Consider the equation of the surface S given by x2z2 + xy + yz = 7. An equation for the plane tangent to S at the point (−1, −1, 3) is given by: Answers in the picture
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Consider the equation of the surface S given by x2z2 + xy + yz = 7. An equation for the plane tangent to S at the point (−1, −1, 3) is given by:
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- Show that z / [(z-1)(z-3)] = -3 Σ [(z-1)n / 2n+2] - [1 / (2(z-1))] for 0 < |z - 1| < 2.A family is coloring eggs and wants to make two shades of purple, “light purple” and “deep purple”. They have 30 tablespoons of red solution and 2 tablespoons of blue solution. If “light purple” consists of 2% blue solution, and “deep purple” consists of 10% blue solution, how much of each version of purple solution can be created? Let x represent thenumber of tablespoons of “light purple” to be created, and let y represent the number of tablespoons of “deep purple”. Based on the information provided, the two tablespoons of blue solution will be distributed according to the following linear equation. 2 = ? x + ? y Complete the equation above by filling in the boxes, then write a similar linear equation that shows the distribution of the red solution. Solve the resulting system of linear equations.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
- Suppose (x1,x2) + (Y1,Y2) is defined to be (x1 + Y2 ,x2 + Y1). With the usual multiplication cx = ( cx1, cx2 ), which of the eight conditions are not satisfied?U.S. Energy Consumption Energy consumptionin the United States in quadrillion BTUs can bemodeled by C(x) = -0.013x2 + 1.281x + 67.147,where x is the number of years after 1970.a. One solution to the equation 87.567 = -0.013x2 +1.281x + 67.147 is x = 20. What does thismean?b. Graphically verify that x = 20 is a solution to87.567 = -0.013x2 + 1.281x + 67.147.c. To find when after 2020 U.S. energy consumptionwill be 87.567 quadrillion BTUs according to themodel, do we need to find the second solution tothis equation? Why or why not?3)The owner of a small-appliance manufacturer finds that if the firm produces and sells x blenders monthly, the total monthly profit P (in dollars) is given by P(x)=8x+0.3x2-0.0013x3-372. The owner wants to produce no more than 225 blenders/month in order to maintain quality. a)How many blenders per month should the company produce in order to have a monthly profit of at least $3000. b)How many blenders should be produced in order to maximize profit? What would the annual profit be, rounded to the nearest dollar, if that many were produced and sold?
- 1. Simplify: a. 3x2y3 / x3y4 b. 5x2y3z2 / 2xy3z c. 14x3y2z5 / 7x2y24 d. (-6xy3) / 3x2z3 2. Simplify: a. (-8x3y2) / -2x)4 b. (-12x2y3) / (3xy2)3 c. 28x3z2 / (-4x3 y2 z2) d. (-3x2y2)3 / (2xy3z)3What is the value of Z if only 1.5% of all possible Z values are larger? The value of Z if only 1.5% of all possible Z values are larger is14 - Since b =2i ̂-j ̂-3k ̂ and c =i ̂-5j ̂+k ̂, what is the result of ( b . c )? a) 4 B) 5i ̂-2j ̂+3k ̂ NS) -16i ̂-5j ̂-25k ̂ D) 16i ̂+5j ̂+25k ̂ TO) 3