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TrianglesTriangles 100 50 25 10 5GraphsGraphs Polar Form FunctionsFunctions LeftoversLeftovers Review for the Final 100 50 25 10 5 100 50 25 10 5 100 50 25 10 5 100 50 25 10 5 The 104 Challenge Review for the Final Final Round

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Triangles

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CheckWork In any right triangle, the sum of the squares of the sides is equal to the square of the hypotenuse. Go Home Go Home 5 Point Question What is the Pythagorean Theorem?

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In the triangle ABC, C = 90 o, A = 25 o and a = 3. Find b. 10 Point Question CheckWork Go Home Go Home b = 6.433

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11.49 25 Point Question Find c in the triangle below: CheckWork Go Home Go Home 12 cm c 38 o 102 o

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13.099 cm 50 Point Question Find the length of the missing side in the triangle below. CheckWork Go Home Go Home 68 o 13 cm 10 cm

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Find all three missing angles in the triangle below. 100 Point Question CheckWork Go Home Go Home A = 44.42 o B = 18.54 o C = 117.04 o 5 14 11 A B C

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Graphs

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CheckWork It has an even degree and negative leading coefficient. Go Home Go Home The graph of a polynomial falls to both the left and right. What can we tell about the polynomial? 5 Point Question

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10 Point Question Sketch the graph of y = 3cos(2x) – 5. CheckWork Go Home Go Home period is Pi, amplitude is 3, midline is -5. It starts at (0,-2).

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25 Point Question CheckWork Go Home Go Home Find the equation for a sine function that matches the graph below. Y = 2sin(x-π/4) +4 (π/4, 4) (9π/4,4)

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Find the equation for the polynomial function graphed below. 50 Point Question CheckWork Go Home Go Home Y = -2(x-3)(x+1) 2 (0,6)

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Find the equation for the rational function graphed below. 100 Point Question CheckWork Go Home Go Home Y = -2(x 2 -9)/(x 2 -x-2) (0,-9)

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Polar Form

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Plot the polar point (3, 150 0 ). 5 Point Question CheckWork Go Home Go Home 30 o 3

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Convert the point (-8,-6) to polar coordinates. 10 Point Question CheckWork Go Home Go Home (10, 216.9 0 )

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-67.29i + 251.14j A plane flies N 15 0 W at a speed of 260 miles per hour. Write the plane’s velocity vector in component form. 25 Point Question CheckWork Go Home Go Home

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50 Point Question Write the complex number 5 – 3i in polar form. CheckWork Go Home Go Home

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Compute (1 – i) 1/3. Write your answer in polar form. 2 1/6 e -πi/12 100 Point Question CheckWork Go Home Go Home

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Functions

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A power function 5 Point Question What type of function is this? F(x) = 3x -2 CheckWork Go Home Go Home

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Find the equation for the power function that passes through (1, 5) and (5, 1/25) 10 Point Question F(x) = 5x -3 CheckWork Go Home Go Home

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Graph the polynomial f(x) = 3(x - 3) 3 (x + 20), labeling all zeros, y-intercepts and asymptotes. 25 Point Question CheckWork Go Home Go Home (3,0), (-20,0), (0,-1620)

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50 Point Question Asymptotes y = 0, x=2, and x=-5, (which doesn’t show well) Intercept Points: (-4,0),(0,1/5) Intercept Points: (-4,0),(0,1/5) Sketch the graph of CheckWork Go Home Go Home (-4,0)

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100 Point Question Find the exact value of cos -1 (cos(28π/25)). 22π/25 CheckWork Go Home Go Home

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Leftovers

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U = 3i – 5 j, V = 4i – 2j. Find the dot product of the vectors U and V. 5 Point Question CheckWork Go Home Go Home22

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What is the equation for a rose curve with 8 petals of length 3. 10 Point Question R=3cos(4Θ) CheckWork Go Home Go Home

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25 Point Question Solve the equation: tan(2Θ) = √3. Θ = π/6 + πk/2 CheckWork Go Home Go Home

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50 Point Question Solve the equation: sin(x) + 2cos 2 (x) = 2 CheckWork Go Home Go Home x = πk, π/6 + 2πk, 5π/6 + 2πk

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Verify the identity: 100 Point Question CheckWork Go Home Go Home sure enough…

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Cable on right: 222 lbs. Cable on left: 141.8 lbs Cable on left: 141.8 lbs A 235 lb weight is suspended by two cables as shown in the diagram. Find the force in each cable. Final Question CheckWork Go Home Go Home 235 lbs 54 o 23 o

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The Pythagorean Theorem. 8/18/20152 The Pythagorean Theorem “For any right triangle, the sum of the areas of the two small squares is equal to the area.

The Pythagorean Theorem. 8/18/20152 The Pythagorean Theorem “For any right triangle, the sum of the areas of the two small squares is equal to the area.

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