Carefully read through the list of terminology we’ve used in Unit 4. Consider circling the terms you aren’t familiar with and looking them up. Then test your understanding by using the list to fill in the appropriate blank in each sentence. d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 x = − b ± b 2 − 4 a c 2 a x = − b 2 a arbitrary binomial coefficient conjecture counterexample deductive reasoning equivalent expanded form exponential decay exponential function exponential growth f(x) factored form factoring factors function growth factor hypotenuse inductive reasoning inverse variation isosceles margin of error parabola parameters perfect squares polynomial prime polynomial profit quadratic function revenue right triangle standard form symmetry terms trinomial vertex zero Each of 49, 25, and 144 are called _______________ because each is the square of a whole number.
Carefully read through the list of terminology we’ve used in Unit 4. Consider circling the terms you aren’t familiar with and looking them up. Then test your understanding by using the list to fill in the appropriate blank in each sentence. d = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 x = − b ± b 2 − 4 a c 2 a x = − b 2 a arbitrary binomial coefficient conjecture counterexample deductive reasoning equivalent expanded form exponential decay exponential function exponential growth f(x) factored form factoring factors function growth factor hypotenuse inductive reasoning inverse variation isosceles margin of error parabola parameters perfect squares polynomial prime polynomial profit quadratic function revenue right triangle standard form symmetry terms trinomial vertex zero Each of 49, 25, and 144 are called _______________ because each is the square of a whole number.
Solution Summary: The author explains that 49, 25 and 144 are called perfect squares because each is the square of a whole number.
Carefully read through the list of terminology we’ve used in Unit 4. Consider circling the terms you aren’t familiar with and looking them up. Then test your understanding by using the list to fill in the appropriate blank in each sentence.
d
=
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
x
=
−
b
±
b
2
−
4
a
c
2
a
x
=
−
b
2
a
arbitrary
binomial
coefficient
conjecture
counterexample
deductive reasoning
equivalent
expanded form
exponential decay
exponential function
exponential growth
f(x)
factored form
factoring
factors
function
growth factor
hypotenuse
inductive reasoning
inverse variation
isosceles
margin of error
parabola
parameters
perfect squares
polynomial
prime polynomial
profit
quadratic function
revenue
right triangle
standard form
symmetry
terms
trinomial
vertex
zero
Each of 49, 25, and 144 are called _______________ because each is the square of a whole number.
1.
Prove the following arguments using the rules of inference. Do not make use of
conditional proof.
(а) а → (ЪЛс)
¬C
..¬a
(b) (pVq) →
→r
יור
(c) (c^h) → j
¬j
h
(d) s→ d
t
d
-d
..8A-t
(e) (pVg) (rv¬s)
Лѕ
קר .'
The graph of f(x) is given below. Select each true statement about the continuity of f(x) at x = 1.
Select all that apply:
☐ f(x) is not continuous at x = 1 because it is not defined at x = 1.
☐ f(x) is not continuous at x = 1 because lim f(x) does not exist.
x+1
☐ f(x) is not continuous at x = 1 because lim f(x) ‡ f(1).
x+→1
☐ f(x) is continuous at x = 1.
2. Consider the following argument:
(a)
Seabiscuit is a thoroughbred.
Seabiscuit is very fast.
Every very fast racehorse can win the race.
.. Therefore, some thoroughbred racehorse can win the race.
Let us define the following predicates, whose domain is racehorses:
T(x) x is a thoroughbred
F(x) x is very fast
R(x) x can win the race
:
Write the above argument in logical symbols using these predicates.
(b)
Prove the argument using the rules of inference. Do not make use of conditional
proof.
(c)
Rewrite the proof using full sentences, avoiding logical symbols. It does not
need to mention the names of rules of inference, but a fellow CSE 16 student should be
able to understand the logical reasoning.
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