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
Because 20 students are boy and they pick more boys because there are 20 boys students
Answer:
The question is incomplete. The complete question and its solution is attached below:
Answer:
Step-by-step explanation:
Angles 1, 2, and 3 are supplementary (they add up to equal 180). If angles 1 and 3 are 20 each, then their sum in 40, making angle 2
180 - 40 = 140. If this central angle is 140 degrees, then the measure of the arc that it cuts off also measures 140 degrees. This is not to be confused with the arc length, which is not even remotely the same thing!
Answer:
Original garden: 42 feet
Enlarged garden: 98 feet
Step-by-step explanation:
Perimeter = length (2) + width (2)
<u>Original perimeter:</u>
P = 15(2) + 6(2)
P = 30 + 12
P = 42 feet
In this problem, similar is proportional, so the new garden will be proportional to the old one.
If the original length was 15 and the new length is 35, then 15 would have had to have been multiplied by 2 1/3. That means you need to multiply 6 by 2 1/3, which is 14. That means the dimensions of the enlarged yard is 14 (width) × 35 (length).
<u>Enlarged perimeter</u>
P = 35(2) + 14(2)
P = 70 + 28
P = 98 feet
