# Precalculus Problem Solver

Pre calculus represents the advanced form of algebra that has many topics such has sets,real numbers complex numbers,inequalities,quadraticfunctions, rational functions and basic calculus.In this section we shall solve some problems based on basic calculus.In basic calculus we shall concentrate on how to solve word problems in precalculus topic.

## Precalculus Word Problem Solver

Example 1
Find the velocity of a body whose equation  S= 3t3-2t2+3t+6  where s is the distance equation and  t is the time variable . find its velocity at t=2sec.
Formula
Step1 V=$\frac{\mathrm{d} s}{\mathrm{d} t}$
Step2 V=$3\frac{\mathrm{d} (t^{3})}{\mathrm{d} t}-2\frac{\mathrm{d}(t^{2}) }{\mathrm{d} t}+3\frac{\mathrm{d} (t)}{\mathrm{d} x}+\frac{\mathrm{d}(6) }{\mathrm{d} t}$
Step3 : The derivative of  t3 is 3t2 and  t2 is 2t and that of t is 1.
Step4: V=3(3t2)-2(2t)+3
Step5: V= 9t2-4t+3
Step6: V=9(2)2-4(2)+3
Step7: V=36-8+3
Step8: V=31.
Solution : 31ms
-1
Example 2
Find the acceleration of the body whose equation is given by  S= 9t3-2t2+6t+6 where s is the distance equation and  t is the time variable . find its acceleration at t=5sec.
Formula
Step1 V=$\frac{\mathrm{d} s}{\mathrm{d} t}$
Step2 V=$9\frac{\mathrm{d} (t^{3})}{\mathrm{d} t}-2\frac{\mathrm{d}(t^{2}) }{\mathrm{d} t}+6\frac{\mathrm{d} (t)}{\mathrm{d} x}+\frac{\mathrm{d}(6) }{\mathrm{d} t}$
Step3 : The derivative of  t3 is 3t2 and  t2 is 2t and that of t is 1.
Step4: V=9(3t2)-2(2t)+6
Step5: V= 27t2-4t+6
Step6: Again we need to differentiate this V the second time as acceleration is defined as the rate of change of velocity
Step7:A=27$\frac{\mathrm{d} (t^{2})}{\mathrm{d} t}-4\frac{\mathrm{d} (t)}{\mathrm{d} t}+\frac{\mathrm{d}(6) }{\mathrm{d} t}$
Step8:A= 56t-4.
Step9: A= 56(5)-4=276ms-2
Solution : 276ms-2
Example 3
Find the Velocity of the body whose equation is given by S= 27sinx-4tanx at x=45
Formula
Step1 V=$\frac{\mathrm{d} s}{\mathrm{d} t}$
Step2 V=27$\frac{\mathrm{d} (sinx)}{\mathrm{d} x}-4\frac{\mathrm{d} (tanx)}{\mathrm{d} x}$
Step3 The derivative of sinx is cosx and the derivative of tanx is sec2x.
Step4 V=27 cosx-4sec2x
Step5 V=27 cos45 - 4 sec245
Step6 V=27/1.414- 4 *2
Step7 V=19.09-8
Step8 V=11.05.
Solution = 11.05ms-1