Answer:
x = 8,49 ft
y = 4,24 ft
Step-by-step explanation:
Let x be the longer side of rectangle and y the shorter
Area of rectangle = 36 ft² 36 = x* y ⇒ y =36/x
Perimeter of rectangle:
P = 2x + 2y for convinience we will write it as P = ( 2x + y ) + y
C(x,y) = 1 * ( 2x + y ) + 3* y
The cost equation as function of x is:
C(x) = 2x + 36/x + 108/x
C(x) = 2x + 144/x
Taking derivatives on both sides of the equation
C´(x) = 2 - 144/x²
C´(x) = 0 2 - 144/x² = 0 ⇒ 2x² -144 = 0 ⇒ x² = 72
x = 8,49 ft y = 36/8.49 y = 4,24 ft
How can we be sure that value will give us a minimun
We get second derivative
C´(x) = 2 - 144/x² ⇒C´´(x) = 2x (144)/ x⁴
so C´´(x) > 0
condition for a minimum
Answer:
- after week 7: 4374 pennies
- 486 pennies: after week 5
Step-by-step explanation:
The sequence values have a first term of 6 and a common ratio of 3, so can be described by the formula ...
an = 6·3^(n-1)
This can be rearranged to ...
an = 2·3^n
__
When n=7, the value is ...
a7 = 2·3^7 = 4374 . . . . pennies saved after 7 weeks
__
To find when there are 486 pennies saved, we can solve the equation ...
486 = 2·3^n
243 = 3^n
log(243) = n·log(3) . . . . . . . take the logarithm
log(243)/log(3) = n = 5 . . . . divide by the coefficient of n
Tabitha will have saved 486 pennies after 5 weeks.
This might help
total surface area Stot = 42.5 ft2
lateral surface area Slat = 30 ft2
top surface area Stop = 6.25 ft2
bottom surface area Sbot = 6.25 ft2
but im thinking they would need 113.7 ft of rapping paper i many be totally wrong tho
Well i don’t know i just need me pints but sorry i’m so sorry
