots of unity (1) and plot them.

The letters x and y represent rectangular coordinates. Write each equation using polar coordinates $(r,\mathrm{θ})$.

$x=4$

Force Vectors A child pulls a wagon with a force of 40 pounds. The handle of the wagon makes an angle of ${30}^o$ with the ground. Express the force vector F in terms of i and j.

Force Vectors A man pushes a wheelbarrow up an incline of ${20}^o$with a force of 100 pounds. Express the force vector F in terms of i and j.

Finding the Actual Speed and Direction of an Aircraft A Boeing 747 jumbo jet maintains a constant airspeed of 550 miles per hour (mi/hr) headed due north. The jet stream is 100 mi/hr in the northeasterly direction.

(a) Express the velocity $v_a$of the 747 relative to the air and the velocity $v_w$of the jet stream in terms of i and j.

(b) Find the velocity of the 747 relative to the ground.

(c) Find the actual speed and direction of the 747 relative to the ground.