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3 years ago

PLEASE HELP ME WITH THIS

Mathematics

1 answer:

SSSSS [86.1K]3 years ago

5 0

Answer:

Step-by-step explanation:

angles on a straight line are 180 so u do 180 minus 47 gives u 133

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Find the exact length of the curve. x=et+e−t, y=5−2t, 0≤t≤2 For a curve given by parametric equations x=f(t) and y=g(t), arc len

Rama09 [41]

The length of a curve C parameterized by a vector function r(t) = x(t) i + y(t) j over an interval a ≤ t ≤ b is

$\displaystyle\int_C\mathrm ds = \int_a^b \sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2} \,\mathrm dt$

In this case, we have

x(t) = exp(t ) + exp(-t ) ==> dx/dt = exp(t ) - exp(-t )

y(t) = 5 - 2t ==> dy/dt = -2

and [a, b] = [0, 2]. The length of the curve is then

$\displaystyle\int_0^2 \sqrt{\left(e^t-e^{-t}\right)^2+(-2)^2} \,\mathrm dt = \int_0^2 \sqrt{e^{2t}-2+e^{-2t}+4}\,\mathrm dt$

$=\displaystyle\int_0^2 \sqrt{e^{2t}+2+e^{-2t}} \,\mathrm dt$

$=\displaystyle\int_0^2\sqrt{\left(e^t+e^{-t}\right)^2} \,\mathrm dt$

$=\displaystyle\int_0^2\left(e^t+e^{-t}\right)\,\mathrm dt$

$=\left(e^t-e^{-t}\right)\bigg|_0^2 = \left(e^2-e^{-2}\right)-\left(e^0-e^{-0}\right) = \boxed{e^2-\frac1{e^2}}$

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3 years ago

How does the rate of change vary from point to point?

Tpy6a [65]

$\bf \begin{array}{|cc|ll} \cline{1-2} x&y\\ \cline{1-2} 40&32\\ 28&16\\ 16&12\\ \cline{1-2} \end{array}~\hfill \stackrel{\textit{average rate of change}}{slope} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{40}~,~\stackrel{y_1}{32})\qquad (\stackrel{x_2}{28}~,~\stackrel{y_2}{16}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{16-32}{28-40}\implies \cfrac{-16}{-12}\implies \boxed{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill$

$\bf (\stackrel{x_1}{28}~,~\stackrel{y_1}{16})\qquad (\stackrel{x_2}{16}~,~\stackrel{y_2}{12}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{12-16}{16-28}\implies \cfrac{-4}{-12}\implies \boxed{\cfrac{1}{3}}$

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3 years ago

Answer number 10 please thank you

galina1969 [7]

Answer:

35%

Step-by-step explanation:

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2 years ago

Please help me! i dont know what to do... And my weekend depends on you

ludmilkaskok [199]

2) 5.3
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3 years ago

Choose the equations that are not linear equations. -x - y = 2 x 2 + y = 4 - y 3 = 1 x = 5

NeX [460]

X² + y = 4 and -y³ = 1x -5 are not linear equation because they contain a variable with a exponents. These types of equation are called quadratic equations.

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3 years ago