Suppose that m and n are positive integer with m > n . If a = m 2 − n 2 , b = 2 m n and c = m 2 + n 2 . Show that a , b , and c are the lengths of the sides of a right triangle. (This formula can be used to find the sides of a right triangle that are integers, such as 3 , 4 , 5 : 5 , 12 , 13 : and so on. Such triplets of integers are called Pythagoras triples).
Suppose that m and n are positive integer with m > n . If a = m 2 − n 2 , b = 2 m n and c = m 2 + n 2 . Show that a , b , and c are the lengths of the sides of a right triangle. (This formula can be used to find the sides of a right triangle that are integers, such as 3 , 4 , 5 : 5 , 12 , 13 : and so on. Such triplets of integers are called Pythagoras triples).
Solution Summary: The author proves that a, b, and c are the lengths of the sides of an right triangle. They can substitute the values directly into the formula.
Suppose that m and n are positive integer with
m
>
n
. If
a
=
m
2
−
n
2
,
b
=
2
m
n
and
c
=
m
2
+
n
2
. Show that a, b, and c are the lengths of the sides of a right triangle. (This formula can be used to find the sides of a right triangle that are integers, such as
3
,
4
,
5
:
5
,
12
,
13
:
and so on. Such triplets of integers are called Pythagoras triples).
How would i solve this. More info is that b =1 but it might be better to solve this before making the substitution
Let m(t) be a continuous function with a domain of all real numbers. The table below shows some of the values of m(t) .
Assume the characteristics of this function are represented in the table.
t
-3 -2 8 11
12
m(t) -7 6
3
-9
0
(a) The point (-3, -7) is on the graph of m(t). Find the corresponding point on the graph of the transformation y = -m(t) + 17.
(b) The point (8, 3) is on the graph of m(t). Find the corresponding point on the graph of the transformation y =
-m (−t) .
24
(c) Find f(12), if we know that f(t) = |m (t − 1)|
f(12) =
Suppose the number of people who register to attend the Tucson Festival of Books can be modeled by P(t) = k(1.1),
where t is the number of days since the registration window opened. Assume k is a positive constant.
Which of the following represents how long it will take in days for the number of people who register to double?
t =
In(1.1)
In(2)
In(2)
t =
In(1.1)
In(1.1)
t =
t =
t =
In(2) - In(k)
In(2)
In(k) + In(1.1)
In(2) - In(k)
In(1.1)
Chapter A Solutions
Pearson eText for Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry -- Instant Access (Pearson+)
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