<h3>Given</h3>
Two positive numbers x and y such that xy = 192
<h3>Find</h3>
The values that minimize x + 3y
<h3>Solution</h3>
y = 192/x . . . . . solve for y
f(x) = x + 3y
f(x) = x + 3(192/x) . . . . . the function we want to minimize
We can find the x that minimizes of f(x) by setting the derivative of f(x) to zero.
... f'(x) = 1 - 576/x² = 0
... 576 = x² . . . . . . . . . . . . multiply by x², add 576
... √576 = x = 24 . . . . . . . take the square root
... y = 192/24 = 8 . . . . . . . find the value of y using the above equation for y
The first number is 24.
The second number is 8.
Step-by-step explanation:
hope you get idea of graphing the four lines
Answer:
y
=
3
2
x
+
1
Explanation:
To find the slope
(
m
)
of the straight line that passes through two points
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
apply:
(
y
1
−
y
2
)
=
m
(
x
1
−
x
2
)
In this example our two points are
(
0
,
1
)
and
(
2
,
4
)
Hence:
(
1
−
4
)
=
m
(
0
−
2
)
−
3
=
−
2
m
→
m
=
3
2
The equation of a straight line in slope
(
m
)
and intercept
(
c
)
form is:
y
=
m
x
+
c
In this example:
y
=
3
2
x
+
c
Since the point
(
0
,
1
)
is on this line
→
1
=
0
+
c
Hence,
c
=
1
∴
y
=
3
2
x
+
1
is our required straight line.
Step-by-step explanation:
we can turn any decimal number to a fraction by <u>using as many zeros at the bottom as there are decimals and losing the dot atop</u>, so let's see, we have 3 decimals in this case, so we'll use 3 zeros at the bottom.
recall that to turn an improper fraction to mixed, we divide numerator by denominator, and the quotient is the number alone and the numerator is the remainder of the division.
