Determine if the following equation is conditional equation, identity or a contradiction.

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

Mr. Foster is starting a new job. His salary for the first year is $30,000. He will receive a 5% raise each year after that. Wri

stira [4]

Answer:

s= 30000+1500x

Step-by-step explanation:

Given data

Le the number of years be x

His salary for the first year is $30,000

5% of $30,000

=5/100*30000

= 0.05*30000

= $1500

Hence for x years the salary can be described as

s= 30000+1500x

6 0

3 years ago

How can you tell if an ordered pair is a solution of a system of linear equations by examining the graphs of the equations?

BlackZzzverrR [31]

Answer:

A.) Both lines pass through the point represented by the ordered pair

Step-by-step explanation:

4 0

2 years ago

a class has six boys and 14 girls what is the ratio in simplest form that compares number of boys the number of students

-BARSIC- [3]

Answer:

3:10

Step-by-step explanation:

Boys- 6

Girls- 14

Total students- 20

Boys:Total students

6 : 20

Simplify:

6/2=3

20/2=10

This is written as:

3:10

➴Hope this helps!

➸CloutAnswers

6 0

2 years ago

Assume two radar stations which are 39 miles apart are both tracking a plane. At a given moment, the angle between station 1 and

SpyIntel [72]

Answer:

37.3 miles

Step-by-step explanation:

180 - 59.83 - 55.54 = 64.63°

39/sin64.63 = X/sin59.83

X = 37.3157217 miles

6 0

3 years ago