Answer:
The value of r to have maximum profit is 3/25 ft
Step-by-step explanation:
To find:
The size of the sphere so that the profit can be maximized.
Manufacturing cost of the solid sphere = $500/ ft^3
Selling price of sphere (on surface area) = $30 / ft^2
We see that the manufacturing cost dealt with he volume of the sphere where as the selling price dealt with the surface area.
So,
To maximize the profit (P) .
We can say that:
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Differentiate "" and find the "" value then double differentiate "", plug the "" values from to find the minimum and maximum values.
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Finding r values :
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Dividing both sides with 240π .
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⇒ and
To find maxima value the double differentiation is :
⇒ ...first derivative
Double differentiating :
⇒ ...second derivative
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Test the value r = 3/25 dividing both sides with 240π
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It passed the double differentiation test.
Extra work :
Thus:
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Finally r =3/25 ft that will maximize the profit of the manufacturing company.
Answer:
Your 3 answers are
- A) y=0.25x
- C) Graph
- E) Table
Step-by-step explanation:
If you were to graph them and compare the original graph they are exactly the same.
A) y=0.25x is the same thing as y= 1/4 * x
slope m is 1/4 on the original graph and given decimal form.
C) Is the same graph but the point given is at (4,1)
E) is the points between 6<x<8 and 1.5<y<2 as the original graph.
Answer:
Dream Studio offers music lessons at $12 per lesson. Fox Studio offers music lessons at $9 per lesson. The better deal here would be Fox Studio. This is because Fox Studio offers cheaper lessons. For eight lessons at Dream Studio it costs $96, where as eight lessons at Fox Studio costs only $72.
Explanation:
Step 1 - Find the cost per lesson at Dream Studio
60 / 5 = 12
So, $12 per music lesson at Dream Studio.
Step 2 - Find the cost per lesson at Fox Studio
72 / 8 = 9
So, $9 per music lesson at Fox Studio.
Step 3 - Find out which offers a better deal
•Dream Studio = $96 for eight music lessons
• Fox Studio = $72 for eight music lessons
Answer is B. Subtract 10 from both sides of the equation
1st step for solving X is Moving all terms to the left of the equation and simplifying
Subtract 10 from both sides of the equation
x^2 + 6x - 1 = 0
Answer:
Step-by-step explanation:
The perimeter of a polygon is equal to the sum of all the sides of the polygon. Quadrilateral PTOS consists of sides TP, SP, TO, and SO.
Since TO and SO are both radii of the circle, they must be equal. Thus, since TO is given as 10 cm, SO will also be 10 cm.
To find TP and SP, we can use the Pythagorean Theorem. Since they are tangents, they intersect the circle at a , creating right triangles and .
The Pythagorean Theorem states that the following is true for any right triangle:
, where is the hypotenuse, or the longest side, of the triangle
Thus, we have:
Since both TP and SP are tangents of the circle and extend to the same point P, they will be equal.
What we know:
Thus, the perimeter of the quadrilateral PTOS is equal to