Answer:
The dimension that maximizes area is 144ft by 144ft
Step-by-step explanation:
Given
-- perimeter
Required
The dimension that gives maximum area
Perimeter is calculated as:
So, we have:
Divide through by 2
Make L the subject
Area is calculated as:
Substitute
Open bracket
Differentiate A with respect to W
Set to 0 to calculate W
Collect like terms
Divide by 2
Recall that:
Answer:
no
Step-by-step explanation:
Establish the nth term formula
There is a common difference d between consecutive terms, that is
d = - 5 - (- 9) = - 1 - (- 5) = 3 - (- 1) = 7 - 3 = 4
This indicates the sequence is arithmetic with nth term
= a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = - 9 and d = 4 , then
= - 9 + 4(n - 1) = - 9 + 4n - 4 = 4n - 13
Equate 4n - 13 to 301
4n - 13 = 301 ( add 13 to both sides )
4n = 314 ( divide both sides by 4 )
n = 78.5
Since n is not an integer then 301 is not in the sequence
Answer:
<em>Answer: 1/4</em>
Step-by-step explanation:
<u>Algebraic Operations</u>
The width of a rectangle is given as W=5x+3 and the length of the rectangle is given as L=20x+12.
It's required to determine the ratio of the width to the length, that is:
This fraction can be simplified if we factor the expression in the denominator. The LCF of 20x and 12 is 4, thus:
Now note we have the exact same expression up and down, thus simplifying:
Answer: 1/4