Jasmine left the house at 7:10 am to go to work. She gets back at 6:35 pm.

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 y 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 |x | ≤ 605.

⇒ -605 ≤ x ≤ 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

Can someone help me with theeseeeeeeee

Whitepunk [10]

Wait but that is a test don't you need to look at a book or something insteadt of waiting for the answers

8 0

3 years ago

Read 2 more answers

Ldentify the following sections of the textbook.

Tema [17]

I don’t know what the drop down options are so I can’t answer your question. Sorry but can u pls help answer my question I just posted? That would be very helpful thx!

7 0

3 years ago

Simplify. -1 + (-1) please help me!!!

stepladder [879]

Answer:Which is the correct path of sperm during fertilization? cervix, vagina, fallopian tube, uterus fallopian tube, uterus, cervix, vagina vagina, cervix, uterus, fallopian tube uterus, fallopian tube, vagina, cervix

answer -2

8 0

3 years ago

PLZ HURRY carrie is 3 times as old as Eva. in 15 years Carrie will be twice as old as Eva. how old are they both now

astraxan [27]

Answer:

Age of Eva = 15 Years

Age of Carrie = 45 Years

Step-by-step explanation:

Let the age of Eva be X years

Given that Carrie is 3 times as old as Eva

Therefore age of Carrie = 3X YEARS.

__________________________________________________________

After 15 years

Age of Eva = X + 15

Age of Carrie = 3X +15

Given that Carrie is twice as old as Eva

so according to this condition

age of Carrie = 2*Age of Eva

Substituting the age of Eva and Carrie

3X +15 = 2*(X + 15 )

=> 3X +15 = 2X +30

=> 3X - 2X = 30 - 15

=> X = 15

Since X was assumed age of Eva so age of Eva is 15 years

age of Carrie = 3X years = 3*15 = 45 years.

4 0

3 years ago