Given a circle with radius r , diameter d , circumference C , and area A . a . Write C as a function of r . b . Write A as a function of r . c . Write r as a function of d . d . Write d as a function of r . e . Write C as a function of d . f . Write A as a function of d . g . Write A as a function of C . h . Write C as a function of A .
Given a circle with radius r , diameter d , circumference C , and area A . a . Write C as a function of r . b . Write A as a function of r . c . Write r as a function of d . d . Write d as a function of r . e . Write C as a function of d . f . Write A as a function of d . g . Write A as a function of C . h . Write C as a function of A .
Solution Summary: The author explains that the required relationship is C(r)=2pi r.
Given a circle with radius r, diameter d, circumference C, and area A.
a
. Write
C
as a function of
r
.
b
. Write
A
as a function of
r
.
c
. Write
r
as a function of
d
.
d
. Write
d
as a function of
r
.
e
. Write
C
as a function of
d
.
f
. Write
A
as a function of
d
.
g
. Write
A
as a function of
C
.
h
. Write
C
as a function of
A
.
A ladder 27 feet long leans against a wall and the foot of the ladder is sliding away at a constant rate of 3 feet/sec. Meanwhile, a firefighter is climbing up the ladder at a rate of 2 feet/sec. When the firefighter has climbed up 6 feet of the ladder, the ladder makes an angle of л/3 with the ground. Answer the two related
rates questions below. (Hint: Use two carefully labeled similar right triangles.)
(a) If h is the height of the firefighter above the ground, at the instant the angle of the ladder with the ground is л/3, find dh/dt=
feet/sec.
(b) If w is the horizontal distance from the firefighter to the wall, at the instant the angle of the ladder with the ground is л/3, find dw/dt=
feet/sec.
Two cars start moving from the same point. One travels south at 60 mi/h and the other travels west at 25 mi/h. At what rate (in mi/h) is the distance between the cars increasing four hours later?
Step 1
Using the diagram of a right triangle given below, the relation between x, y, and z is
z²
= x²+
+12
x
Step 2
We must find dz/dt. Differentiating both sides and simplifying gives us the following.
2z
dz
dt
dx
2x.
+2y
dt
dx
dy
dz
x
+y
dt
dt
dt
2z
dy
dt
×
dx
(x+y
dt
dy
dt
An elastic rope is attached to the ground at the positions shown in the picture. The rope is being pulled up along the dotted line. Assume the units are meters.
9
ground level
Assume that x is increasing at a rate of 3 meters/sec.
(a) Write as a function of x: 0=
(b) When x=10, the angle is changing at a rate of
rad/sec.
(c) Let L be the the left hand piece of rope and R the right hand piece of rope. When x=10, is the rate of change of L larger than the rate of change of R?
○ Yes
○ No
Intro Stats, Books a la Carte Edition (5th Edition)
Knowledge Booster
Learn more about
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