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Find an equation? (answer)

Use point-slope form, y + 6 = (-1/4)(x + 1) -------- Attn: You don't need to change it to slope-intercept form.

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Find an antiderivative? (answer)

Use mental substitution, ∫e^(x+e^x)dx = ∫e^x * e^(e^x) dx = ∫e^(e^x) de^x = e^(e^x) <==Answer

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Find the rate of the jet (answer)

Let v = the rate of the holicopter. So 4v = the rate of the jet. Balance by the total time, 1080/(4v) + 180/v = 5 Multiply both sides by 4v, 1080+720 = 20v v = 90 mph 4v = 360 mph Answer: The rate of the jet is 360 mph.  

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amount originated (answer)

Let x be the original amount. Balance by spending, x - (4/5)^2 x = 72, focusing on the remaining part each time. Solve for x, x = $200 Answer: The original amount was $200. ------- Hi Murtaza; You are correct. I misread the problem. This problem can be done as above...

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Write sin(sin^-1x-cos^-1x as an algrebraic expression in x. (answer)

sin(sin^-1x-cos^-1x) = sin(sin^-1x)cos(cos^-1x) - cos(sin^-1x)sin(cos^-1x)  = x^2 - (1-x^2) = 2x^2 - 1 ------ Attn: cos(sin^-1x) = sqrt(1-x^2), since the domain of sin^-1x is in the first and fourth quadrants, where cos x is positive. sin(cos^-1x) = sqrt(1-x^2),...

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Rewrite sin(x+pi)+sin(x-pi) as a product. (answer)

Method 1. sin(x+pi)+sin(x-pi) = 2sin x cos pi, after expanding and collecting like terms = -2sin x   Method 2. sin(x+pi)+sin(x-pi) = -sin x - sin x, using reference angle = -2sin x

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