Problem 3. The linear transformation T : C²(R) –→ C°(R) is defined by d d T(f) drzf +3-f – 4f. Show that the functions y1 (x) and y2() from Problem 1 and Problem 2 form a basis for kerT. (Hint: By Theorem 8.1.6, the set of solutions to a second order differential equation y" + 3y' – 4y = 0 is a vector space of dimension 2.)

y = demand for the large bottle of Fresh in the sales period(Demand)x1 = the price of product 1x2 = the price of product 2x3 = the advertising expenditure for Freshx4 = the price difference in the sales periodAdver = types of advertising campaignsCampaign A consists entirely of television commercials, campaign B consists of a balancedmixture of television and radio commercials, and campaign C consists of a balanced mixture oftelevision, radio, newspaper, an dmagazine ads. To ultimately increase the demand for Fresh,Enterprise Industries’ marketing department is comparing the effectiveness of three differentadvertising campaigns. To compare the effectiveness of advertising campaigns A, B, and C, wedefine two dummy variables. Specifically, DB is 1 if campaign B is used and 0 otherwise, DC is1 if campaign C is used and 0 otherwise. Our proposed model is  y = β0 + β1x4 + β2x3 + β3x 2 3 + β4x4x3 + β5DB + β6DC

lotal Revenue for a procluctis R=-x²+456y2+5250o How many R=-x³+456y units should be produced to revenue! maximize

ek of 3/8/2021 Question Details Do Now 3/8/2021 Determine if the equation is a linear equation write yes or no if yes write the equation in standard form. y%=D4x + 3 O9 A 2:30