I need help please if you can help I will give you 10 points

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

2 years ago

Meghan says the difference between the least amount of time it takes a student to say the alphabet and the greatest amount of th

kupik [55]

Answer:

67 eghan says the difference between the least amount of time it takes a student to say the alphabet and the greatest amount

Step-by-step explanation:

4 0

2 years ago

Can the polynomial equation have exactly 1 real solution, including any repeated solutions? (Use the Fundamental Theorem of Alge

Kryger [21]

yes, there are infinitety many polynomial that have exactly one real root just like your example, to determine the real root first let the real root is a, and the complex roots are b±ic the polynomial satisfy

-9x³ + 19x² + 17 = -(x - a)(x - b - ic)(x - b + ic)

9x³ - 19x² - 17 = (x - a)(x - b - ic)(x - b + ic)

5 0

2 years ago

A father is 60 years old just son is half his age how old was the boy when his father was four times his age

gayaneshka [121]

So, what you would have to do is figure out how old he is not which is 30 yrs old because it is half of 60.

So, after this you would have to find a number that would go into 60 four times which is 15.

So, your answer would be 15.

HOPES THIS HELPS!!!!

6 0

2 years ago

1. (10 points) Let f(x) = −cos(x). Compute ˆφ = c0π0 + c1π1 where π0 = 1 and π1 = x.

Bad White [126]

4.While not rounding the answer is 500°

3 0

2 years ago