6 A company manufactures and sells x headphone per day. If the cost and revenue equations are: C(x)= 7,000 - 2x and R(x)= 10x -0.001x². 0≤x≤ 10,000 a) Use the differentials to approximate change in revenue if production increase from 2000 to 2010 per day? b) Use the differentials to approximate change in profit if production increase from 2000 to 2010 per day? c) Use part (a) and (b) to approximate change in cost if production increase from 2000 to 2010 per day

How to work out the slop on y= 3x -4

2. Expand and simplify to express each equation in standard form. [2, 2, 2, 3, 3, 2] a) y = (x + 5)(x + 2) b) y = (x- 4)(x+ 3) c) y = (2x- 3)(x-6) d) y = (3x + 4)2 e) y = 3(x – 4)2 +1 f) y = (4x + 3)(4x- 3)

You are part of a government task force evaluating whether new models of cars will meet fuel efficiency standards set out by the newly signed climate bill.  You have run an ANCOVA model that predicts fuel efficiency (in miles per gallon) as a function of vehicle weight (measured in thousands of lbs, where a value of 2.5 would correspond to 2,500 lbs), horsepower, and number of cylinders in the car (cylinders is a factor in this model with 3 levels: 4 cylinders, 6 cylinders, and 8 cylinders).  Your analysis tells you the following; The mean miles per gallon of all cars analyzed is 20.09 The mean weight of all cars analyzed is 3.217 thousand lbs The mean horsepower of all cars analyzed is 146.7 The regression coefficient for weight is -3.18 miles per gallon per additional thousand lbs  The regression coefficient for horsepower is -0.023 miles per gallon per additional unit of horsepower Cars with 4 cylinders get 2.13 more miles per gallon, on average, than the average car Toyota is…

What is the dependent variable in y= -3x+2 and x= -1,0,3

Show that the equation x+y+z=4,2x+5y-2z=3,x+7y-7z=5 are not constant

2. AMBK Company manufactures furniture such as sofas and tables. In their current inven- tory, a total of 48 planks of wood are left. Each sofa needs four planks of wood to be made while each table needs two planks of wood to be made. The company earns a profit of hundred pesos where P(x, y) = 12xy for selling a units of sofas and y units of tables. With their current inventory of woods, how many sofas and tables are needed to be produced to maximize their profit? (Use the Lagrange method of optimization.)

" Coefficients linear in the two variables " ASAP. Thank you

1. calculate the following:  a. (-3x2y2) X (-2x3y) X (-3y2) b. (-5x23) X (-2x3y2) X z4 c. 3y2z X (-4y2x) X (x2y)3 d. 4x2y3z2 X x3y2z3 X (-2xz3) e. (-3yz)2 X (2x2)3 X (x2y3)2 f. 3xyz2 X x3y2 X 2xy4 g. 6x2z2 X 2x3z X (x2y)3