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
.
An open-top rectangular box is being constructed to hold a volume of 150 in³. The base of the box is made
from a material costing 7 cents/in². The front of the box must be decorated, and will cost 11 cents/in².
The remainder of the sides will cost 3 cents/in².
Find the dimensions that will minimize the cost of constructing this box. Please show your answers to at
least 4 decimal places.
Front width:
Depth:
in.
in.
Height:
in.
Find and classify the critical points of z = (x² – 8x) (y² – 6y).
Local maximums:
Local minimums:
Saddle points:
-
For each classification, enter a list of ordered pairs (x, y) where the max/min/saddle occurs. Enter DNE if
there are no points for a classification.
Suppose that f(x, y, z) = (x − 2)² + (y – 2)² + (z − 2)² with 0 < x, y, z and x+y+z≤ 10.
1. The critical point of f(x, y, z) is at (a, b, c). Then
a =
b =
C =
2. Absolute minimum of f(x, y, z) is
and the absolute maximum is
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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