Solve the problem.An object is propelled upward at an angle ?, 45° < ? < 90°, to the horizontal with an initial velocity of v0 feet per second from the base of a plane that makes an angle of 45° with the horizontal. If air resistance is ignored, the distance R that it travels up the inclined plane is given by the function R(?) = [sin(2?) - cos(2?) - 1]. Show that R(?) = [sin ?(cos ? + sin ?) - 1]. 

What will be an ideal response?


R(?) = [sin(2?) - cos(2?) - 1] = [2 sin? cos ? - (1 - 2 sin2 ?) - 1]  =  ? 2 [sin? (cos ? + sin ?) - 1)] 

Mathematics

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A. - 
B. ?
C.
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Let C be a smooth curve defined by r(t) = 2i+3tj+2tk, and let T(t) and N(t) be the unit tangent vector and unit normal vector to C corresponding to t. The plane determined by T and N is called the osculating plane. Find an equation of the osculating plane of the curve described by r(t) at t = 1.

a. z=2 b. y=3 c. 2x+3y+2z=1 d. x=2

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Provide an appropriate response.Find the area of the circle whose diameter is 28.5 feet to the nearest hundredth.

A. 203.06 ft2 B. 637.94 ft2 C. 89.54 ft2 D. 2,551.76 ft2

Mathematics

Write the answer to the problem as an algebraic expression.Susan has 7 cats. She gave s to her lonely aunt. How many does she have left?

A. 7 - s cats B. s + 7 cats C. s - 7 cats D. 7 + s cats

Mathematics