captain-matticus-landpiratesinc
captain-matticus-landpiratesinc
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P = A * 2^t t is in minutes A = 1 P = 1 * 2^47 So, when P = 2^47, the dish is half full The dish is 1/3 full when P = (2/3) * 2^47 (2/3) * 2^47 = 2^t 2^48 / 3 = 2^t ln(2^48 / 3) = t * ln(2) ln(2^48) - ln(3) = t * ln(2) t = (48 * ln…
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A geometric series progresses like so: a , ar , ar^2 , ar^3 , ar^4 , .... , ar^n So, the second term would be a * r, the fourth term would be a * r^3 a * r = 100 a * r^3 = 64 (ar^3) / (ar) = 64 / 100 r^2 = 64/100 r = +/- 8/10 r = +…
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L = P * sum((1 / (1 + r/12))^t , t = 1 , t = n) r = annual rate n = number of payments L = loan amount 1 / (1 + r/12)) => 1 / (1 + 0.1021 / 12) => 1 / (12.1021 / 12) => 12 / 12.1021 sum(x^t , t = 1 , t = n) = S S = x + x^…
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L = P * sum((1 / (1 + r/12))^t , t = 1 , t = n) r = annual rate n = number of payments L = loan amount 1 / (1 + r/12)) => 1 / (1 + 0.1021 / 12) => 1 / (12.1021 / 12) => 12 / 12.1021 sum(x^t , t = 1 , t = n) = S S = x + x^…
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cos(arcsin(t)) = sin(arccos(t)) = sqrt(1 - t^2) t = 2x sqrt(1 - 4x^2)
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30x + 60y = 50 * 60 x + y = 60 30 * (x + 2y) = 50 * 30 * 2 x + 2y = 100 x + 2y - x - y = 100 - 60 y = 40 x + y = 60 x + 40 = 60 x = 20 20 liters of 30% 40 liters of 60%
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First, find the slope between the points m = (y2 - y1) / (x2 - x1) = (3 - 6) / (5 - 10) = -3/-5 = 3/5 Right off the bat, we can see that none of the choices are correct. Let's go ahead and figure out the formula for the line anyway y - k =…
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First, find the slope between the points m = (y2 - y1) / (x2 - x1) = (3 - 6) / (5 - 10) = -3/-5 = 3/5 Right off the bat, we can see that none of the choices are correct. Let's go ahead and figure out the formula for the line anyway y - k =…
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e^(-x) * dx + x^2 * e^(-x) * dx -e^(-x) + int(x^2 * e^(-x) * dx) u = x^2 du = 2x * dx dv = e^(-x) * dx v = -e^(-x) -e^(-x) + (x^2 * (-e^(-x)) - (-2) * int(x * e^(-x) * dx)) => -e^(-x) - e^(-x) * x^2 + 2 * int(x * e^(-x) * dx) …
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222.7 = v * t 222.7 = (v + 5) * (t - 1/6) (v + 5) * (t - 1/6) = vt vt + 5t - v/6 - 5/6 = vt 5t = (v + 5) / 6 30t = v + 5 222.7 = (v + 5) * (t - 1/6) 222.7 = (30t) * (t - 1/6) 222.7 = 30t^2 - 5t 0 = 30t^2 - 5t - 222.7 t = (5 +/- sqrt(25…
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Integrate by parts: int(e^(4x) * cos(x - 6) * dx) = ? u = e^(4x) du = 4 * e^(4x) * dx dv = cos(x - 6) * dx v = sin(x - 6) int(e^(4x) * cos(x - 6) * dx) = uv - int(v * du) int(e^(4x) * cos(x - 6) * dx) = e^(4x) * sin(x - 6) - int(4 * e^(…
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Integrate by parts: int(e^(4x) * cos(x - 6) * dx) = ? u = e^(4x) du = 4 * e^(4x) * dx dv = cos(x - 6) * dx v = sin(x - 6) int(e^(4x) * cos(x - 6) * dx) = uv - int(v * du) int(e^(4x) * cos(x - 6) * dx) = e^(4x) * sin(x - 6) - int(4 * e^(…
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cos(2 * (pi - t)) => cos(2pi - 2t) => cos(2pi)cos(2t) + sin(2pi)sin(2t) => 1 * cos(2t) + 0 * sin(2t) => cos(2t)
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cos(2 * (pi - t)) => cos(2pi - 2t) => cos(2pi)cos(2t) + sin(2pi)sin(2t) => 1 * cos(2t) + 0 * sin(2t) => cos(2t)
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cos(2 * (pi - t)) => cos(2pi - 2t) => cos(2pi)cos(2t) + sin(2pi)sin(2t) => 1 * cos(2t) + 0 * sin(2t) => cos(2t)
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cos(2 * (pi - t)) => cos(2pi - 2t) => cos(2pi)cos(2t) + sin(2pi)sin(2t) => 1 * cos(2t) + 0 * sin(2t) => cos(2t)
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cos(2 * (pi - t)) => cos(2pi - 2t) => cos(2pi)cos(2t) + sin(2pi)sin(2t) => 1 * cos(2t) + 0 * sin(2t) => cos(2t)
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Integrate by parts: int(e^(4x) * cos(x - 6) * dx) = ? u = e^(4x) du = 4 * e^(4x) * dx dv = cos(x - 6) * dx v = sin(x - 6) int(e^(4x) * cos(x - 6) * dx) = uv - int(v * du) int(e^(4x) * cos(x - 6) * dx) = e^(4x) * sin(x - 6) - int(4 * e^(…
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Integrate by parts: int(e^(4x) * cos(x - 6) * dx) = ? u = e^(4x) du = 4 * e^(4x) * dx dv = cos(x - 6) * dx v = sin(x - 6) int(e^(4x) * cos(x - 6) * dx) = uv - int(v * du) int(e^(4x) * cos(x - 6) * dx) = e^(4x) * sin(x - 6) - int(4 * e^(…
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Integrate by parts: int(e^(4x) * cos(x - 6) * dx) = ? u = e^(4x) du = 4 * e^(4x) * dx dv = cos(x - 6) * dx v = sin(x - 6) int(e^(4x) * cos(x - 6) * dx) = uv - int(v * du) int(e^(4x) * cos(x - 6) * dx) = e^(4x) * sin(x - 6) - int(4 * e^(…
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Integrate by parts: int(e^(4x) * cos(x - 6) * dx) = ? u = e^(4x) du = 4 * e^(4x) * dx dv = cos(x - 6) * dx v = sin(x - 6) int(e^(4x) * cos(x - 6) * dx) = uv - int(v * du) int(e^(4x) * cos(x - 6) * dx) = e^(4x) * sin(x - 6) - int(4 * e^(…
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First, find the slope between the points m = (y2 - y1) / (x2 - x1) = (3 - 6) / (5 - 10) = -3/-5 = 3/5 Right off the bat, we can see that none of the choices are correct. Let's go ahead and figure out the formula for the line anyway y - k =…
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30x + 60y = 50 * 60 x + y = 60 30 * (x + 2y) = 50 * 30 * 2 x + 2y = 100 x + 2y - x - y = 100 - 60 y = 40 x + y = 60 x + 40 = 60 x = 20 20 liters of 30% 40 liters of 60%
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L = P * sum((1 / (1 + r/12))^t , t = 1 , t = n) r = annual rate n = number of payments L = loan amount 1 / (1 + r/12)) => 1 / (1 + 0.1021 / 12) => 1 / (12.1021 / 12) => 12 / 12.1021 sum(x^t , t = 1 , t = n) = S S = x + x^…