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Basile [38]
4 years ago
15

Esmerelda and Brittany are at the library working on their algebra homework. Esmerelda is 7/9 done with her homework, and Britta

ny is 31/36 done with the same work. They want to compare these fractions to know who is closer to being done, but they know they cannot compare the fractions until they have the same denominator. What are these two fractions rewritten with a common denominator?
Mathematics
2 answers:
vfiekz [6]4 years ago
8 0

7/9= 28/36

28/36 < 31/36

(7/9 < 31/36)

aivan3 [116]4 years ago
7 0

Answer: The two fractions with a common denominator would be

\dfrac{28}{36}\ and\ \dfrac{31}{36}

Step-by-step explanation:

Since we have given that

Part of work done by Esmerelda with her homework = \dfrac{7}{9}

Part of work done by Brittany with her homework = \dfrac{31}{36}

We need to rewritten with common denominator.

As we know that

L.C.M. of 9 and 36 = 36

So, \dfrac{7}{9} can be rewritten as

\dfrac{7\times 4}{9\times 4}=\dfrac{28}{36}

and other fraction is already written with denominator 36.

So, the two fractions with a common denominator would be

\dfrac{28}{36}\ and\ \dfrac{31}{36}

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Area of the whole circle = 3.14 * 7.5^2

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Assume that the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder. Based on this assumption,
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If the flask shown in the diagram can be modeled as a combination of a sphere and a cylinder, then its volume is

V_{flask}=V_{sphere}+V_{cylinder}.

Use following formulas to determine volumes of sphere and cylinder:

V_{sphere}=\dfrac{4}{3}\pi R^3,\\ \\V_{cylinder}=\pi r^2h,

wher R is sphere's radius, r - radius of cylinder's base and h - height of cylinder.

Then

  • V_{sphere}=\dfrac{4}{3}\pi R^3=\dfrac{4}{3}\pi \left(\dfrac{4.5}{2}\right)^3=\dfrac{4}{3}\pi \left(\dfrac{9}{4}\right)^3=\dfrac{243\pi}{16}\approx 47.71;
  • V_{cylinder}=\pi r^2h=\pi \cdot \left(\dfrac{1}{2}\right)^2\cdot 3=\dfrac{3\pi}{4}\approx 2.36;
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Answer 1: correct choice is C.

If both the sphere and the cylinder are dilated by a scale factor of 2, then all dimensions of the sphere and the cylinder are dilated by a scale factor of 2. So

R'=2R, r'=2r, h'=2h.

Write the new fask volume:

V_{\text{new flask}}=V_{\text{new sphere}}+V_{\text{new cylinder}}=\dfrac{4}{3}\pi R'^3+\pi r'^2h'=\dfrac{4}{3}\pi (2R)^3+\pi (2r)^2\cdot 2h=\dfrac{4}{3}\pi 8R^3+\pi \cdot 4r^2\cdot 2h=8\left(\dfrac{4}{3}\pi R^3+\pi r^2h\right)=8V_{flask}.

Then

\dfrac{V_{\text{new flask}}}{V_{\text{flask}}} =\dfrac{8}{1}=8.

Answer 2: correct choice is D.


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Romashka [77]

9.42 Units

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The fraction represents how much of the circle that arc covers

Now we have to find the circumference which would be

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Now that we have the circumference of the WHOLE circle we multiply it by 3/4 to find out the arc length

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