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Over [174]
3 years ago
6

Find the Least Common Multiple of 15w and 6w^2.

Mathematics
2 answers:
Arada [10]3 years ago
7 0

For this case, we have that by definition, the LCM of two or more natural numbers, is the smallest natural number that is a common multiple of all of them.

 Then the LCM of 15 and 6 is the smallest positive integer that divides the numbers 15 and 6 without leaving a residue.

Multiples of each number:

15: 15,30,45 ...

6: 6,12,18,24,30

So, the LCM is 30w ^ 2

Answer:

30w ^ 2

Lina20 [59]3 years ago
3 0

15= 1,3,5,15

6^2= 36

36=1,2,3,4,6....

LCM of 15W and 6W^2=3

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An open box is to be made from a 3 ft by 8 ft rectangular piece of sheet metal by cutting out squares of equal size from the fou
Burka [1]

Answer:

Maximum volume of the box will be 7.41 cubic feet.

Step-by-step explanation:

Open box has been made from a metal sheet measuring 3 ft and 8 ft.

Let four square pieces were removed from the four corners with one side measurement x ft.

Volume of the open box = Length × width × height

Length of the box = (3 - 2x) ft

Width of the box = (8 - 2x) ft

Height of the box = x ft

Volume of the box = (3 - 2x)(8 - 2x)x

V = (24 - 6x - 16x + 4x²)x

V = 24x - 22x² + 4x³

Now we take the derivative of V with respect to x and equate the derivative to zero,

\frac{d}{dx}(V)=\frac{d}{dx}(24x - 22x^{2}+4x^{3})

V' = 24 - 44x + 12x²

V' = 0

12x² - 44x + 24 = 0

3x² - 11x + 6 = 0

3x² - 9x - 2x + 6 = 0

3x(x - 3) - 2(x - 3) = 0

(3x - 2)(x - 3) = 0

(3x - 2) = 0

and (x - 3) = 0

Therefore, x = 3, \frac{2}{3}

For x = 0.67

Length of the box = (3 - 2x) = 3 - 1.34

                              = 1.66 ft

Width of the box = (8 - 2x) = 8 - 1.34

                            = 6.66 ft

Volume of the box = 0.67 × 1.66 × 6.66

V = 7.41 cubic feet.

Similarly, for x = 3,

Length of the box = (3 - 2\times 3) = -3

which is negative but the length of the box can not be negative.

Therefore, maximum volume of the box will be 7.41 cubic feet.

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3 years ago
Houston recipes shown below to make punch for a party when she was four cups pineapple juice or cups tropical juice a good ginge
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3 years ago
A solution containing 12% alcohol is to be mixed with a solution containing 4% alcohol to make 20 gallons of solution containing
stepan [7]

Answer:

Step-by-step explanation:

Given that a solution containing 12% alcohol is to be mixed with a solution containing 4% alcohol to make 20 gallons of solution containing 9% alcohol.

Let x gallons of 12% alcohol be mixed with y gallons of 4% alcohol.

Total gallons= x+y = 20

Alcohol content in the total mixture = 0.12x+0.04y =9% of x+y

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x+y = 20\\12x+4y = 180

c) This is of the form Ax = B

where A =\left[\begin{array}{ccc}1&1\\12&4\end{array}\right]

Inverse is \frac{1}{4-12} \left[\begin{array}{ccc}4&-1\\-12&12\end{array}\right]\\=\frac{-1}{8} \left[\begin{array}{ccc}4&-1\\-12&12\end{array}\right]\\

Solution set is A inverse *B

= x \    12.5\\y  \     7.5

7 0
3 years ago
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