a projectile launched at t=0 (t is measured in seconds) follows a path given by x=30t, y=-5t^2+80t, where x is the horizontal direction and y is the upward direction. the projectile lands after  a. 16 seconds b. 8 seconds c. 4seconds

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A: Let us considre the function y=f(x) The derivative the function is denoted as dydx=f'(x) Derivative…

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A:

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A: This question is based on application of Derivative.

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A: We have to find absolute value of gradient at x=2 for the given function.

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A: To find the equation of tangent and equation of normal at the given curve .

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A: we have to find an equation of the form y=f(x) for a curve with x-intercept 2 whose tangent line at…

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A:

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A: To find - Point on the given line closest to the origin.

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A: 2x + √(x+y) = y  So,  √(x+y) = y - 2x So, x+y = (y-2x)² So, x+y = y² + 4x² - 4xy  So, y(1+4x) - y² =…

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A: Use distance formula between two point and then differentiate

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A:

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A: Topic:- application of derivatives

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A: Let (m,n) be the point on the line which is closest to the origin.Put n = m, y = n, in y = 5x + 3…

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A: A particle is moving along a line in such a way that v centimeters per second is the velocity of the…

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A: Topic:- application of derivatives

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A: Find the point on the line y = 4x +5 that is closest to the origin. (x,y) = ____

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A: Let L be the length of curve  F(x) = 3x + sinx

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A: Consider the following equation of parabola: y=x2 Differentiate y with respect to x: dydx=ddxx2=2x

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A: The solution is given below in the next step:

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A: Suppose a line passing through with slope  m then equation of line is .