Solve the initial value problem for r as a vector function of t. dr Differential equation: = - ti-5tj-5t k dt Initial condition: r(0) = 9i + 8j + 5k r(t) = (O i+ (O i+ (O k

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A: We have to find force as per given conditions.

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A: Given that      V =FA0κCA02∫0X(1+εX)2(1-X)2dX                        let us assume 1-X = t…

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A: This question is related to definite integration, we will solve it using given information.

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there were 50…

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A: We can explain the answer as below.

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A: Given r=3cosθr=1+cosθ

Q: 2. Evaluate ř(t) dt: 4 4t ř(t) t2 + 5t + 6' î + 2e4t cos t j - k; a = 0 and b = 4 t2 + 1

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A: we know  ex = 1+ x/1! + x2/2! +.....

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A: Given f(x)=5-5x2  interval [1,5]Number of rectangle =4

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A: We have to choose the correct option from the given options according to the given information

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A: Solution is given below:

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A: Given query is to find statement is true or false.

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A: The given integral: ∫sinh x-1cosh xdxWe need to find the antiderivatives.

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Q: Find fxx​(x,y), fxy​(x,y), fyx​(x,y), and fyy​(x,y) for the following function.…

A: To find fxxx, y, fxyx, y, fyxx, y and fyyx, y for the following function.fx, y=3x2y2+4x3+6y

Q: 7. Let E be the region in R enclosed by the cone z = Va2 + y? and the paraboloid z = a2 + y?. Then…

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Q: fxx​(x,y), fxy​(x,y), fyx​(x,y), and fyy​(x,y) for the following function.   ​f(x,y)=5x2y2+2x7+3y

A: Partial derivative

Q: A firm produces two types of calculators each​ week, x of type A and y of type B. The weekly revenue…

A: A firm produces two types of calculators each​ week, x of type A and y of type B. The weekly revenue…

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Q: .

A: We will find the derivative.

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A: We have to find the area between the curves.

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A: The solution is given in the next steps.

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

Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = e-9x.

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