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MrRa [10]
4 years ago
9

Find the dimensions of a rectangle whose perimeter is 22 meters and whose area is 28 square meters.

Mathematics
2 answers:
Sav [38]4 years ago
8 0

Answer:

The length is 7 meters.

The width is 4 meters.

Step-by-step explanation:

The area of the rectangle is = 28 sq meter

The perimeter of the rectangle is = 28 sq meter

Now, in terms of formula these can be written as :

l\times w=28  

or l=\frac{28}{w}     ....(1)

2l+2w=22      

Dividing by 2

l+w=11   .... (2)

Now, putting (1) in (2)

\frac{28}{w}+w=11

28+w^{2} =11w

w^{2}-11w+28=0

w^{2}-7w-4w+28=0

w(w-7)-4(w-7)=0

(w-4)(w-7)=0

This gives width as 4 , so length = 7

Or width as 7 , so length = 4

Therefore, the length is 7 meters.

The width is 4 meters.

UkoKoshka [18]4 years ago
3 0
I hope this helps you

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3 years ago
A disease is infecting a colony of 1000 penguins living on a remote island. Let P(t) be the number of sick penguins t days after
MAXImum [283]

Answer:

a. P = 1000 - Ce^{-\frac{kt^2}{2} }

b. C = 950

c. P = 1000 - 950e^{-\frac{kt^2}{2} }

Step-by-step explanation:

a. Let the number of penguins who have the disease t days after the outbreak be P

Initial number of penguins = 1000

Therefore, current number of penguins = 1000 - P

And the rate of spread of disease according to the statement is

\frac{dP}{dt}\alpha   t(1000-P)\\\frac{dP}{dt}=kt(1000-P)

where k is the constant of proportionality

\frac{dP}{1000-P}=kt.dt

Integrating both sides

-ln(1000-P) = \frac{kt^2}{2}+c\\\frac{1}{(1000-P)} = Ce^{\frac{kt^2}{2} }\\ (1000-P) = Ce^{-\frac{kt^2}{2} }\\P = 1000 - Ce^{-\frac{kt^2}{2} }

b. Seeing as 50 penguins had the disease initially,

t = 0

P = 50

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c. Therefore, the solution that satisfies the initial condition is

P = 1000 - 950e^{-\frac{kt^2}{2} }

4 0
4 years ago
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