Find the quotient. 492 ÷ 4 = ? HELP PLEASE

Mathematics

1 answer:

velikii [3]3 years ago

7 0

Answer:

123

Step-by-step explanation:

492 divided by four equals 123

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Write an equation for each line in point-slope form and then convert it to standard form

asambeis [7]

Answer:

x + 2y = 14
2x -y = 13

Step-by-step explanation:

I find it easier to work with the given standard-form equation. The parallel line will have the same x- and y-coefficients and a new constant. That constant can be found by substituting the given x- and y-values into the left-side expression:

x + 2y = 8 + 2·3 = 14

The parallel line is x + 2y = 14.

The perpendicular line will have the x- and y-coefficients swapped and one of them negated. (In standard form, the x-coefficient is positive, so in this case it is convenient to negate the y-coefficient.) Then the perpendicular line through (8, 3) is ...

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A rectangular storage container with an open top is to have a volume of 10 m3. The length of this base is twice the width. Mater

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L=2W, V=LWH using L=2W in the Volume equation we get:

V=2W^2H and V=10 so

10=2W^2H now we can solve this for H

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C=20LW+12*2LH+12*2WH

C=20LW+24LH+24WH using our H and L found earlier...

C=20(2W^2)+24(2W*5/W^2)+24(W*5/W^2)

C=40W^2+240/W+120/W making a common denominator...

C=(40W^3+240+120)/W

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d2C/dW2=(80W^3+720)/W^3

Since d2C/dW2 is positive for all possible values of W (as W>0), when dC/dW=0, C(W) will be at an absolute minimum value...

dC/dW=0 only when 80W^3-360=0

80W^3=360

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So our minimum cost is:

C(45^(1/3))=(40W^3+360)/45^(1/3)

C(45^(1/3))=(40*45+360)/45^(1/3)

C(45^(1/3))=2160/45^(1/3)

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