Check Point 5 An archer’s arrow follows a parabolic path. The height of the arrow, f(x), in feet, can be modeled by f ( x ) = − 0.005 x 2 + 2 x + 5 , where x is the arrow’s horizontal distance, in feet. a. What is the maximum height of the arrow and how far from its release does this occur? b. Find the horizontal distance the arrow travels before it hits the ground. Round to the nearest foot. c. Graph the function that models the arrow’s parabolic path.
Check Point 5 An archer’s arrow follows a parabolic path. The height of the arrow, f(x), in feet, can be modeled by f ( x ) = − 0.005 x 2 + 2 x + 5 , where x is the arrow’s horizontal distance, in feet. a. What is the maximum height of the arrow and how far from its release does this occur? b. Find the horizontal distance the arrow travels before it hits the ground. Round to the nearest foot. c. Graph the function that models the arrow’s parabolic path.
Solution Summary: The author calculates the maximum height of the arrow and distance from its release using a quadratic function.
Use the information to find and compare Δy and dy. (Round your answers to four decimal places.)
y = x4 + 7 x = −3 Δx = dx = 0.01
Δy =
dy =
4. A car travels in a straight line for one hour. Its velocity, v, in miles per hour at six minute intervals is shown
in the table. For each problem, approximate the distance the car traveled (in miles) using the given method,
on the provided interval, and with the given number of rectangles or trapezoids, n.
Time (min) 0 6 12 18|24|30|36|42|48|54|60
Speed (mph) 0 10 20 40 60 50 40 30 40 40 65
a.) Left Rectangles, [0, 30] n=5
b.) Right Rectangles, [24, 42] n=3
c.) Midpoint Rectangles, [24, 60] n=3
d.) Trapezoids, [0, 24] n=4
The bracket BCD is hinged at C and attached to a control cable at B. Let F₁ = 275 N and F2 = 275 N.
F1
B
a=0.18 m
C
A
0.4 m
-0.4 m-
0.24 m
Determine the reaction at C.
The reaction at C
N Z
F2
D
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY