A parabolic arch sculpture is on top of a city bank. A model of the arch is y = −0.005x^2 + 0.3x where x and y are in feet. The image is of a rectangle which represents the building of a Bank and its height is 30 feet. On top of it a semi circle is placed whose diameter is equal to the width of the rectangle. a. What is the distance from the highest point of the arch to the ground? b. What is the width of the bank?

You need to figure out at which x-value does the graph has a tangent line slope of -1.remember, the derivative is the slope of the tangent line. so find the derivative function and set it to equal -1 to find the x-value that will have a tangent line slope of 0.differentiate with the chain rule.    set the derivative to equal -1 and solve for x.      take log base 10 of both sides. also recall that  .    so the x-coord of the point of tangency is .the y-coordinate of this point of tangency can be calculated using the original function:     using point-slope form, the equation of the tangent line is      the x-intercept of this tangent line is when the graph is at y=0.    this rounds off to  .choice c.

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answer:

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explanation: