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).
8. For x>_1, the continuous function g is decreasing and positive. A portion of the graph of g is shown above. For n>_1, the nth term of the series summation from n=1 to infinity a_n is defined by a_n=g(n). If intergral 1 to infinity g(x)dx converges to 8, which of the following could be true? A) summation n=1 to infinity a_n = 6. B) summation n=1 to infinity a_n =8. C) summation n=1 to infinity a_n = 10. D) summation n=1 to infinity a_n diverges.
PLEASE SHOW ME THE RIGHT ANSWER/SOLUTION
SHOW ME ALL THE NEDDED STEP
13: If the perimeter of a square is shrinking at a rate of 8 inches per second, find the rate at which its area is changing when its area is 25 square inches.
DO NOT GIVE THE WRONG ANSWER
SHOW ME ALL THE NEEDED STEPS
11: A rectangle has a base that is growing at a rate of 3 inches per second and a height that is shrinking at a rate of one inch per second. When the base is 12 inches and the height is 5 inches, at what rate is the area of the rectangle changing?
Chapter A Solutions
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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