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2 years ago

These lines all have an attribute that allows us to classify them as:

Mathematics

1 answer:

marissa [1.9K]2 years ago

4 0

Answer:

parallel

Step-by-step explanation:

no matter how far the lines stretch, they will all never meet, so they are all parallel

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Express the function g in the form f ∘ g. (there is more than one correct answer. the function is of the form y = f(g(x)). use n

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1/x+7

Step-by-step explanation:

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A bag contains 3 blue and 2 green marbles. What is the probability of drawing a blue marble folowed by a green marble, without r

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3 years ago

Select the curve generated by the parametric equations. Indicate with an arrow the direction in which the curve is traced as t i

bixtya [17]

Answer:

length of the curve = 8

Step-by-step explanation:

Given parametric equations are x = t + sin(t) and y = cos(t) and given interval is

−π ≤ t ≤ π

Given data the arrow the direction in which the curve is traces means

the length of the curve of the given parametric equations.

The formula of length of the curve is

$\int\limits^a_b {\sqrt{\frac{(dx}{dt}) ^{2}+(\frac{dy}{dt}) ^2 } } \, dx$

Given limits values are −π ≤ t ≤ π

x = t + sin(t) ...….. (1)

y = cos(t).......(2)

differentiating equation (1) with respective to 'x'

$\frac{dx}{dt} = 1+cost$

differentiating equation (2) with respective to 'y'

$\frac{dy}{dt} = -sint$

The length of curve is

$\int\limits^\pi_\pi {\sqrt{(1+cost)^{2}+(-sint)^2 } } \, dt$

$\int\limits^\pi_\pi \, {\sqrt{(1+cost)^{2}+2cost+(sint)^2 } } \, dt$

on simplification , we get

here using sin^2(t) +cos^2(t) =1 and after simplification , we get

$\int\limits^\pi_\pi \, {\sqrt{(2+2cost } } \, dt$

$\sqrt{2} \int\limits^\pi_\pi \, {\sqrt{(1+1cost } } \, dt$

again using formula, 1+cost = 2cos^2(t/2)

$\sqrt{2} \int\limits^\pi _\pi {\sqrt{2cos^2\frac{t}{2} } } \, dt$

Taking common $\sqrt{2}$ we get ,

$\sqrt{2}\sqrt{2} \int\limits^\pi _\pi ( {\sqrt{cos^2\frac{t}{2} } } \, dt$

$2(\int\limits^\pi _\pi {cos\frac{t}{2} } \, dt$

$2(\frac{sin(\frac{t}{2} }{\frac{t}{2} } )^{\pi } _{-\pi }$

length of curve = $4(sin(\frac{\pi }{2} )- sin(\frac{-\pi }{2} ))$

length of the curve is = 4(1+1) = 8

<u>conclusion</u>:-

The arrow of the direction or the length of curve = 8

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3 years ago

Which is the solution to the system of equations?2x+y=7 and 3x−4y=5

uysha [10]

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Step-by-step explanation:

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2 years ago

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