Problem 7  A trough is 4 feet long and 1 foot high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y=x^6 from x=−1 to x=1. The trough is full of water. Find the amount of work required to empty the trough by pumping the water over the top. Note: The weight of water is 62 pounds per cubic foot. Work=___________

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Q: Problem 4 State whether false or true: The parabola is an even function. All functions are either…

A: Note:- This are multiple questions and according to our comapny guideline we can do maximum 3…

Q: Problem 4. Find an equation of the tangent line to the curve at the following point: y = (1 – 82)1",…

A: The equation of tangent is  y-y1= m(x-x1)  Where is m is slope

Q: Problem 3. Find an equation of the parabola that has a vertical axis, its vertex at (-2, 4), and…

A: Topic- equation of parabola

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A: solution of the given problem is below ..

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Q: Problem 8. Cost engineers at NASA have the task of projecting the cost P of major space projects. It…

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Q: In Problems 27 through 31, a function y = g(x) is describe by some geometric property of its graph.…

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Q: Given f (x) = x^4– 6x + 2. By using second derivative test, estimate the critical number, concavity…

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Q: Problem 1 Pr A weather balloon is released and rises vertically such ( that its distance s(t) above…

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Q: Problem 3. If the temperature of the body drops from 120° C to 80° C in 15 minutes when the…

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Q: Problem 7 Using the position function s(t) = -4.9t2 + vot + s, Determine the maximum height achieved…

A: Given that v0= 96 and s0= initial height =at the ground = 0 feet Plug them in the given equation.

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Q: Question 7 A cable of length L is cut into 2 pieces. One piece of the cable is used to form a square…

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Q: Question 5 5 Draw a large, neat and accurate sketch of the graph of y=x²-7x+10. Use rectangles of…

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Q: Question 8. Find an equation of the tangent line to the graph of y = x² +1 at the point (2, 5).

A: given function is y=x2+1 point is (2,5).

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Q: QUESTION 7 Given the quadratic function f(x)=2x2-8x +3 a) state the x - intercepts h)state the y…

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Q: Problem #8: A rocket is being launched. After a while, it rises at a constant velocity of 30 miles…

A: Let's find.

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Q: Problem 1. The function h = f(t) = 90 – 5(t – 2)2 , 0<t < 6, %3D gives the height of a rock (in…

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Q: Problem 3. Consider the graph of the function defined by the equa- tion x + xy+y° =3. The slope of…

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Q: QUESTION 6 Find an equation for the tangent to the curve at the given point. y = x2 - 3, (-3, 6) O y…

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Q: Please show all steps to your solution and explain all work clearly. Midterm is based on Chapters P…

A: Given:

Q: Please show all steps to your solution and explain all work clearly. Midterm is based on Chapters P…

A: X- intercept – It is a point on the graph where y is zero and the graph crosses the x-axis.…

Q: Problem 5. An observer is positioned 3km away from a rocket launch pad. How fast is the distance…

A: This question can be solved using the concept of rate of change.

Q: Problem 6. A rectangular box with a square base has a volume of 150 cubic feet. Find a formula for…

A: Use the formula of volume and surface area of rectangular box with square base.

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.