The average speed of a certain particle in meters per second is given by the equation...

       

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The average speed of a certain particle in meters per second is given by the equation S(t) = 2 +81 +5 1+3 Find the average rate of change as time changes from 0 seconds to 3 seconds. Explain the meaning of this rate of change. 10) Complete the chart for the following trigonometric functions. Equation y=-2 sin 2(0)+1 Amplitude Period Phase Shift Vertical Shift Axis of the curve Range y = cos(20+) 4 [7 A] 15) Prove the following identity sin (a - b) sina sinb cot(a)-cot(b) = 16) Solve for x, correct to 3 decimal places where necessary. a) 9* =81(27") c) log x= 2log 3+3 log 2 d) log(x+1)=2 [4 C] 17) Distance in km above sea level is given by the formula d = 500[log(P)-1.5] 27 where P is the atmospheric pressure in kilopascals, kPa. Find the atmospheric pressure at the top of a mountain 6.0 km above sea level. Round your answer to one decimal place. 18) Given f(x)=x and g(x)=cos(x): a) Identify the domain of y=f(x) g(x). b) Identify the domain of y f(x) g(x) c) Identify which of y=f(x), y-g(x), y=f(x)-g(x), are even functions and which are odd functions. 19) Explain why cross-multiplication is NOT the right method to use in solving the following inequality x-2 3 x+5 5 20) For x > 0, what values of x gives the least sum of x and its reciprocal? The average speed of a certain particle in meters per second is given by the equation S(t) = 2 +81 +5 1+3 Find the average rate of change as time changes from 0 seconds to 3 seconds. Explain the meaning of this rate of change. 10) Complete the chart for the following trigonometric functions. Equation y=-2 sin 2(0)+1 Amplitude Period Phase Shift Vertical Shift Axis of the curve Range y = cos(20+) 4 [7 A] 15) Prove the following identity sin (a - b) sina sinb cot(a)-cot(b) = 16) Solve for x, correct to 3 decimal places where necessary. a) 9* =81(27") c) log x= 2log 3+3 log 2 d) log(x+1)=2 [4 C] 17) Distance in km above sea level is given by the formula d = 500[log(P)-1.5] 27 where P is the atmospheric pressure in kilopascals, kPa. Find the atmospheric pressure at the top of a mountain 6.0 km above sea level. Round your answer to one decimal place. 18) Given f(x)=x and g(x)=cos(x): a) Identify the domain of y=f(x) g(x). b) Identify the domain of y f(x) g(x) c) Identify which of y=f(x), y-g(x), y=f(x)-g(x), are even functions and which are odd functions. 19) Explain why cross-multiplication is NOT the right method to use in solving the following inequality x-2 3 x+5 5 20) For x > 0, what values of x gives the least sum of x and its reciprocal?