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3 years ago

ASAP!!!!

Mathematics

1 answer:

Elza [17]3 years ago

8 0

Answer:

y = -15x - 3.04

Step-by-step explanation:

1) First place down what you are given.

Y = a(x - p) (x - q)

2) Then Substitute.

a = -16

p = -0.12

q = 1.12

y = (-16)(x - (-0.12))(x - (1.12)

3) Do order of operations (PEMDAS)

y = (-16)(x + 0.12)(x - 1.12)

Now distribute

y = − 16 x − 1.92 + (x - 1.12)

y = -16x - 1.92 + x - 1.12

y = -16x + x - 1.92 - 1.12

y = -15x - 3.04

You answer is:

y = -15x - 3.04

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Answer:

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Now, let

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

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

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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.

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