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DedPeter [7]
2 years ago
11

Please help me solving this problem.

Mathematics
1 answer:
Illusion [34]2 years ago
7 0

(a) The radius of the circle is the distance the wave travels since it first formed, so if <em>g(t)</em> is the radius of the circle at time <em>t</em>, then it changes at a rate according to

d<em>g</em>/d<em>t</em> = 60 cm/s

Integrate both sides with respect to <em>t</em> to solve for <em>g</em> :

∫ d<em>g</em>/d<em>t</em> d<em>t</em> = ∫ (60 cm/s) d<em>t</em>

<em>g(t)</em> = (60 cm/s) <em>t</em> + <em>C</em>

but <em>C</em> = 0 since the radius at <em>t</em> = 0 must be 0.

<em>g(t)</em> = (60 cm/s) <em>t</em>

<em />

(b) The area of any circle with radius <em>r</em> is <em>πr</em> ². So

<em>f(r)</em> = <em>πr</em> ²

(c) The composition of <em>f</em> with <em>g</em> represents the area of water encircled by the wave at time <em>t</em> :

<em>(f</em> o <em>g)(t)</em> = <em>f(g(t))</em> = <em>π</em> <em>g(t) </em>²

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Hope this helps!

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John, Johan, and Jonathan collect postage stamps. Johan and Jonathan have the same number of stamps. Two times Johan’s collectio
MrRissso [65]

The number of postage stamps in John’s collection is 27.

We have given that,

John, Johan, and Jonathan collect postage stamps. Johan and Jonathan have the same number of stamps.

<h3>What is an elimination method?</h3>

The elimination method is the process of eliminating one of the variables in the system of linear equations using the addition or subtraction methods in conjunction with the multiplication or division of coefficients of the variables.

Johan and Jonathan have the same number of stamps.

Let x be the Johan and Jonathan postal stamps.

Let y be the John postal stamps.

Two times Johan’s collection is eleven less than five times John’s collection.

2x = 5y - 11............(1)

Three times Jonathan’s collection is three less than seven times John’s collection.

3x = 7y - 3............(2)

Multiply equation 1 with 3

3(2x = 5y - 11)

⇒ 6x = 15y - 33.........(3)

Multiply equation 2 with 2

2(3x = 7y - 3)

⇒ 6x = 14y - 6.............(4)

Subtract equation 4 from equation 3

⇒ 6x - 6x = 15y - 33 - (14y - 6)

⇒ 0 = y - 27

⇒ y = 27

Hence, the number of postage stamps in John’s collection is 27.

Find more information about the elimination method here

brainly.com/question/13877817

#SPJ1

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