Kevin drove for 4 hours and then stopped to eat dinner. The total distance he had driven at different time intervals is shown on
the graph below.⬇️
• Using the information in the graph, determine Kevin’s average speed during these 4 hours.
• Kevin will drive for an additional 2 hours after dinner. He expects to drive 130 miles during these 2 hours, under the same driving conditions as the trip represented in the graph. Is this a reasonable expectation? Explain your answer and show your work.
• Using the information in the graph, determine Kevin’s average speed during these 4 hours.
• Kevin will drive for an additional 2 hours after dinner. He expects to drive 130 miles during these 2 hours, under the same driving conditions as the trip represented in the graph. Is this a reasonable expectation? Explain your answer and show your work.
1 answer:
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a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have
Evaluate the integral to solve for y :
Use the other known value, f(2) = 18, to solve for k :
Then the curve C has equation
b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:
The slope of the given tangent line is 1. Solve for a :
so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).
Decide which of these points is correct:
So, the point of contact between the tangent line and C is (-1, -3).
Answer:
see the attachment
Step-by-step explanation:
1. Two angles that sum to 90° are <em>complementary</em>, whether they are adjacent or not. Angles LMN and NMP are also <em>adjacent</em>.
2. Vertical angles created by two distinct lines are <em>never adjacent</em>. The sides of the angles are created by the same lines, and the angles share a vertex, but there is no ray that is a side common to both angles.
3. Angle GMK is supplementary to angle JMG.
4. Vertical angles are congruent. See question 2.
5. See question 1.
