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VARVARA [1.3K]
3 years ago
8

A hotel wants to put a fence around a circular spa. The radius of the spa is 5/√2-1 feet. If the fence is built along the immedi

ate edge of the spa, what is the perimeter of the fence? (Recall that the
perimeter of a circle is 2πr , where r is the radius of the circle.)
Physics
1 answer:
Vlad [161]3 years ago
5 0
It is important to look at all the information's that are given in the question very closely. Let us write them write first.

Radius of the spa = <span>5/√2-1 feet
Now
Perimeter of the circle = </span><span>2πr
                                    = 2</span>π (5/√2-1) 
                                    = <span>π(5/(√2-1)*(√2+1)/(√2+1) </span>
<span>                                    = 2π(5/(√2+1))/(2-1) </span>
<span>                                    = 10π(√2+1)  

I hope that the procedure is clear enough for you to understand.</span>
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7 0
3 years ago
A sinusoidal voltage is given by the expression ????(????)=20cos(5π×103 ????+60°) V. Determine its (a) frequency in hertz, (b) p
MA_775_DIABLO [31]

<em>There are some placeholders in the expression, but they can be safely assumed</em>

Answer:

(a) f=1617.9\ Hz

(b) T=0.618\ ms

(c) A=20 \ Volts

(d) \varphi=60^o

Explanation:

<u>Sinusoidal Waves </u>

An oscillating wave can be expressed as a sinusoidal function as follows

V(t)&=A\cdot \sin(2\pi ft+\varphi )

Where

A=Amplitude

f=frequency

\varphi=Phase\  angle

The voltage of the question is the sinusoid expression  

V(t)=20cos(5\pi\times 103t+60^o)

(a) By comparing with the general formula we have

f=5\pi\times 103=1617.9\ Hz

\boxed{f=1617.9\ Hz}

(b) The period is the reciprocal of the frequency:

\displaystyle T=\frac{1}{f}

\displaystyle T=\frac{1}{1617.9\ Hz}=0.000618\ sec

Converting to milliseconds

\boxed{T=0.618\ ms}

(c) The amplitude is

\boxed{A=20 \ Volts}

(d) Phase angle:

\boxed{\varphi=60^o}

4 0
3 years ago
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