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Roman55 [17]
3 years ago
14

Write an equation and then use it to solve: Sasha gives half of her books to the local library and keeps the other half. Her bes

t friend gives her 3 more books. She now has 57 books. How many books did she have to begin with?
Mathematics
1 answer:
boyakko [2]3 years ago
8 0

Answer:

120 books

Step-by-step explanation:

57 + 3 = 60

60 x 2 = 120

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Identify the median for the data summarized on the boxplot.
LuckyWell [14K]

Answer:

a.17.5

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
The profile of the cables on a suspension bridge may be modeled by a parabola. The central span of the bridge is 1210 m long and
brilliants [131]

Answer:

The approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

Step-by-step explanation:

The equation of the parabola is:

y=0.00035x^{2}

Compute the first order derivative of <em>y</em> as follows:

 y=0.00035x^{2}

\frac{\text{d}y}{\text{dx}}=\frac{\text{d}}{\text{dx}}[0.00035x^{2}]

    =2\cdot 0.00035x\\\\=0.0007x

Now, it is provided that |<em>x </em>| ≤ 605.

⇒ -605 ≤ <em>x</em> ≤ 605

Compute the arc length as follows:

\text{Arc Length}=\int\limits^{x}_{-x} {1+(\frac{\text{dy}}{\text{dx}})^{2}} \, dx

                  =\int\limits^{605}_{-605} {\sqrt{1+(0.0007x)^{2}}} \, dx \\\\={\displaystyle\int\limits^{605}_{-605}}\sqrt{\dfrac{49x^2}{100000000}+1}\,\mathrm{d}x\\\\={\dfrac{1}{10000}}}{\displaystyle\int\limits^{605}_{-605}}\sqrt{49x^2+100000000}\,\mathrm{d}x\\\\

Now, let

x=\dfrac{10000\tan\left(u\right)}{7}\\\\\Rightarrow u=\arctan\left(\dfrac{7x}{10000}\right)\\\\\Rightarrow \mathrm{d}x=\dfrac{10000\sec^2\left(u\right)}{7}\,\mathrm{d}u

\int dx={\displaystyle\int\limits}\dfrac{10000\sec^2\left(u\right)\sqrt{100000000\tan^2\left(u\right)+100000000}}{7}\,\mathrm{d}u

                  ={\dfrac{100000000}{7}}}{\displaystyle\int}\sec^3\left(u\right)\,\mathrm{d}u\\\\=\dfrac{50000000\ln\left(\tan\left(u\right)+\sec\left(u\right)\right)}{7}+\dfrac{50000000\sec\left(u\right)\tan\left(u\right)}{7}\\\\=\dfrac{50000000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+5000x\sqrt{\dfrac{49x^2}{100000000}+1}

Plug in the solved integrals in Arc Length and solve as follows:

\text{Arc Length}=\dfrac{5000\ln\left(\sqrt{\frac{49x^2}{100000000}+1}+\frac{7x}{10000}\right)}{7}+\dfrac{x\sqrt{\frac{49x^2}{100000000}+1}}{2}|_{limits^{605}_{-605}}\\\\

                  =1245.253707795227\\\\\approx 1245.25

Thus, the approximated length of the cables that stretch between the tops of the two towers is 1245.25 meters.

7 0
3 years ago
Find the centroid for an area defined by the equations y = x² + 3 and y = - (x – 2)² + 7
meriva
The points where the 2 graphs intersect is  where x = 0 and x = 2.

-                 2                                  2
x   =    INT               x dA     /    INT        dA
                  0                                  0

INT dA   = INT -x^2 + 4x + 3 - (x^2 + 3 ) dx  =      INT -2x^2  + 4x
               =   -2 x^3/3 + 2x^2
               =   2.667  between 0 and 2

xdA  =   -2x^3 + 4x^2  INT xdA  =   -x^4/2 + 4x^3/3 = 2.667

centroid = 2.667 / 2.667  = 1  (x = 1)
3 0
3 years ago
Read 2 more answers
Students surveyed about birthdays. How many more students were born on monday than friday?
Varvara68 [4.7K]
C) 2 students
Explanation
Take Monday’s amount and subtract Friday’s
3-1=2
3 0
2 years ago
Bro I don't get this at all
antiseptic1488 [7]

E

2x  -  48  =  10x

-2x                -2x

-48  =   8x

/8          /8

-6   =  x

if you move all of your x's on to the same side it is easier to solve

7 0
3 years ago
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