In the triangle pictured, let A, B, C be the angles at the three vertices, and let a,b,c be the sides opposite those angles. C a A B C According to the law of sines," you always have: b_sinB a sinA Suppose that a and b are pieces of metal which are hinged at C. At first the angle A is */4 radians=45° and the angle B is x/3 radians = 60°. You then widen A to 46°, 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: dA cos(A) cos(B) (b) Calculate when A=x/4 and B=л/3; leave your answer in EXACT FORM: √√3 dB dA (c) Write the linear approximation of fat A= x/4: (A - π/4) + A right circular cone of height h and base radius r has total surface area S consisting of its base area plus its side area, leading to the formula: S=πr² + √√²+h2 Suppose you start out with a cone of height 8 cm and base radius 6 cm, and you want to change the dimensions in such a way that the total surface area remains the same. Suppose you increase the height by 5/100. In this problem, use tangent line approximation to estimate the new value of r so that the new cone has the same total surface area. The estimated value of r =

Find the unknown value. 27. y varies jointly with x and the cube root of 2. If when x=2 and z=27,y=12, find y if x=5 and z=8.

The approximate distance d (in feet) that travel after noticing that they must come to a sudden stop is given by the following formula, where x is the speed of the car (in mi/h): d=x+x220 If a car travels 75 ft. before slopping, what was its speed before the brakes were applied?