In Exercises 15-42, translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if, applicable, compare the argument’s symbolic form to a standard valid or invalid form. (You can ignore difference in past, present, and future tense.) If I watch Schindler’s List and milk, I am aware of the destructive nature of intolerance. Today I did not watch S c i n d l e r ' s L i s t or I did not watch M i l k . ∴ Today I ma not aware of the destructive nature of intolerance .
In Exercises 15-42, translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if, applicable, compare the argument’s symbolic form to a standard valid or invalid form. (You can ignore difference in past, present, and future tense.) If I watch Schindler’s List and milk, I am aware of the destructive nature of intolerance. Today I did not watch S c i n d l e r ' s L i s t or I did not watch M i l k . ∴ Today I ma not aware of the destructive nature of intolerance .
Solution Summary: The author explains that each argument into symbolic form and determine whether it is valid or invalid.
In Exercises 15-42, translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if, applicable, compare the argument’s symbolic form to a standard valid or invalid form. (You can ignore difference in past, present, and future tense.)
If I watch Schindler’s List and milk, I am aware of the destructive nature of intolerance.
Today
I did
not
watch
S
c
i
n
d
l
e
r
'
s
L
i
s
t
or
I
did
not
watch
M
i
l
k
.
∴
Today
I
ma
not
aware
of
the
destructive
nature
of
intolerance
.
Now consider equations of the form ×-a=v
= √bx + c, where a, b, and c
are all positive integers and b>1.
(f) Create an equation of this form that has 7 as a solution and
an extraneous solution. Give the extraneous solution.
(g)
What must be true about the value of bx + c to ensure that
there is a real number solution to the equation? Explain.
The equation ×+ 2 = √3x+10 is of the form ×+ a = √bx + c, where a, b, and
c are all positive integers and b > 1. Using this equation as a
model, create your own equation that has extraneous solutions.
(d) Using trial and error with numbers for a, b, and c, create an
equation of the form x + a = √bx + c, where a, b, and c are all
positive integers and b>1 such that 7 is a solution and there
is an extraneous solution. (Hint: Substitute 7 for x, and
choose a value for a. Then square both sides so you can
choose a, b, and c that will make the equation true.)
(e) Solve the equation you created in Part 2a.
A basketball player made 12 out of 15 free throws she attempted.
She wants to know how many consecutive free throws she
would have to make to raise the percent of successful free
throws to 85%.
(a) Write an equation to represent this situation.
(b) Solve the equation. How many consecutive free throws
would she have to make to raise her percent to 85%?
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