The maximum area of the pen is the highest area the pen can have
The maximum area is 16200 square yards
Let the dimension be x and y.
So, the perimeter is given as:
Because it has one additional fence, the perimeter is calculated as:
Make y the subject
The area is calculated as:
Substitute
Expand
Differentiate
Set to 0
Rewrite as:
Divide both sides by 4
Substitute 90 for x in
Hence, the maximum area is 16200 square yards
Read more about maximum areas at:
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The Multiplicative Identity Property. This means that you can multiply 1 to any number... and it keeps its identity! The number stays the same!
PLEASE HELPPPPP ME PLEASE I DONT KNOW WHAT TO DO ☹️#8
Sin^6 x + cos^6 x =
= ( sin² x + cos² x ) ( sin^4 x - sin² x cos² x + cos^4 x ) =
= sin^4 x + 2 sin²x cos² x + cos^4 x - 2 sin² x cos² x - sin² x cos² x =
= ( sin² x + cos² x )² - 3 sin² x cos² x =
= 1 - 3 sin² x cos² x
After that:
1 - 3 sin² x cos² x = 5/8
1 - 5/8 = 3 sin² x cos² x
3/8 = 3 sin² x cos² x / : 3
1/8 = sin² x cos² x / * 4
1/2 = 4 sin² x cos² x
1/2 = ( 2 sin x cos x )²
√2 / 2 = 2 sin x cos x
sin 2 x = √ 2 / 2
2 x = π / 4, or x = 3 π / 4
Answer:
x 1 = π / 8, x 2 = 3 π / 8.
So we basically reverse it. 56 divided by ? =4. So we divide 56 by 4 which is 14. So the number of friends is 14
