Answer:
Derived from the Pythagorean Theorem, the distance formula is used to find the distance between two points in the plane. The Pythagorean Theorem,
a
2
+
b
2
=
c
2
, is based on a right triangle where a and b are the lengths of the legs adjacent to the right angle, and c is the length of the hypotenuse. The relationship of sides
|
x
2
−
x
1
|
and
|
y
2
−
y
1
|
to side d is the same as that of sides a and b to side c. We use the absolute value symbol to indicate that the length is a positive number because the absolute value of any number is positive. (For example,
|
−
3
|
=
3
. ) The symbols
|
x
2
−
x
1
|
and
|
y
2
−
y
1
|
indicate that the lengths of the sides of the triangle are positive. To find the length c, take the square root of both sides of the Pythagorean Theorem.
c
2
=
a
2
+
b
2
→
c
=
√
a
2
+
b
2
It follows that the distance formula is given as
d
2
=
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
→
d
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
We do not have to use the absolute value symbols in this definition because any number squared is positive.
A GENERAL NOTE: THE DISTANCE FORMULA
Given endpoints
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
, the distance between two points is given by
d
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
Step-by-step explanation:
Answer: 7/3 or 2.3333333(repeating forever)
Step-by-step explanation: 7/3 is an improper fraction, and 2.333333 is a decimal
The original price of the pants were 48 dollars
Answer:
The domain that makes sense for this function is all values greater than or equal to 0.
Step-by-step explanation:
A ball is thrown into the air from a height of 4 feet at time <em>t</em> = 0. It is modeled by the function:
The domain of the function is time <em>t</em>. The range of the function is the ball's height in the air <em>h</em>.
Since time is our domain, we must restrict our domain to values equal to or greater than 0 since time cannot be negative.
Therefore, the domain that makes sense for this function is all values greater than or equal to 0.
In interval notation, this is:
And as an inequality:
Volume= length* width* height
V=11*6*5
V=330 inches
