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sashaice [31]
4 years ago
10

the number of grams a woman should eat in a day to maintain her weight is proportional to her weight. a woman weighing 102 pound

s should eat only 34 grams of fat in a day to maintain her weight, at this rate how many grams of fat should a woman that weighs 180 pounds eat in a day to maintain her weight
Mathematics
1 answer:
vitfil [10]4 years ago
7 0
Given:
grams of fat : 34 grams TO weight of woman : 102 pounds
grams of fat : ? TO weight of woman : 180 pounds

This is a proportion problem: 34 grams to 102 pounds.

We first have to convert a unit of measure to another to maintain uniformity of measure. let us convert pounds to grams:

102 pounds * 453.592 grams / pound = 46,266.384 grams
180 pounds * 453.592 grams / pound = 81,646.560 grams

34 grams to 46,266.384 grams = x grams to 81,646.560 grams

proportion: a:b = c:d where ad = bc

34 grams * 81,646.560 grams = x * 46,266.384 grams
2,775,983.04 grams² = x * 46,266.384 grams
2,775,983.04 grams² ÷ 46,266.384 grams = x
60 grams = x 

A woman weighing 180 pounds should eat 60 grams of fat to maintain her weight.
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Answer:

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Step-by-step explanation:

We are trying to evaluate this integral.

\int\limits_{0}^{4/\sqrt{2}}\,\,\int\limits_{y}^{\sqrt{16-y^2}}  xy \,\,dxdy

The first thing that we have to do is understand this region in the plane.

\{ (x,y) \in \mathbb{R} :  0\leq y \leq \frac{4}{\sqrt{2}} \,\, , y \leq x \leq \, \sqrt{16-y^2}   \}

If you graph it looks something like the photo I join.

Now we need to describe that same region in polar coordinates.

That same region in polar coordinates would be

\{ (r,\theta) : \,\, 0 \leq \theta \leq \frac{\pi}{4}  \,\,\, 0\leq r \leq 4  \}

Now remember that when we do the polar transformation we use the following formula

\int\limits_{a}^{b} \, \int\limits_{c}^{d}    f(x,y) \,dxdy =  \int\limits_{\theta_1}^{\theta_2} \, \int\limits_{r_1}^{r_2}    r* f(rcos(\theta),rsin(\theta))  \,drd\theta

Then our integral would be

\int\limits_{0}^{4/\sqrt{2}}\int\limits_{y}^{\sqrt{16-y^2}}  xy \, dxdy =  \int\limits_{0}^{\pi/4} \, \int\limits_{0}^{4}    r^3 cos(\theta)\sin(\theta) \,\,  drd\theta = 16

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3 years ago
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D

Step-by-step explanation:

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3 (15 - x)

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Answer:

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Step-by-step explanation:

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y - Decimal part, formed by a digit onwards.

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