iclo iv 1) \( x^{3}-2 x^{4}+5 x-7+\left(5 x^{3}+x\right) \) \( \left.-9 x^{2}+6 x-3\right) \) 3) \( \left(4 x^{2}+3 x+5+\left(-9 x^{4}+5 x^{2}+6 x^{2}-2 x+7\right)+\left(-4 x^{2}+\right.\right. \) 1) \( \left(10-2 x^{2}-3 x\right)+\left(4 x^{2}+5-3 x\right) \) \( 5 x^{2}+2 x+3 \) Por \( 5 x^{3} \) 1) \( 15 x^{3}-12 x^{2}+6 \div 3 x \).

In this problem, please evaluate the trig functions without a calculator and do not use a decimal point in your answer. An equation of the tangent line to the curve \( y=\sin (x) \) at \( x=5 \pi / 6 \) is \( y=\square+(x-5 \pi / 6) \) An equation of the tangent line to the curve \( y=\cos (x) \) at \( x=0 \) is \( y=\square+\square \cdot(x-0) \)

4. How many terms of the AP: \( 9,17,25, \ldots \) must be taken to give a sum of 636 ?

2. A ladder of length 8 m rests against a wall so that the angle between the ladder and the wall is \( 31^{\circ} \). How far is the base of the ladder from the wall?

Question 2 Consider the following (inverse) supply and dernand (linear) functions/equations: \( P=10+1.55 Q^{s} \) \( P=35-0.95 Q^{d} \) Here you have two equations and three unknowns: \( P, Q^{s} \), and \( Q^{d} \). In order to find a unique solution, leverage the following condition (identity) that holds when the market is at equilibrium \( Q^{d}=Q^{s}=Q^{e} \) Therefore, the supply and demand functions can be rewritten such you end up with two equations and two unknowns, as follows: \( P=10+1.55 Q^{e} \) \( P=35-0.95 Q^{e} \) \( 2 a \). ( 20 POINTS) Solve for the values of P and \( Q^{e} \). Show the work that leads to your answer. \( 2 b \). ( 20 POINTS) Calculate consumer surplus (CS) and producer surplus (PS). Show the work that leads to your answer. Keep in mind that CS is the area belo) demand curve and above the price line, whereas PS is the area above the supply curve and below the price line. Also, remember that the area of a triangle calculated as: (base \( x \) height) /2.

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