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Mathematics

1 answer:

nikitadnepr [17]2 years ago

7 0

Answer:

if you know the diameter then double it to get the answer

Step-by-step explanation:

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Determine the area of the figure on the coordinate grid. Round to the nearest hundredth if needed. Show all work to receive cred

AleksandrR [38]

Answer:

I can't currently fully answer, hoping someone can come along and help-

Step-by-step explanation:

separate the shape into 3 triangles and 1 rectangle and then add all the areas together

area of a triangle is 1/2 base times height and area of a rectangle is length multiplied by width

5 0

2 years ago

∫∫(x+y)dxdy ,d là miền giới hạn bởi x²+y²=1

igor_vitrenko [27]

It looks like you want to compute the double integral

$\displaystyle \iint_D (x+y) \,\mathrm dx\,\mathrm dy$

over the region D with the unit circle x ² + y ² = 1 as its boundary.

Convert to polar coordinates, in which D is given by the set

D = {(r, θ) : 0 ≤ r ≤ 1 and 0 ≤ θ ≤ 2π}

and

x = r cos(θ)

y = r sin(θ)

dx dy = r dr dθ

Then the integral is

$\displaystyle \iint_D (x+y)\,\mathrm dx\,\mathrm dy = \iint_D r^2(\cos(\theta)+\sin(\theta))\,\mathrm dr\,\mathrm d\theta \\\\ = \int_0^{2\pi} \int_0^1 r^2(\cos(\theta)+\sin(\theta))\,\mathrm dr\,\mathrm d\theta \\\\ = \underbrace{\left( \int_0^{2\pi}(\cos(\theta)+\sin(\theta))\,\mathrm d\theta \right)}_{\int = 0} \left( \int_0^1 r^2\,\mathrm dr \right) = \boxed{0}$