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
Hey there! I'm happy to help!
Let's have the adult tickets be a and the children tickets be c.
a=2c (twice as many adult tickets as child tickets)
5a+2c=700 (dollar value of each ticket)
Have a wonderful day! I hope that the helps! :D
Answer:
153 cm^2
Step-by-step explanation:
The area is given by
A = b*h
= 17*9
=153 cm^2
Answer:
Step-by-step explanation:
<h3>Given</h3>
- d = 2.5 ft
- Distance = 1250 ft
<h3>To find</h3>
<h3>Solution</h3>
<u>Circumference of the wheel is the one full rotation:</u>
- C = πd = 3.14*2.5 = 7.85 ft
<u>Number rotations:</u>
<u>Correct option is</u> 159 times
