The radius r, in inches, of a spherical balloon isrelated to the volume, V, by r ( V ) = 3 V 4 π 3 . Air is pumped into the balloon, so the volume after t seconds is given by V ( t ) = 10 + 20 t . a. Find the composite function r ( V ( t ) ) . b.Find the exact time when the radius reaches 10 inches.
The radius r, in inches, of a spherical balloon isrelated to the volume, V, by r ( V ) = 3 V 4 π 3 . Air is pumped into the balloon, so the volume after t seconds is given by V ( t ) = 10 + 20 t . a. Find the composite function r ( V ( t ) ) . b.Find the exact time when the radius reaches 10 inches.
The radius r, in inches, of a spherical balloon isrelated to the volume, V, by
r
(
V
)
=
3
V
4
π
3
. Air is pumped into the balloon, so the volume after t seconds is given by
V
(
t
)
=
10
+
20
t
.
a. Find the composite function
r
(
V
(
t
)
)
.
b.Find the exact time when the radius reaches 10 inches.
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
5. (20%) The linear transformation L: P3 → P2 defined by L(f(x)) = f'(x)+
f(0).
(a) Find the representing matrix A of L with respect to the ordered basis
{x2, x, 1} for P3, and the ordered basis {2,1 - x} for P2.
(b) Find the coordinates of the f(x) = 2x² +2 in P3 with respect to the
ordered basis {x2,-x, 1}, and find the coordinates of L(f(x)) with respect
to the ordered basis {2,1-x}
For the spinner below, assume that the pointer can never lie on a borderline. Find the following probabilities. (enter the probabilities as fractions)
Questions
1. Identify and describe potential bias in the study.
2. Identify and describe the way in which the selected participants may or may not represent the population as a whole.
3. Identify and describe the possible problems with the end results since the majority will be from females rather than an even
split.
4. Identify and describe the possible problems with identifying females as possibly more vulnerable based on the data
collected.
5. Identify a possible null hypothesis and problems in how the study might address this null hypothesis.
6. Identify one possible method of improving the study design and describe how it would improve the validity of the
conclusions.
7. Identify a second possible method of improving the study design and describe how it would improve the validity of the
conclusions.
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Definite Integral Calculus Examples, Integration - Basic Introduction, Practice Problems; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=rCWOdfQ3cwQ;License: Standard YouTube License, CC-BY