Question

engineers have determined that the maximum forces in tons that a particular bridge can carry is related to the distance in meters between its supports by following function: t(d)=(12.5/d)^3. How far should tje supports be if the bridge is to support 6.5 tons? ​

Answer 1

Supports  should be 6.698 m far if bridge is to support 6.5 tons

Given : the maximum forces in tons that a particular bridge can carry is related to the distance in meters between its supports by following function:

$t(d)=\left(\dfrac{12.5}{d} \right)^3$

To Find :  How far should the supports be if the bridge is to support 6.5 tons

Solution:

$t(d)=\left(\dfrac{12.5}{d} \right)^3$

Taking cube root both sides

$\sqrt[3]{ t(d)}= \dfrac{12.5}{d}$

$d= \dfrac{12.5}{\sqrt[3]{ t(d)}}$

$d(t)= \dfrac{12.5}{\sqrt[3]{ t }}$

bridge is to support 6.5 tons

t = 6.5

$d(6.5)= \dfrac{12.5}{\sqrt[3]{ 6.5 }}$

d(6.5)  = 6.698

Hence supports  should be 6.698 m far if bridge is to support 6.5 tons

Learn More:

क्या निम्नलिखित वास्तविक चर के वास्तविक-मानित फलन का प्रतिलोम फलन प्राप्त होग

कारण  f(x)=|x|

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