Solve ln 3 + ln (4x) = 4 round your answer to the nearest hundredth
2 answers:
Answer:
x = 4.55.
Step-by-step explanation:
Given : ln 3 + ln (4x) = 4.
To find : Solve round your answer to the nearest hundredth.
Solution : We have given that
ln 3 + ln (4x) = 4.
By the logarithm rule : ln a + ln b = ln (ab).
Then,
ln 3 + ln (4x) = ln (3 * 4x )
ln 3 + ln (4x) = ln (12 x )
Then ,
ln (12 x ) = 4
Taking exponential both side
12x = .
12 x = 54.59.
12 x = 54 .59
On dividing by 12 both sides
x = 4.55.
Therefore, x = 4.55.
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Answer: (A)
(B) Length varies between 1 and 150
(C) Largest area is 22500ft²
Step-by-step explanation: Suppose length is l and width is w.
The rectangular garden has perimeter of 600ft, which is mathematically represented as
Area of a rectangle is calculated as
Now, we have a system of equations:
Isolate w, so we have l:
w = 300 - l
Substitute in the area equation:
A = l(300 - l)
A = 300l - l²
(A) <u>Function of area in terms of length is given by </u><u>A = 300l - l²</u>
(B) The practical domain for this function is values between 1 and 150.
(C) For the largest area, we need to determine the largest garden possible. For that, we take first derivative of the function:
A' = 300 - 2l
Find the values of l when A'=0:
300 - 2l = 0
2l = 300
l = 150
Replace l in the equation:
w = 300 - 150
w = 150
Now, calculate the largest area:
A = 150*150
A = 22500
<u>The largest area the fence can enclose is </u><u>22500ft².</u>
