3. 4. If u=[2,-5] and v=[k,4], and u is orthogonal (perpendicular) to v, then the value of k is: a) -10 b) -2.5 c) 10 d)2.5 Which point is not a solution to the equation 2x + 4y − z + 14 = 0? a)(0,0,14) b)(1,0,16) c)(1,1,20) d)(2,0,22)

5. Which point is not a solution to the equation 3x - 4y + z-12=0? a) (-8,-9,0) b) (4,1,4) c) (16,10,4) d) (18,12,2)

Q2: Choose the correct answer for the following: 1) The values of x and y for this equation (x – 3) + i (y + 2) = -1+ i 3 are: a) x =-2, y =1 b) x=2, y = 1 c) x = 2, y = -1 d)x =-2, y =-1 -x, +4x, +. 2) If 2x, +2x, =1 +3.x3 =2 , the values ofx1, x2 and x3 for the following system of x; – 3x, +5x3 = 0 equations are: (Use Cramer's rule) 3 2 3 Xz = 7" 3 b) x1 4 а) x, = - ,Xz = 14' 14 14 14 14 c) 3 4 3 d) 3 2 3 X =- 14 14 =- 14 14 14 1/ x 1 3) , dx, where t =. The result of this integral is: (Use by parts method) 3 1/ x 1/ x e 1/x e 1/x а) +e' 1/x b) 1/x +C c) +e"x+c_d) 1/x 1/x -e +c +c x 4) [x y'dA,R is the triangular region with points (0, 0), (1, 0), and (1, 1), where R (dA means dx dy or dy dx). The value of the double integral is: b) 1 c)_1 15 1 d) 13 1 а) 16 14 2 Jx 3 y T y'e*dydx 5) b).

12. Expand and simplify. (5x + 3y)² - (4x + y) (6y - x) 13. The formula V = nr³h represents the volume of a cylinder. Identify the variables and constant(s) in this formula. a) b) c) d) Which variable(s) in the formula V = nr³h would you need to set as a constant to generate i) a linear equation and ii) a quadratic equation? How should r and h be related to generate a cubic equation? Determine the radius of a cylinder with volume 600 cm³ and height 10 cm.

formulate this probblem. There are currently 3 machines in a factory: P1, P2, and P3. Assume that this rectilinear shaped factory is located on the first quadrant of the coordinate system and one corner is at the origin (point (0,0)). The coordinates of the existing machines are as follows: P1=(10,15), P2=(20,25) ve P3=(40,5) To meet the increasing demand and respond to changing customer demands, the company decided to grow and acquired two new machines: N1 and N2. When these two machines are put into operation, they will exchange materials with each other and with the other three machines. 400 units of material will be transported between the 2 two new machines in a week. Similarly, 400 units will be transported between N1 and P1, 0 between N1 and P2, and 500 units between N1 and P3. The transportation between N2 and P1, P2, and P3 are 200, 100, and 0, respectively. Materials are transported with an overhead crane. This crane can move linearly in x and y coordinates and can move…

15) Parallelogram ABCD has coordinates A(1,5), B(6,3), C(3,–1), and D(-2,1). What are the coordinates of E, the intersection of diagonals AC and BD?

Express P,P2 in the form v = vi+V½]+V3k if P, is the point (5, -6,-5) and P2 is the point (7, - 9, - 9). O A. V= - 21 + 3j + 4k O B. v= 21- 3j- 4k O C. v -21-3j + 4k O D. v= -2i + 3j - 4k Click to select your answer. 9 Type here to search a 99

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3) Solve the defferential equation..(b and variables) are D2+4D+3)b=1+ 2g +3g ² CS CamScanner ile tarandı

P.MS.A... S1.P3.G... Co you want to do =、三 A Styles v ... 11 Question * (5 Points) In rectangle RSTU diagonals RT and SU intersect at O. If RT = 6x +4 and OS = 7x - 6, what is US? (GCO.10d) U. a 64 b. 10 c. 16 d. 2 Enter your answer DELL !!!