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Kay [80]
2 years ago
5

Ramsay cuts out a piece from a circular cardboard for a school project. The radius of the cardboard is 10 inches and the measure

of the central angle is 54 degrees, as shown.
What is the length of the curved boundary of the piece of the cardboard Ramsay cuts out?
Leave in terms of π.

Mathematics
1 answer:
inysia [295]2 years ago
6 0

Answer:

34 inches

Step-by-step explanation :

54/360 X 20

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In an insect colony there are 270 insects after 9 days. If there were initially 80 insects how long will it take the population
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Answer:

The time it will take the population to grow to 800 insects is 17 days.

Step-by-step explanation:

The growth function of the insects is exponential.

The exponential growth function is:

y=a(1+r)^{t}

Here,

<em>y</em> = final value

<em>a</em> = initial value

<em>r</em> = growth rate

<em>t</em> = time taken

It is provided that there were 270 insects after 9 days and initially there were 80 insects.

Compute the value of <em>r</em> as follows:

y=a(1+r)^{t}\\\\270=80(1+r)^{9}\\\\3.375=(1+r)^{9}\\\\\ln(3.375)=9\cdot \ln(1+r)\\\\0.135155=\ln(1+r)\\\\1+r=1.14471\\\\r=0.145

Now, compute the time it will take the population to grow to 800 insects as follows:

800=80(1+0.145)^{t}\\\\10=(1.145)^{t}\\\\\ln(10)=t\cdot \ln(1.145)\\\\t=17.00522\\\\t\approx 17

Thus, the time it will take the population to grow to 800 insects is 17 days.

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Step-by-step explanation:

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