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The engine of a sports car rotates at 5,000 revolutions per minute (rpm). Calculate the angular speed of the engine in radians per second.
Use DeMoirvre’s Theorem to find the indicated power of the complex number. Write answer in rectangular form.
The components of v = 240i +300j represent the respective number of gallons of regular and premium gas sold at a gas station.
A pilot in a helicopter sights an ambulance heading toward an accident scene. He measures the angles of depression to the ambulance.
A bicycle tire has a diameter of 20 inches and is revolving at a rate of 10 rpm. At t =0, a certain point is at height 0.
A plane sets a course to fly with a ground speed of 200 km/h due east while climbing at an angle of 14 degrees.
Draw a square on each of the sides of the triangles. Compute the areas of the squares and use this information to investigate.
The line l1 passes through O and through the midpoint of the face ABFE. The line l2 passes through A and through the midpoint of the edge FG.
In the triangle with sides a= 21 cm, b=45cm, and c = 60 cm, where the angle gamma is between the sides a and b.
Use trigonometry to find the height of Building B and the distance between the two buildings. Round your answers to the nearest metre.
A function f:reals->reals is said to be periodic on the reals if there exists a number p greater than zero such that f(x+p)=f(x) for all x in the reals.
Let (x, sin x) be a point on the graph of g near (0,0), and write a formula for the slope of the secant line joining (x, sin x) and (0,0).
If p>3, show that p divides the sum of its quadratic residues that are also least residues.
Find the angle that you would have to shoot it at (assuming the same Vi) in order to hit me between the eyes.
The Pythagorean Theorem can also be proved directly, by choosing 0 at the right angle of a right-angled triangle whose other two vertices are u and v.
The sides of a square are lengthened by 6 cm, the area become 121 cm^2. Find the length of a side of the original square.
An airplane flies 180 kilometers from an airport in a direction of 260 degrees. How far west of the airport is the airplane? How far south?
Assume that the terminal side of an angle of t radians passes through the point (.9, -.4) . Find sin (t), cos (t), tan (t).
Simplify the given expression. Compute the exact answer as a fraction, it should not contain sin, cos, or tan.
Two stations are 190 miles apart, station A directly south of station B. Both spot a fire. The bearing of the fire from station A.
An airplane flies over an observer with a velocity of 400 mph and at an altitude of 2640 ft.
If in a triangle the square on one of the sides be equal to the squares on the remaining two sides of the triangle.
The number of hours of daylight in city A is given by the following equation, where x is the number of days after January 1.
How far Michelle is from the buoy, how high was the rescue team and how long was the rope that they had to throw to Sean?
Find the value of each of the following under the given conditions: tan alpha = -4/3, alpha lies in quadrant 2; cos beta = 5/6, beta lies in quadrant 1