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Advocard [28]
3 years ago
15

Whats the surface area of this figure

Mathematics
1 answer:
irakobra [83]3 years ago
5 0

Answer:

504

Step-by-step explanation:

The area of the base is 14 x 14 which is 196

The area of one triangle is 1/2 x base length x height which is:

1/2 x 14 x 11 = 77

So the area of one triangle is 77. The area of all the triangles is the same and there are 4 triangles.

So the surface area is

196 + 77 + 77 + 77 + 77 = 504

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A rumor spreads through a small town. Let y(t) be the fraction of the population that has heard the rumor at time t and assume t
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Answer:

The answer is shown below

Step-by-step explanation:

Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor.

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b)

\frac{dy}{dt}=ky(1-y)\\\frac{dy}{y(1-y)}=kdt\\\int\limits {\frac{dy}{y(1-y)}} \, =\int\limit {kdt}\\\int\limits {\frac{dy}{y}} +\int\limits {\frac{dy}{1-y}}  =\int\limit {kdt}\\\\ln(y)-ln(1-y)=kt+c\\ln(\frac{y}{1-y}) =kt+c\\taking \ exponential \ of\ both \ sides\\\frac{y}{1-y} =e^{kt+c}\\\frac{y}{1-y} =e^{kt}e^c\\let\ A=e^c\\\frac{y}{1-y} =Ae^{kt}\\y=(1-y)Ae^{kt}\\y=\frac{Ae^{kt}}{1+Ae^{kt}} \\at \ t=0,y=10\%\\0.1=\frac{Ae^{k*0}}{1+Ae^{k*0}} \\0.1=\frac{A}{1+A} \\A=\frac{1}{9} \\

y=\frac{\frac{1}{9} e^{kt}}{1+\frac{1}{9} e^{kt}}\\y=\frac{1}{1+9e^{-kt}}

At t = 2, y = 40% = 0.4

c) At y = 75% = 0.75

y=\frac{1}{1+9e^{-0.8959t}}\\0.75=\frac{1}{1+9e^{-0.8959t}}\\t=3.68\ days

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