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2 years ago

Which function has an inverse function?

Mathematics

1 answer:

Sergeu [11.5K]2 years ago

8 0

F(x)=x^5-3 is the answere

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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

William says that 15years from now his age will be 3 times his age 5 years ago if x represents williams present age complete the

Kay [80]

Answer:

Is the question complete

5 0

2 years ago

Which of the following equations represents the line that is graphed on the coordinate grid below

vladimir2022 [97]

Answer:

Step-by-step explanation:

the factor of x in the equation is the slope, which is the ratio y/x indicating how many units y changes, when x changes a certain amount of units.

going from the left point to the right point x changes by +3 units, and y changes by -1 unit.

so, the slope (and factor of x in the equation) is -1/3.

and the constant term in the equation is the y (axis) intercept of the line.

this is the y value, when x = 0 (intercepting the y axis).

and we see in the graph, when x = 0, the line goes through y = 2.

so, the equation has to be

y = -1/3 × x + 2

therefore, C is the right answer.

7 0

2 years ago

Math help please I need it ASAP

statuscvo [17]

Answer:

x=10.5

Step-by-step explanation:

$\frac{x}{6} =\frac{7}{4} \\x=\frac{7}{4} \times 6\\=\frac{21}{2} \\=10.5$

4 0

2 years ago

Can someone PLEASE solve this quadratic equation by factoring with the steps? :(

salantis [7]

Answer:

There are no simple factors to this expression. You can however solve for x, giving you:

x = -1 ± √(y + 3)

Step-by-step explanation:

There is no simple pair of factors to this equation, so we'll have to go through the full process. You can see that by observing that there is no pair of rational numbers that add to make 2 and multiply to make -2. We can however solve for x:

$y = x^2 + 2x - 2\\y + 2 = x^2 + 2x\\y + 3 = x^2 + 2x + 1\\y + 3 = (x + 1)^2\\(x + 1)^2 = y + 3\\x + 1 = \pm \sqrt{y + 3}\\x = -1 \pm \sqrt{y + 3}$

5 0

2 years ago