answer all with steps. 2.11

a Question 1 a on pt .9 2 3 93 6) Details Suppose that z' + yd = 82. d (1) Use the method of implicit differentiation to find y. dz En: d:_. (2) Find the equation of the tangent line at the point (z, y) = (3, 1). The equation is y = Question Help: E Video C Question 2. E [H1 pt '5.) 2 Z 99 6} Details Use implicit differentiation to determine 3!" given the equation :3 +3} 2 3. Question Help: E '-.'ideo C Question 3 E [H1 pt '0 2 Z 99 G) Details dy Given the equation below. find E. 35a:9 + 101mg + if = 25 y d: Now. find the equation of the tangent line to the curve at [1 _. 11. Write your answer in m: + b format 5". Question Help: E Video . Question 4 3 W1 pt '9 2 8 99 6) Details d'l' dA Let A bethe area ofa Circle with radius 1'. If E = 3. find E when 1' = 2. l: Question Help: E '-.'ideo O Question 5 8 [H1 pt '0 2 Z 99 G) Details Aspherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 crni'min. At what rate is the volume of the snowball decreasing when the radius is 18 cm. [Note the answer is a positive num ber]. CIIIIa min 4 Hint: The volume of a sphere of radius r is V = Em; Question Help: El '-.'ideo a Question 6 a on pt '0 2 z 99 6) Details When air expands adiabatically [without gaining or losing heat}J its pressure P and volume V are related by the equation W" = C where C is a constant. Suppose that at a certain irstant the volume is 640 cubic centimeters and the pressure is 81 kPa and is decreasing at a rate of 12 kPae'minute. At what rate in cubic centimeters per minute is the volume increasing at this instant? cma min (Pa stands for Pascal -- it is equivalent to one Newtonrirneter squared}: I-(Pa is a kiloPascal or 1000 Pascals. .1 Question Help: El Video U Question ? B 0.91 pt '5'.) 2 Q 99 G) Details Acompany's revenue from selling 2 units of an item is given as R = 15004:: 2:]. If sales are increasing at the rate of 35 units per day. how rapidly is revenue increasing [in dollars per day) when 160 units have been sold? dollars per day Question Help: El Video . Question 3 B 0.91 pt '9 2 Q 99 G) Details Acompany selling widgets has found that the number of items sold 3 depends upon the price p at Which 700m they're sold, according the equation 3 = '34? 1 Due to inflation and increasing health benefit costs. the company has been increasing the price by $2 per month. Find the rate at Which revenue is changing when the company is selling widgets at $1?U each. ' dollars per month I Question 1 a on pt '5) 2 Q 99 6) Details Given the function below z) = {/1333 + 9 Find the equation of the tangent line to the graph of the function at z = 1. Answer in m: + b form. Ma) =|_ I Use the tangent line to approximate ll). 141.1) =|_ J Compute the actualvalue of f[l.l). What is the error between the function value and the linear approximation? Answer as a positive value only; error 2' J {Approximate to at least Edecimai places.) Question Help: E Video I Question 2 B 0.91 pt '3 2 Q 99 G) Details Use linear approximation. i.e. the tangent line, to approocir'nate {I 64.2 as follows: Let Hz} = {f}. The equation of the tangent line to x) at z = 641.can bewritten in the form y = m: + b where m is: l J and where b is: l I Using this. we nd our approucimation for {.- 642 isl Question Help: E '-.'ideo a Question 3 a on pt '0 2 z 99 6) Details Given the demand function DU?) 2 375 31). Find the Elasticity of Demand at a price of 536 At this price, we would say the demand is: Elastic Unitary Inelastic Based on this, to increase revenuewe should: Raise Prices Lower Prices Keep Piices Unchanged Question Help: E Video . Question 4 Given the demand function 93:] = 17" 3px, Find the Elasticity of Demand at a price of 52 At this priceJ we wuld say the demand is: Inelastic Elastic Unitary Based on this, to increase revenue we should: Keep Prices Unchanged Lower Prices Raise Prices Question Help: EI'-.'ideo . Question 5 200 p .' Find the Elasticity of Demand at a price 01'543 l At this price, we would say the demand is: Given the demand function 03:] = Elastic Inelastic Unitary Based on this, to increase I'evenuewe shduld: Lower Prices Keep Prices Unchanged Raise Prices Ban pt '5) 2 3 99 @Details BUM pt '9 2 8 99 @Details 0 Question 6 a on pt '0 2 3 99 G) Details Given the demand function D'P) = 250 219. Find the Elasticity of Demand at a price 0f 5120 At this priceJ we would say the demand is: Inelastic Elastic Unitaryr Based on this, to increase revenue we should: Lower Prices Keep Plices Unchanged Raise Prices I Question 7 B on pt '0 2 3 99 G) Details Suppdse the demand for a product is given by Dfp} = 5p + 236. A} Calculate the elasticity of demand at a price 01' 534. Elasticity =| ] [Round to three decimal places.) B] At what price do you have unit elasticity? (Round yd ur answer to the nearest penny.) Price = S I ]