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35 Cards in this Set
- Front
- Back
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Arc Length Formula |
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Surface Area |
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Surface Area about y = c |
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Surface Area about x = d |
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Find fluid pressure |
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Force due to fluid pressure with easy centroid |
( weight density of liquid) × (depth of centroid) × (area of plate) |
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Centroid no area |
x = My/sum(masses) y = Mx/sum(masses) |
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Centroids of triangles |
Measure 2/3 along the line connecting a vertex to the midpoint of the opposite side |
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Centroid of complex object |
x = sum(each center x*each area)/total area y = sum(each center y*each area)/total area |
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Volume centroid |
2π × (distance from centroid to rotation axis) × (area) |
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Find centroid with area |
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Find moment y and x when given point and masses |
Mx = each y point * point mass My = each x point * point mass |
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Find moment about x-axis |
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Find moment about y-axis |
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Find equation of tangent line to the curve |
y-y0 = m(x-x0) find x0 and y0 by replacing t in each formula m = (dy/dt)/(dx/dt) |
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Find where concave up/down |
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Find horizontal and vertical tangents |
to find vertical: take the derivative of x formula make it equal to 0 find t / theta to find horizontal: take the derivative of y formula make it equal to 0 find t / theta apply back in x and y formula to find x and y of horizontal |
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Arclength parametric |
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Surface parametric x-axis |
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Surface parametric y-axis |
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Area under the curve parametric x-axis |
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Area under the curve parametric y-axis |
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Polar important formulas |
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Arclength Polar |
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Area Polar |
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Parabola |
When the parabola is vertical: 4d(y - k) = (x - h)^2 Vertex: (h, k) Focus: (h, k + d) Directrix: y = k - d When the parabola is horizontal: 4d(x - h) = (y - k)^2 Vertex: (h, k) Focus: (h + d, k) Directrix: x = h - d |
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Ellipse |
(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1
c^2 = |a^2 − b^2 | horizontal if a > b vertical if b > a circle if a = b center: (h, k) vertices: (h − a, k), (h + a, k), (h, k − b), (h, k + b) If a > b the foci are (h − c, k), (h + c, k) If a < b the foci are (h, k − c), (h, k + c) |
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Hyperbola |
(x − h)^2 / a^2−(y − k)^2 / b^2= 1 c^2 = a^2 + b^2 Center: (h, k) Vertices: (h − a, k), (h + a, k) Foci: (h − c, k), (h + c, k) Asymptotes: y − k = ±b/a(x − h) (y − k)^2 / b^2−(x − h)^2 / a^2= 1 c^2 = a^2 + b^2 Center: (h, k) Vertices (h, k − b), (h, k + b) Foci: (h, k − c), (h, k + c) |
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Eccentricity |
|PF|=r |Pl|= d-rcosθ |
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How to define which conic |
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Polar Equation with eccentricity |
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Perihelion |
Is the smaller distance from the vertices to a point on the major axis, and its defined by a(1 - e). Where a is the semimajor axis. |
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Aphelion |
Is the largest distance from the vertices to a point on the major axis, and its defined by a(1 + e). Where a is the semimajor axis. |
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Polar Equation with semimajor axis |
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Hydrostatic Pressure and Force |
P = F/A = pgd |
