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algol [13]
3 years ago
9

A circular trampoline has a radius of 8 feet. Wendy wants to buy a cover for the trampoline. What will be the area of the cover

Mathematics
1 answer:
padilas [110]3 years ago
3 0

Answer:

Option (3)

Step-by-step explanation:

Area of a circle is given by the formula,

Area = πr²

Here, r = radius of the circle

Since, radius of the circular trampoline = 8 feet

Area of the cover required for the circular trampoline = π(8)²

                                                                                         = 64π square feet

Therefore, Option (3) will be the answer.

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Answer:

36/120 x 100

= 30%

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5. What is the simplest way to write
inysia [295]

Answer:

2m+3r-2x-2y

Step-by-step explanation:

2m+3r=2m+3r

-2×x=-2x

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6 0
3 years ago
Apply the method of undetermined coefficients to find a particular solution to the following system.wing system.
jarptica [38.1K]
  • y''-y'+y=\sin x

The corresponding homogeneous ODE has characteristic equation r^2-r+1=0 with roots at r=\dfrac{1\pm\sqrt3}2, thus admitting the characteristic solution

y_c=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x

For the particular solution, assume one of the form

y_p=a\sin x+b\cos x

{y_p}'=a\cos x-b\sin x

{y_p}''=-a\sin x-b\cos x

Substituting into the ODE gives

(-a\sin x-b\cos x)-(a\cos x-b\sin x)+(a\sin x+b\cos x)=\sin x

-b\cos x+a\sin x=\sin x

\implies a=1,b=0

Then the general solution to this ODE is

\boxed{y(x)=C_1e^x\cos\dfrac{\sqrt3}2x+C_2e^x\sin\dfrac{\sqrt3}2x+\sin x}

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\implies r^2-3r+2=(r-1)(r-2)=0\implies r=1,r=2

\implies y_c=C_1e^x+C_2e^{2x}

Assume a solution of the form

y_p=e^x(a\sin x+b\cos x)

{y_p}'=e^x((a+b)\cos x+(a-b)\sin x)

{y_p}''=2e^x(a\cos x-b\sin x)

Substituting into the ODE gives

2e^x(a\cos x-b\sin x)-3e^x((a+b)\cos x+(a-b)\sin x)+2e^x(a\sin x+b\cos x)=e^x\sin x

-e^x((a+b)\cos x+(a-b)\sin x)=e^x\sin x

\implies\begin{cases}-a-b=0\\-a+b=1\end{cases}\implies a=-\dfrac12,b=\dfrac12

so the solution is

\boxed{y(x)=C_1e^x+C_2e^{2x}-\dfrac{e^x}2(\sin x-\cos x)}

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r^2+1=0\implies r=\pm i

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Assume a solution of the form

y_p=(ax+b)\cos(2x)+(cx+d)\sin(2x)

{y_p}''=-4(ax+b-c)\cos(2x)-4(cx+a+d)\sin(2x)

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so the solution is

\boxed{y(x)=C_1\cos x+C_2\sin x-\dfrac13x\cos(2x)+\dfrac49\sin(2x)}

7 0
3 years ago
5. Solve 2(1 - x) > 2x.
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Answer:

I do not know for sure but i think it might be B.

Step-by-step explanation:

Im not the smartest so yeah hopefully that is the answer you are looking for tho :D

4 0
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Tim is an elementary school art teacher. His students are sculpting a replica of a shark out of clay. Tim has given them one blo
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8 0
3 years ago
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