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DENIUS [597]
3 years ago
10

A shadow 2 meters long is cast by a statue that is 2.1 meters tall. If a stucco column close by casts a shadow 4 meters long, ho

w tall is the stucco column? Please show thought process.
Mathematics
1 answer:
Semenov [28]3 years ago
3 0
The stucco column is 4.2 meters tall.
You have to set up a ratio.    X              2.1           
                                            ----------  =    ----------  
                                                 4               2  
Make sure to keep the heights and shadow equal to each other. then cross multiply (2.1*4) and divide (8.4/2)  
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A quantity P is an exponential function of time I, such that P = 160 when t = 6 and P = 150 when I = 4. Use the given informatio
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Step-by-step explanation:

Perhaps you want to use the points (t, P) = (4, 150) and (6, 160) to find the parameters P0 and k in the equation ...

  P(t)=P_0\cdot e^{kt}

We know from the given points that we can write the equation as ...

  P(t)=150\left(\dfrac{160}{150}\right)^{(t-4)/(6-4)}=150\left(\dfrac{16}{15}\right)^{\frac{t}{2}-2}\\\\=150\left(\dfrac{16}{15}\right)^{-2}\times\left(\left(\dfrac{16}{15}\right)^{\frac{1}{2}}\right)^t

Comparing this to the desired form, we see that ...

  P_0=150\left(\dfrac{16}{15}\right)^{-2}\approx 131.836\\\\e^{k}=\left(\dfrac{16}{15}\right)^{1/2}\rightarrow k=\dfrac{1}{2}(\ln{16}-\ln{15})\approx 0.0322693

So, the approximate equation for P is ...

  P(t)=131.836\cdote^{0.032t}

And the parameters of interest are ...

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