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3 years ago

12

The diagram shows a semi circle inside a rectangle of length 150 m. The semi circle touches the rectangle at a b and c. Calculat

e the perimeter of the shaded region.

2 answers:

belka [17]3 years ago

5 0

Answer:

Step-by-step explanation:

<h3>C=π×d=3.142×160=502.72 </h3><h3>502.72/4=125.68cm </h3><h3>Because we can make from the rectangle two squares and then we would have 4 squares in total.</h3><h3>That is for 2 marks.If you have got any ideas for the other two marks,I would love to hear from you.I am doing the same question.Also,I see you have done question 7.Would you mind to help me with it?</h3>

evablogger [386]3 years ago

3 0

Answer:

Perimeter of the shaded region is 268 m

Step-by-step explanation:

In this diagram a semi circle is drawn inside a rectangle of length 150m.

Length of diameter of a semicircle = 150 m

So radius of the semicircle = $\frac{150}{2}=75 m$

We have to find the perimeter of the shaded region.

Perimeter of the shaded region = length of tangents drawn on the circle at A and B + m(arc AB)

Length of tangents = radius of the semi circle = 75 m

and m(arc AB) = $\frac{\text{Perimeter of the circle}}{4}=\frac{2\pi r}{4}$

= $\frac{2\pi (75)}{4}$

= $\frac{2(3.14)(75)}{4}$ \

= $\frac{471}{4}$

= 117.75 m

Now Perimeter of the shaded region = 75 + 75 + 117.75

P = 267.75 ≈ 268 m

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A. The city we will use is Orlando, Florida, and we are going to examine its population growth from 2000 to 2010. According to the census the population of Orlando was 192,157 in 2000 and 238,300 in 2010. To examine this population growth period, we will use the standard population growth equation $N_{t} =N _{0}e^{rt}$
where:
$N(t)$ is the population after $t$ years
$N_{0}$ is the initial population
$t$ is the time in years
$r$ is the growth rate in decimal form
$e$ is the Euler's constant
We now for our investigation that $N(t)=238300$ , $N_{0} =192157$ , and $t=10$ ; lets replace those values in our equation to find $r$ :
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Now lets multiply $r$ by 100% to obtain our growth rate as a percentage:
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We just show that Orlando's population has been growing at a rate of 2.2% from 2000 to 2010. Its population increased from 192,157 to 238,300 in ten years.

B. Here we will examine the population decline of Detroit, Michigan over a period of ten years: 2000 to 2010.
Population in 2000: 951,307
Population in 2010: 713,777
We know from our investigation that $N(t)=713777$ , $N_{0} =951307$ , and $t=10$ . Just like before, lets replace those values into our equation to find $r$ :
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$e^{10r} = \frac{713777}{951307}$
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C. Final equation from point A: $N(t)=192157e^{0.022t}$ .
Final equation from point B: $N(t)=951307e^{-0.029t}$
Similarities: Both have an initial population and use the same Euler's constant.
Differences: In the equation from point A the exponent is positive, which means that the function is growing; whereas, in equation from point B the exponent is negative, which means that the functions is decaying.

D. To find the year in which the population of Orlando will exceed the population of Detroit, we are going equate both equations $N(t)=192157e^{0.022t}$ and $N(t)=951307e^{-0.029t}$ and solve for t:
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$\frac{192157e^{0.022t} }{951307e^{-0.029t} } =1$
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