Suppose that a and b are pieces of metal which are hinged at C. At first the angle A is ?/4 radians=45o and the angle B is ?/3 radians = 60o. You then widen A to 46o, without changing the sides a and b. Our goal in this problem is to use the tangent line approximation to estimate the angle B.(a) Notice that the angle B is a function of the angle A; i. e. B=f(A). Consequently, it makes sense to calculate the implicit derivative:dB/dA=(?3) / (?2)=(b) CalculatedB/dAwhen A=?/4 and B=?/3; leave your answer in EXACT FORM:(c) Write the linear approximation of f at A= ?/4:(A � ?/4) +(d) Using (c), when A= 46o, B is approximatelydegrees; either answer exactly or to three decimal places.

An airplane consumes fuel at a constant rate while flying through clear skies, and it consumes fuel at a rate of 64 gallons per minute while flying through rain clouds. let c represent the number of minutes the plane can fly through clear skies and r represent the number of minutes the plane can fly through rain clouds without consuming all of its fuel. 56c+64r < 900056c+64r< 9000 according to the inequality, at what rate does the airplane consume fuel while flying through clear skies, and how much fuel does it have before takeoff? the airplane consumes fuel at a rate of gallons per minute while flying through clear skies, and it has gallons of fuel before takeoff. does the airplane have enough fuel to fly for 60 minutes through clear skies and 90 minutes through rain clouds?

Suppose g(x) = f(x + 3) + 4. which statement best compares the graph of g(x) with the graph of f(x)?

21 a stick 7 inches long is broken into two pieces, so that one piece is twice as long as the other one. how long are the two pieces?