Match the equation with its graph. y=x²-x 10 2.5 8 2 2. y 1.5 4 -2...
6. Match the following equations to the graph that represents it. [4 Points] Equation A: y = x2 + 2 Equation B: y = -x + 2 Equation C: y = (x - 2)2 Equation D: y = 2x2 y 37 Y 3 -3 3 X -3 LL 3 3 x -11 Equation: Equation: Equation: Equation: 7. Let f(x) = Vx. Write the equation for the resulting function when the following transformations are performed in order) onf (x): [3 Points]...
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d.
Match the following z-plane diagrams to their corresponding difference equations 1.5 1.5 0.5 .' 05 05 05 Real Part Real Pat 1.5 1.5 0.5 0.5 05 05 ' Real Part Real Part 1.5 1.5 0.5 05 Real Part Real Part Difference Equation Options: Equation 1: y[n] 0.5yIn-1] + xm Equation 2: yn0.9yfn - 1] + 0.5x[n +0.5xn -1] Equation 3: y[n] =-0.9y[n-1] + 0.5z[n] _ 0.5z[n-1] Equation 4: y[n] = z[n] + x[n-1] + z[n-2 + z[n-3] Equation...
Match each function with its graph. Give reasons for your choices. 1. / (x,y) = 1 +sin y 2. S (x,y)= 4-r - 4. S (x,y) - In (x2 + y2 + 1) 5. S (x,y)=x? / 3. S (x,y) = cos(x + y) 6. f(x,y) = xy 0 55 0X A 10 800
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7. Sketch the graph of f(z, y) 2.5 60 40 20 1.5 20 -40 0.5 -1 0.5 0 0.5 1 -3-2-101 2 3 (a) s 3 2 1 0 1 -2 10 1 -2 01
7. Sketch the graph of f(z, y) 2.5 60 40 20 1.5 20 -40 0.5 -1 0.5 0 0.5 1 -3-2-101 2 3 (a) s 3 2 1 0 1 -2 10 1 -2 01
Consider the function x) = 6x + x2 and the point P(-2,-8) on the graph of f (a) Graph f and the secant lines passing through P(-2, -8) and Q(x, f(x)) for x-values of -3, -2.5, -1.5 -10 -8 68 10 -10 -8 2 46 810 -2 -8 8 10 8 10 -10-8 -10-8 -8 (b) Find the slope of each secant line (line passing through Q(-3, f(x))) (line passing through Q(-2.5, f(x))) (line passing through Q(-1.5, f(x))) (c) Use...
Matching: Match the equation of each plane to its scalar form 2x-y-2-6.0 b.y Answer Alternate Equation 17 [x, y, :1 = [3, 2, 1]+42. 0, 31+13.0,2]s,t ER. 18. [x,y,:] = [5.-2. 31+43.-2.4]여5.-2, 6] s, t E R. 19. -1+2+3 20. [x,y,s]-[5, 4,-2]+42,-1,-1] 1.3.3]stER. 21. x--t + 22 y-2-1+4s s,tER. 22. Find the values of k such that the three planes never intersect in a point. (3 marks 4x+y- 17- x-y-kz+11-0 Page 3 of 6 23. The equation of a plane...
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2.5 N 1.5 1 0.5 Temperature (deg C) 0 -0.5 -1 -1.5 -2 1 6 -2.5 0 2 3 4 5 Time (min) Graph 1. Freezing point of pure solvent (2) On Graph 1, extrapolate and give the freezing point of the pure solvent to the nearest 0.1°C. Show the extrapolation on graph 1.
The graph of y = f(x) is shown below: y = f(.) 1 2 3 4 5 6 7 8 9 For which values of S and is the following statement FALSE: If 2 - 51 < 8, then f(x) - 2 < 8=1, € = 2 • 8 = 2, = 1.5 8 = 1, € = 3 6= 3, € = 1.5
5. Which is the graph of the following parametric equation? (1 point) 2 x-E and y 2-3 .y t-4 5 t-4 3- 2- 3- 2- 5 -4 -3 -2 10 -1 2 3 4 t-1 t=0 it 6: Parametric Functions 6 3 2- 1- -5-4-3-2-1.0 -1 -2 -3 t 0 2- t= 16 2 4 -3 2 1 12 3 4 5 -1 1 -2 -4 ametric Functions Test 6: Parametric Functions t 16 1- 1/2 3 4 5 -1...
P(X < 0.5, Y < 1.5 ) =
P(X ≤ 1) =
P(X < 1.5) =
P(X > 0.5, Y < 1.5 ) =
E(X) =
V(X) =
E(Y) =
V(Y)=
The following is a joint probability mass function. x xx (x,) 1/4 0 1 1/8 10 1/8 1 1 1/4 2 2 1/4 Determine the following. Give exact answers in form of fraction.