Answer:
C = 0.5t + 12. Independent variable is t and the dependent variable is C.
Step-by-step explanation:
$12 is constant, and then $0.50 is multiplied to the amount of toppings (t). So C= 0.5t + 12 and the cost is dependent on the amount of toppings.
Answer:
The farmer should make the enclosure 36 feet wide to have the maximum area for his pigs.
Step-by-step explanation:
The question tests the applications of differential calculus. We are informed that the farmer will use the wall of his barn as one side of the enclosure implying that the 144 feet of fencing will only be used to form the three remaining sides of the rectangular enclosure.
If we let x denote the width of this rectangular enclosure to be formed, then its length will be 144-2x since we shall be having two sides each measuring x and the total length of the fencing is 144. 2x will be used on the width leaving 144-2x for the length since one side of the length is formed by the wall.
If we let A denote the area of the rectangular enclosure, then;
A = x(144 - 2x)
since the area of a rectangle is simply the product of the length and the width. We open the brackets;
A = 144x - 2x^2
Clearly, the Area is a function of the width that is A is the dependent variable while x is the independent one.
At the maximum area, the slope of the tangent to the curve 144x - 2x^2 is 0. Therefore, we differentiate the given function of x with respect to x then set the resulting expression to 0 to determine x that will maximize A;
dA/dx = 144 - 4x
We set this expression to 0 and solve for x;
144 - 4x = 0
144 = 4x
x = 36
Therefore, the farmer should make the enclosure 36 feet wide to have the maximum area for his pigs.
Answer:
Step-by-step explanation:
-60 plus 85 equals 25 so she has 25 dollars in the bank now.
Answer:
If both parties are over the age of 18, a lawsuit is likely to occur.
Step-by-step explanation:
Ben would likely try and sue Catalina for theft, however she wouldn't be found guilty because of the transfer of property, goods, and or services was entirely legal in this case.
