A stunt man drives a car at a speed of 25 m/sec off a 10 -m cliff. The road leading to the edge of the cliff is inclined upward at an angle of 16 ° . Choose a coordinate system with the origin at the base of the cliff directly under the point where the car leaves the edge. a. Write parametric equations defining the path of the car. b. How long is the car in the air? Round to the nearest tenth of a second. c. How far from the base of the cliff will the car land? Round to the nearest foot.
A stunt man drives a car at a speed of 25 m/sec off a 10 -m cliff. The road leading to the edge of the cliff is inclined upward at an angle of 16 ° . Choose a coordinate system with the origin at the base of the cliff directly under the point where the car leaves the edge. a. Write parametric equations defining the path of the car. b. How long is the car in the air? Round to the nearest tenth of a second. c. How far from the base of the cliff will the car land? Round to the nearest foot.
Solution Summary: The author calculates the parametric equation that represents the path of the car if it cliff off with an initial speed of 25m/sec.
A stunt man drives a car at a speed of
25
m/sec
off a
10
-m
cliff. The road leading to the edge of the cliff is inclined upward at an angle of
16
°
. Choose a coordinate system with the origin at the base of the cliff directly under the point where the car leaves the edge.
a. Write parametric equations defining the path of the car.
b. How long is the car in the air? Round to the nearest tenth of a second.
c. How far from the base of the cliff will the car land? Round to the nearest foot.
Formula Formula A polynomial with degree 2 is called a quadratic polynomial. A quadratic equation can be simplified to the standard form: ax² + bx + c = 0 Where, a ≠ 0. A, b, c are coefficients. c is also called "constant". 'x' is the unknown quantity
Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties
to find lim→-4
1
[2h (x) — h(x) + 7 f(x)] :
-
h(x)+7f(x)
3
O DNE
17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t).
(a) How much of the slope field can
you sketch from this information?
[Hint: Note that the differential
equation depends only on t.]
(b) What can you say about the solu-
tion with y(0) = 2? (For example,
can you sketch the graph of this so-
lution?)
y(0) = 1
y
AN
(b) Find the (instantaneous) rate of change of y at x = 5.
In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of
change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the
following limit.
lim
h→0
-
f(x + h) − f(x)
h
The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule
defining f.
f(x + h) = (x + h)² - 5(x+ h)
=
2xh+h2_
x² + 2xh + h² 5✔
-
5
)x - 5h
Step 4
-
The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x).
-
f(x + h) f(x) =
= (x²
x² + 2xh + h² -
])-
=
2x
+ h² - 5h
])x-5h) - (x² - 5x)
=
]) (2x + h - 5)
Macbook Pro
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.
RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY