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Alekssandra [29.7K]
3 years ago
5

how many wall are there in your room? what are the shape of the floor and ceiling in your room ? how can you find the area of ea

ch shape?prepare the answer. present the conclusion in the form of report. plz answer the question in right.​
Mathematics
1 answer:
Triss [41]3 years ago
7 0

My room is made up of four walls, both the floor and the ceiling are rectangular in shape.

  • There are four walls in my room.
  • The shape of the floor is a rectangle and given that the ceiling is the same form above the floor, it is also shaped as a rectangle.

To get the area of a rectangle, you use this formula since my floor and ceiling are rectangle.

Area = L * W

where

L = length

W= width

But if you have a square floor and ceiling, the area of a square is

Area = s²

given that it is side * side.

<em>In conclusion, there are </em><em>4 walls</em><em> in every room. The shape of the ceiling or floor could be a </em><em>rectangle or a square</em><em>. It depends on your room and its measurements. To get the area, </em><em>multiply </em><em>the length by the width.</em>

<em>read more at brainly.com/question/24359958?referrer=searchResults</em>

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A function f(t) is periodic if there is some constant k such that f(t+k)=f(k) for all t in the domain of f(t). Then k is the "period" of f(t).

Example:

If f(x)=\sin x, then we have \sin(x+2\pi)=\sin x\cos2\pi+\cos x\sin2\pi=\sin x, and so \sin x is periodic with period 2\pi.

It gets a bit more complicated for a function like yours. We're looking for k such that

\pi\sin\left(\dfrac\pi2(t+k)\right)+1.8\cos\left(\dfrac{7\pi}5(t+k)\right)=\pi\sin\dfrac{\pi t}2+1.8\cos\dfrac{7\pi t}5

Expanding on the left, you have

\pi\sin\dfrac{\pi t}2\cos\dfrac{k\pi}2+\pi\cos\dfrac{\pi t}2\sin\dfrac{k\pi}2

and

1.8\cos\dfrac{7\pi t}5\cos\dfrac{7k\pi}5-1.8\sin\dfrac{7\pi t}5\sin\dfrac{7k\pi}5

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\begin{cases}\cos\dfrac{k\pi}2=1\\\\\sin\dfrac{k\pi}2=0\\\\\cos\dfrac{7k\pi}5=1\\\\\sin\dfrac{7k\pi}5=0\end{cases}

The first two equations are satisfied whenever k\in\{0,\pm4,\pm8,\ldots\}, or more generally, when k=4n and n\in\mathbb Z (i.e. any multiple of 4).

The second two are satisfied whenever k\in\left\{0,\pm\dfrac{10}7,\pm\dfrac{20}7,\ldots\right\}, and more generally when k=\dfrac{10n}7 with n\in\mathbb Z (any multiple of 10/7).

It then follows that all four equations will be satisfied whenever the two sets above intersect. This happens when k is any common multiple of 4 and 10/7. The least positive one would be 20, which means the period for your function is 20.

Let's verify:

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f(t)=\displaystyle\sum_{i=1}^n(a_i\sin(b_it)+c_i\cos(d_it))

is periodic with period \mbox{lcm}(b_1,\ldots,b_n,d_1,\ldots,d_n).
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