At what point on the curve x=t³, y=9t, z= is the normal plane parallel to the plane 3x+9y-4z=4?


Mathematics

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Find the area of the specified region.Shared by the circle r = 6 and the cardioid r = 6(1 + sin ?)

A. 0 B. 9(5? - 8) C. 9(5? + 8) D. 36

Mathematics

Find the perimeter of the polygon.

A. 80 m B. 91 m C. 108 m D. 95 m

Mathematics

Solve the problem.The work W (in joules) done by a force F (in newtons) moving an object through a distance x (in meters) is given by  Find a formula for W, if  and k is a constant.

A. W =  + C
B. W = kx2 + C
C. W = k + C
D. W =  + C

Mathematics

Solve the problem.A company packages its powdered iced tea mix in containers in the shape of a cylinder. The top and bottom are made of a plastic product that costs 5 cents per square centimeter. The side of the container is made of a cheaper material that costs 1 cent per square centimeter. The height of the cylinder can be found by dividing its volume by the area of its base. (i) If x is the radius of the base (in centimeters), write a rational expression in x whose values give the cost of each container, assuming that the capacity of the container is 70 cubic centimeters.(ii) Find the cost of a container whose base is 8 centimeters in diameter, using 3.14 as an approximation of ?. Round to the nearest cent, if necessary.

A. (i) ;
(ii) $0.74
B. (i) ;
(ii) $2.31
C. (i) ;
(ii) $74.25
D. (i) ;
(ii) $231.25

Mathematics