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1 year ago

PLS HELP!!!! WILL MAKE BRAINLIEST!!

Mathematics

2 answers:

Luden [163]1 year ago

8 0

Answer:

(-1,-3)

Step-by-step explanation:

it's where the ponts at

tankabanditka [31]1 year ago

5 0

Answer:

The slope is -3

Step-by-step explanation: Use rise over run

rise/ run = -3/1

so the slope is -3

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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

Solve the proportion: A printer can print 11 color pages in 2 minutes. How many color pages can the printer print in 7 minutes?

Ann [662]

Answer:

38.5

Step-by-step explanation:

7/2 = 3.5. 11×3.5= 38.5

6 0

3 years ago

Write the equation of the line in point-slope form that passes through (5, -1) and has a slope of 2/3

kolezko [41]

Answer:

y-(-1)=2/3(x-5)

Step-by-step explanation:

Point slope form is

y-y_1=m(x-x_1) where m is the slope, x_1 is the x coordinate of a point that the line passes through, and y_1 is the y coordinate of a point the line passes through.

Substituting, we get

y-(-1)=2/3(x-5)

5 0

3 years ago

Can someone please show me how 19169000*e^(0.15)= 222712201 When e= 2.7182818284?

Ierofanga [76]

Answer:

It doesn't. x = 22 271 201

Step-by-step explanation:

You are going to need a calculator no matter how you do it.

$x =19 169 000 \times e^{0.15}$