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Answer:
w = 5
Discussion:
48 = 2 (2w) + (4 + 2w)2 =>
48 = 4w + 4*2 + (2w)*2 =>
48 = 4w + 8 + 4w => as 4w + 4w = 8w
48 = 8w + 8 => subtracting 8 from each side
48 - 8 = 8w => divide both sides by 8
(48 -8 )/8 = w =>
40/8 = w =>
w = 5 =>
Check: 2(10) + ( 4 + 2*5)*2 = 20 + 14*2 = 20 + 28 = 48
Thank you,
MrB
C. 2
2x10 = 20 +10x10=100 100+20= 120
12x10=120
C. is the answer.
Corrected Question
The volume of air inside a rubber ball with radius r can be found using the function V(r) = four-thirds pi r cubed. What does V(5/7) represent?
Answer:
(B)the volume of the rubber ball when the radius equals five-sevenths feet
Step-by-step explanation:
The Volume of a sphere of radius r can be found using the formula:
Therefore comparing the expression: with V(r):
Thus, is the volume of a ball of radius feet.
The correct option is B.
9514 1404 393
Answer:
split the number into equal pieces
Step-by-step explanation:
Assuming "splitting any number" means identifying parts that have the number as their sum, the maximum product of the parts will be found where the parts all have equal values.
We have to assume that the number being split is positive and all of the parts are positive.
<h3>2 parts</h3>
If we divide number n into parts x and (n -x), their product is the quadratic function x(n -x). The graph of this function opens downward and has zeros at x=0 and x=n. The vertex (maximum product) is halfway between the zeros, at x = (0 + n)/2 = n/2.
<h3>3 parts</h3>
Similarly, we can look at how to divide a (positive) number into 3 parts that have the largest product. Let's assume that one part is x. Then the other two parts will have a maximum product when they are equal. Their values will be (n-x)/2, and their product will be ((n -x)/2)^2. Then the product of the three numbers is ...
p = x(x^2 -2nx +n^2)/4 = (x^3 -2nx^2 +xn^2)/4
This will be maximized where its derivative is zero:
p' = (1/4)(3x^2 -4nx +n^2) = 0
(3x -n)(x -n) = 0 . . . . . . . . . . . . . factor
x = n/3 or n
We know that x=n will give a minimum product (0), so the maximum product is obtained when x = n/3.
<h3>more parts</h3>
A similar development can prove by induction that the parts must all be equal.
Answer: A <em>plane </em>
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