The height above ground of an object movingvertically is given bys = -16t2 + 96t + 112,with s in feet and t in seconds. Find its maximum height and when it occurs

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A: We, know at maximum or minimum of a function f(x), the first derivative, f'(x)=0. At maximum,…

Q: The path of a diver is modeled by f(x)= -4/9x2 + 24/9x + 9 where f(x) is the height (in feet) and x…

A: Since, we have been given the path of driver by :-f(X)=Y=-49X2+249X +9 -(i)Our aim is to find the…

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Q: Find the equation of the quadratic function f whose graph is shown below. (5, 4) s(x) = | 10 12 14…

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Q: (3) If a projectile is launched into the air at 29.4 feet per second from aheight of 60 feet, its…

A: 3. given that                                                         u=29.4 feet per secondh=60…

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Q: The maximum running speed (in km/h) of mammals is given byVmax= ƒ(x) = 23.6x0.165,where x is the…

A: (i) As the body mass of the given species is 62 kg,  we get the maximum running speed of  the…

Q: Find the length of the curve. 1 10x3' y 6 + 1 ≤ x ≤4

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Q: If A toy rocket is launched straight up from the roof of a garage with an initial velocity of 80…

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Q: The height, h metres, of an object thrown vertically upwards at time t seconds after its release is…

A: Given function represents height of the object at time t.

Q: The profit from producing n quilts per year is given by the function P(n)=−15n^2+270n−840, where P…

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Q: 2. For the quadratic relation, y= -(x+0) (x + 6) explain how to find Equation of the axis of…

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Q: Complete the following table. Amount Invested Annual Intesest Rate Accumulate Amount Time (t) in…

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Q: Approximate the solution(s) to x3-2x+2=0 using a graphing utility

A: x3-2x+2=0

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Q: The path of a diver is modeled byf(x) = (−4/9)x2 + (24/9) x + 12where f(x) is the height (in feet)…

A: Givenf(x) = -49x2+249x+12here, a = -49 , b = 249this is downward opening parabola.

Q: If a projectile is launched into the air at 29.4 feet per second from a height of 60 feet, its…

A: A projectile is launched into the air at 29.4 feet per second from a height of 60 feet, its height…

Q: The daily profit from the sale of a product is given by P = 32x − 0.2x2 − 200 dollars, where x is…

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Q: Find a formula for the quadratic function whose graph has its vertex at (−3,2) and its y-intercept…

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Q: Every second counts You must get from a point P on the straightshore of a lake to a stranded swimmer…

A: Since you have posted multiple questions. We will solve first two questions for you. If you want any…

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A: To determine the price will yield a maximum revenue.

Q: dy Find dr - 6.3% +1-6x (а) () (ii) Hence find the maximum height of the tunnel.

A: The height of the tunnel, in meters is y = -0.1 x3 +0.8 x2,     2≤x≤8

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Q: The annual revenue and cost functions for a manufacturer of zip drives are approximately…

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Q: A ball is thrown into the air and its position is given by h(t) = - t2 + 73t + 10 where h is the…

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Q: Given: y = 2x3 – 6x + 2 i. Determine its relative maximum point. ii. Determine its inflection point.

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Q: Find the maximum value of 5x2 - 4xy+ 8y subject to x+y? = 1..

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Q: (3) If a projectile is launched into the air at 29.4 feet per second from a height of 60 feet, its…

A: Since you have posts the multiple question. I am answering the first one. Please posts the question…

Q: What is the equation of a quadratic function y = f(x) with two irrational zeros,-h and h where h is…

A: Given,         The equation of a quadratic function y=fx with two irrational zeros, -h          and…

Q: The given figure shows that when a football is kicked, the nearest defensive player is 6 feet from…

A: (Note: we are entitled to solve only one question at a time and upto 3 subparts only)  Given: The…

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Q: at the one-dimensional and n are constants.

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Q: Approximate the solution(s) to x3 = x2 - 5 using a graphing utility.

A: We have to approximate the solution(s) to x3=x2-5 using the graphing utility .

Q: If a projectile is fired straight upward from the ground with an initial speed of 128 feet per​…

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Q: The owner of a video store has determined that the profits P of the store are approximately given by…

A: Solve for the maximum profit

Q: When a ball is tossed into the air, the height h is feet of the ball t seconds from the time that…

A: ht=-16t2+80t+4 Comparing with ht=at2+bt+c, we get a=-16, b=80 & c=4 Now maximum value occurs at,…

Q: Find the 2 points where the absolute maximum and absolute minimum of the function occur: m(x) = 2x²…

A: Given equation is   m(x)=2x2-7x+9 We have to find the absolute maximum and minimum of the given…

Q: Antoine stands on a balcony and throws a ball to his dog, who at his ground level. The balls height…

A: Given :   To find the maximum height and the time it takes to reach the maximum height.

Q: A tour operator believes that the profit P, in dollars, from selling x tickets is given by P(x) =…

A: Given relation:P(x)=50x-0.25x2Where,P(x)=Profitx-number of tickets Differentiate P(x) with respect…

Q: Find the value of x that results in a maximum value of y if -2=x^2+y^2-4x+4y?

A: The given equation is -2=x2+y2-4x+4y. To find the value of x that results in a maximum value of y,…

Q: 3. Determine the equation of the cubic function with zeros -1, 213 and 3, passing through (4, 5).

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Q: Approximate the solution(s) to x3 - 2x + 2 = 0 using a graphing utility.

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Q: The height of a stone catapulted into the air is given by h(x)=−1/480x2+3x+2 where x is the…

A: Given:  The height of a stone catapulted into the air is given by h(x)=-1480x2+3x+2 where x is the…

Q: The owner of a video store has determined that the profits P of the store are approximately modeled…

A: Profit function, P(x) = -x2 + 30x + 76

Q: The number of newspaper copies produced from 1995 to 2002 is given by C = 50t2 - 200t + 10,000,…

A: Here we want to find minimum number of copies of newspaper produced. Here we use application of…

Q: A tour operator believes that the profit P, in dollars, from selling x tickets is given by…

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Q: The height of a projectile, in metres, is modelled by H(t) = -5t2 + 10t + 8, where time, t, is in…

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Q: What is the maximum value of the function y = -x² + 6x – 7?

A: 3 To find the maximum value of the given function y = -x2 +6x -7

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.