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Answers by Philip P.

The equation of a line is y = mx + b where m is the slope and b is the y-intercept.  The derivative of f at x=A is the slope of the tangent line: f '(A) = 2.2 = m.  So the equation of the tangent line so far is y = 2.2x + b.  To find b, you need to plug in the x and y-values...

For a trapezoid, AREA = (1/2)(base1 + base2)*height.  Let x = the length of the shorter base (base1): The larger base (base2) is three times as long as the shorter base: base2 = 3x The height is 2 inches linger than the shorter base: height = x + 2 The AREA = 70 in2        ...

Let x = the weight of the peanuts that the biker added to the 11 pounds of raisins.  The weight of the final mixture of raisins and peanuts is 11 + x.   11*($2.30) + x*($4.50) = (11+x)*($3.29)   25.30 + 4.5x = 36.19 + 3.29x   Solve...

Word Problem (answer)

This is an exponential growth:         Output = (Output0)*(1 + r)t   Where: OUTPUT is the output of the factory = 2*OUTPUT0 at t=2 OUTPUT0 is the initial factory output at t = 0 r is the growth rate expressed as a decimal = unknown...

Let's break the problem up into three segments segment 1 is distance traveled while the train is accelerating at 1 m/s2 segment 2 is the distance traveled at constant speed - given as 2100 m segment 3 is the distance traveled while decelerating at 2 m/s2   In segment...

As you point out, d(tan-1t)/dt = 1/(1+t2).  But here, you have tan-1(1/t).  So you need to use the chain rule (not the product rule):         df(u)/dt = df(u)/du * du/dt   Let u = 1/t:   d(tan-1u)/dt = d(tan-1u)/du *...

Question below (answer)

(2/3)*Cost = $18   Multiply both sides of the equation by 3/2:   Cost = $18*(3/2) = _____