Jessica wants to make a ramp using a board so that she can ride her bike onto the front porch. The ramp must reach from the grou
nd to the floor of the porch, which is 2 1/2
ft above the ground. Jessica has decided that the ramp cannot have an incline of more than 35°.
What length board should Jessica buy if she uses the maximum angle of incline?
Enter your answer in the box. Round only your final answer to the nearest tenth.
ft above the ground. Jessica has decided that the ramp cannot have an incline of more than 35°.
What length board should Jessica buy if she uses the maximum angle of incline?
Enter your answer in the box. Round only your final answer to the nearest tenth.
2 answers:
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Explanation
We must the tangent line at x = 3 of the function:
The tangent line is given by:
Where:
• m is the slope of the tangent line of f(x) at x = h,
,• k = f(h) is the value of the function at x = h.
In this case, we have h = 3.
1) First, we compute the derivative of f(x):
2) By evaluating the result of f'(x) at x = h = 3, we get:
3) The value of k is:
4) Replacing the values of m, h and k in the general equation of the tangent line, we get:
Plotting the function f(x) and the tangent line we verify that our result is correct:
AnswerThe equation of the tangent line to f(x) and x = 3 is:
Answer:
y = 0
Step-by-step explanation:
The line y = 0 is cutting your triangle in half with perfect symmetry.
