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Brrunno [24]
3 years ago
7

Write and solve a proportion to complete the statement. Round your answer to the nearest hundredth.

Mathematics
1 answer:
Maurinko [17]3 years ago
8 0

Answer:

3.73

Step-by-step explanation:

3.728 rounded to the hundredth would mean u take away the 8 and the 2 would go up to a 3 giving u the product of 3.73

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Let divf = 6(5 − x) and 0 ≤ a, b, c ≤ 12. (a) find the flux of f out of the rectangular solid 0 ≤ x ≤ a, 0 ≤ y ≤ b, and 0 ≤ z ≤
dusya [7]
Continuing from the setup in the question linked above (and using the same symbols/variables), we have

\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_{\mathcal R}(\nabla\cdot f)\,\mathrm dV
=\displaystyle6\int_{z=0}^{z=c}\int_{y=0}^{y=b}\int_{x=0}^{x=a}(5-x)\,\mathrm dx\,\mathrm dy\,\mathrm dz
=\displaystyle6bc\int_0^a(5-x)\,\mathrm dx
=6bc\left(5a-\dfrac{a^2}2\right)=3abc(10-a)

The next part of the question asks to maximize this result - our target function which we'll call g(a,b,c)=3abc(10-a) - subject to 0\le a,b,c\le12.

We can see that g is quadratic in a, so let's complete the square.

g(a,b,c)=-3bc(a^2-10a+25-25)=3bc(25-(a-5)^2)

Since b,c are non-negative, it stands to reason that the total product will be maximized if a-5 vanishes because 25-(a-5)^2 is a parabola with its vertex (a maximum) at (5, 25). Setting a=5, it's clear that the maximum of g will then be attained when b,c are largest, so the largest flux will be attained at (a,b,c)=(5,12,12), which gives a flux of 10,800.
7 0
3 years ago
1. Sort the numbers into 2 groups, rational or irrational. Write the numbers in the appropriate bubble.
rodikova [14]

Answer:

[see below]

Step-by-step explanation:

  • All natural numbers, whole numbers, integers, fractions (with integers), and numbers with terminating or repeating decimals are rational.
  • Irrational numbers cannot be written as fractions with integers. This includes non-germinating and non-repeating decimals.

Rational Numbers:

  • 0.8
  • 64
  • 0 (it can be written as \frac{0}{1})
  • 32
  • -19
  • -100
  • 3
  • 7
  • 175
  • 2
  • 6
  • 12.67
  • 1121
  • 12
  • 5
  • 3/7

Irrational Numbers:

  • 2.343443444...
  • π

Hope this helps.

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3 years ago
Which expression does NOT have a Greatest Common Factor?
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All of them Are correct, assuming this is the recipe. 
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gas prices decreased this week from $4 per gallon to 3.80 dollars per gallon what is the percent decrease​
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Is the percentage

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