1) An ostrich runs along a mountain path with coordinates given by r(t) =< et, e-t, √2 t> a) What is the change in the ostrich's altitude (z-direction) from t=0 to t=10? b) What is the ostrich's speed in the x-direction when t=4? c) What is ostrich's speed in the y-direction when t=4? d) Find a formula for the total distance travelled by the ostrich from t=0 to t=4

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A: This question can be solved using the concept of higher order derivatives.

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A: We have to do the partial derivatives

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A: Above question is solved.

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A: A tunnel is constructed with a semielliptical arch. The width of the tunnel is 60 feet, and the…

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A: Given,   y=e2x-e-2xe2x+e-2x

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A: This question can be solved using the concept of planes in three dimensional geometry.

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A: We can solve this as follows:

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A: We have to evaluate ∫4x+4 dx.

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A: See the answer below

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A: Given.

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A: Given function, f(x)=3-2-xThat isy=3-2-xReplace x and yx=3-2-yAdd 3 on  both sidex-3=-2-ySquaring on…

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A: To find and plot the domain of the given functions.

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Q: 10. Find similarities and differenced between the quadratic, the sine, and the exponential functions…

A: Here, the given functions are: f(x)=x2, g(x)=sin(x), h(x)=2x

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A: Given :∫4x2-64dx