8.  a model rocket is propelled upward from the top of a building 110 feet tall at an intial velocity of 192 feet per second. The fuction that describes the height of the rocket in terms of time t is s(t)=-16t^2+192t+110. Determine the maximum height that the rocket reaches

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Q: 1. Sand is being poured into a conical pile in such a way that the height is always one-third of the…

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Q: 12)Estimate rio by using a linear approximation at aこ 9. timi

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A: Given: The dimensions of a closed rectangular box are measured as 90 centimeters, 80 centimeters and…

Q: 5. Assume an American football has an ellipsoid shape and has a length of 27 cm and a height of 16…

A: Length in x-direction = 27cm    The point endsheight in  y-direction = 8cmheight in  z-direction =…

Q: 7)If a ball is Ehrown into Ehe air with a velociby of sIftis, it's height in feet after t seconds…

A: Please refer the attached image for complete solution.

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Q: b) write an expression for the position in terms of time t, use c (lower case) to denote constant of…

A: a =dv/dt where a is acceleration

Q: Determine the dimensions of the inscribed rectangle of maximum area. y = e¯*

A: Let the point on the curve for the rectangle with maximum area is (x,y) It can be written as: so…

Q: The length and width of a rectangle are measured as 35 cm and 28 cm, respectively, with an error in…

A: To determine the maximum error in the area.

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A: Given that a cylindrical specimen of a titanium alloy having original diameter of 2.96 mm…

Q: A ball is thrown vertically upward with a speed of 15 m/s. Determine the maximum height and the time…

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Q: The length and width of a rectangle are measured as 25 cm and 36 cm, respectively, with an error in…

A: Given length of a rectangle, l =25 cm           Width of a rectangle, w=36 cm We know that,  Area of…

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Q: Suppose a rocket is launch on a platform of height 9 meters with an initial velocity of 6 meters per…

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Q: Suppose that 3 of work is needed to stretch a spring from its natural length of 30 cm to a length of…

A: we know the work needed to stretch the spring W=12kx2 where x is the elongation. x=xf-xi=45-30=15…

Q: 3. A body of mass 5 kg is dropped from a height of 100ft with zero velocity. Assuming no air…

A: Given: A body of mass 5 kg is dropped from a height of 100 ft with zero velocity. To Find: To find…

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Q: The dimensions of a closed rectangular box are measured as 80 centimeters, 60 centimeters, and 100…

A: Let the dimensions of a closed rectangular box are: Length=L=80 cmWidth=W=60 cmHeight=H=100 cm And…

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Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: What values of a and b maximize the value of (x – x²) dx? |(Hint: Where is the integrand positive?)

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Q: Suppose that 3 ] of work is needed to stretch a spring from its natural length of 30 cm to a length…

A: Given problem:- Suppose that 3 of work is needed to stretch a spring from its natural length of 30…

Q: he measurement of the edge of a cube is found to be 15 inches, with a possible error of 0.03 inch.…

A: Given edge a =15±0.03  inch

Q: 1.) If the ball IS Thrown. vertically upward with a veloorty of 15 m/s then ts height after t…

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Q: The edge of a cube was found to be  60cm with a possible error of 0.1 cm. Use differentials to…

A: The volume of cube, V = x3, where x is the edge of the cube.

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A: Solution

Q: Use differentials to estimate the maximum error in the volume of a rectangular box with square base…

A: Here we find the error in volume by using differential.

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Q: (x) = 5sin2x

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Q: Suppose that a car starts from rest, its engine providing an acceleration of 10 ft/s2, while air…

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Q: √35.9

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Q: A miniature quadcopter flies in a curve line from one point to another. Suppose that the path of the…

A: The path of the quadcopter is given by the equation y=2.15+2.09x-0.41x2, 0≤x≤3.6 (i) The distance of…

Q: 4. Four identical bricks are stacked up on top of each other. Each has a length of a and a mass of…

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Q: Determine the dimensions of the inscribed rectangle of maximum area.

A: Determine the dimensions of the inscribed rectangle of maximumarea.

Q: Find the fourth iteration value in finding an extremum (maximum/minimum) value of              f(x)…

A:

Q: The length and width of a rectangle are measured as 38 cm and 34 cm, respectively, with an error in…

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Q: 4. Use your figure to study the sign of vr(t) in the time interval [-4 : 4]. Does vr(t) have any…

A: Given voltage potential v(t) is, vt=0.250t4+0.166t3-0.500t2                   .......1 and the…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.