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Slav-nsk [51]
4 years ago
10

Kiyo used to wire fencing to form a border around a circular region in his backyard. If the radius of the circular region was 5

yards, what was the total length of the border, rounded to the nearest tenth of a yard ?
Mathematics
1 answer:
kakasveta [241]4 years ago
6 0

Answer:

The total length of the border is 31.4\ yd

Step-by-step explanation:

we know that

The circumference of a circle is equal to

C=2\pi r

we have

r=5\ yd

assume

\pi=3.14

substitute

C=2(3.14)(5)=31.4\ yd

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F⃗ (x,y)=−yi⃗ +xj⃗ f→(x,y)=−yi→+xj→ and cc is the line segment from point p=(5,0)p=(5,0) to q=(0,2)q=(0,2). (a) find a vector pa
DerKrebs [107]

a. Parameterize C by

\vec r(t)=(1-t)(5\,\vec\imath)+t(2\,\vec\jmath)=(5-5t)\,\vec\imath+2t\,\vec\jmath

with 0\le t\le1.

b/c. The line integral of \vec F(x,y)=-y\,\vec\imath+x\,\vec\jmath over C is

\displaystyle\int_C\vec F(x,y)\cdot\mathrm d\vec r=\int_0^1\vec F(x(t),y(t))\cdot\frac{\mathrm d\vec r(t)}{\mathrm dt}\,\mathrm dt

=\displaystyle\int_0^1(-2t\,\vec\imath+(5-5t)\,\vec\jmath)\cdot(-5\,\vec\imath+2\,\vec\jmath)\,\mathrm dt

=\displaystyle\int_0^1(10t+(10-10t))\,\mathrm dt

=\displaystyle10\int_0^1\mathrm dt=\boxed{10}

d. Notice that we can write the line integral as

\displaystyle\int_C\vecF\cdot\mathrm d\vec r=\int_C(-y\,\mathrm dx+x\,\mathrm dy)

By Green's theorem, the line integral is equivalent to

\displaystyle\iint_D\left(\frac{\partial x}{\partial x}-\frac{\partial(-y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=2\iint_D\mathrm dx\,\mathrm dy

where D is the triangle bounded by C, and this integral is simply twice the area of D. D is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.

4 0
3 years ago
Write a polynomial of degree 3 that satisfies each of the given conditions.
shutvik [7]

Answer:

https://www.jacksonsd.org/cms/lib/NJ01912744/Centricity/Domain/504/BI%207-8.pdf

Step-by-step explanation:

the link to help you with the answers

5 0
3 years ago
Algebra
vladimir2022 [97]
(2x + 3y = 12) x (-2)
(4x - 3y = 6) x 1

-4x - 6y = -24
4x - 3y = 6

You can cancel out the x values by adding the two equations together. 
(-4x + 4x) + (-6y - 3y) = (-24 + 6)
-9y = -18
y = 2

Solve for x now...
4x - 3(2) = 6
4x - 6 = 6
4x = 12
x = 3

Check... (x = 3, y = 2)
2(3) + 3(2) = 12 
6 + 6 = 12
12 = 12 <- this works! 

4(3) - 3(2) = 6
12 - 6 = 6
6 = 6 <- this works!
5 0
3 years ago
Read 2 more answers
Some friends made $48 selling
Nikolay [14]
4
Explanation: 12*4 =48
8 0
4 years ago
Read 2 more answers
Help please, HELP PLEASE, HELP PLEASE. HELP PLEASE., HELP PLEASE, HELP PLEASE.
V125BC [204]

Answer: B,C,E

hope it helps :)

3 0
3 years ago
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