Suppose that a price p and demand x are related through the price-demand equation  x+400p=8,000 calculate the elasticity of demand when p=25

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A: Concept: Gradient of function g(x, y) ∇g(x,y)=∂g∂x,∂g∂y Equation of the tangent line at g at point…

Q: A storage shed is to be built in the shape of a box with square base. It is to have a volume of 539…

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Q: Order One Differential Equations Solve the ff. DE Equations 1 3. (2x+3)y' = y + (2x + 3)² When x=…

A: As per our guideline we can solve maximum one question you can repost other one

Q: Let F(t) = (4t¹ +4, t² − 4t³, 2tª). Find the line (L) tangent to r(t) at the point (68, 36, 32) L:…

A: Given vector:- r→t=4t4+4,t2-4t3,2t4

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Q: Evaluate the definite integral by the limit definition. Lxdx

A: evaluate the definite integration by limit definition

Q: X y' - m₂y = C₁ e¹₁x, c₁,m,, m² are constants, 1 m ₁ m₂ I

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Q: Use the given information to find the indicated probability. A ∩ B = ∅, P(A) = 0.5, P(A ∪ B) = 0.7.…

A: Topic = Probability

Q: If f(4) = 13 and f '(x) ≥ 1 for 4 ≤ x ≤ 7, how small can f(7) possibly be? Need Help? Read It Watch…

A: See this solution in below.

Q: Evaluate the integral. √2 sin 3 3 sin 6x cos 6x dx √2 sin ³6x cos ³6x dx = 3

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Q: Determine the intervals on which the given function is concave up or down and find the points of…

A: Topic - Inflection points and concavity  of a function We are given, f(x) = (x^2−3)e^x we know that…

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Q: Evaluate the given integral by changing to polar coordinates. JJ 5(x + y) dA where R is the region…

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Q: g(x) = 7 cos(x), 0 14 0 1 T O 1 T

A: Given query is to find average value of the function.

Q: The quantity demanded per month of an item is related to the unit price by the 45 demand equation…

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Q: Solve the DE. xdygda x² + y² O 2arctan(-) =e- +C ( ² ) = 2e=²¹² + C O arctan -xe-r2 O arctan(-) =…

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Q: 2. Let f(x) be a differentiable function such that f(3) = 15, ƒ(6) = 3, ƒ'(3) = -8, and ƒ' (6) = -2.…

A: Given that f(x) be a differentiable function such that f(3)=15, f(6)=3,f'(3)=-8 and f'(6)=-2.

Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

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Q: Evaluate the integral. S- dx √64x² A. X= OB. x= Which substitution transforms the given integral…

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Q: 4. How far from y-axis is the center of the circle 2x² + 2y² + 10x - 6y - 55 = 0? 5. How far from…

A: Given the equation of a circle, 2x2+2y2+10x-6y-55=0

Q: 3. The slope of a curve at the point (x, y) is given by 3x²y + 2y. Find the equation of this curve…

A: To find the equation of the curve with given slope

Q: Q4 d. lim ²+5x+6 x²-4 x112 e. limx→∞ (1-x²)³+40x6+x 3x6 +3

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Q: Sketch the curve. Show all x and y intercepts if they exist, any asymptotes or end behavior, local…

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Q: Question Determine the interval of convergence for the power series that can be used to represent…

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Q: The same capacitor circuit is now charged up to 12V and the instantaneous voltage is v=121-e -e²²).…

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Q: Complete the following: In √√√x(y² + z²) = C' ln x + D ln(y² + z²) with C' = and D =

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Q: Use sigma notation to write the Maclaurin series for the COS TTX.

A: Maclaurin series of f(x) about is given by, f(x)=f(0)+(x-0)f'(0)/2!+(x-0)²f"(0)/3!+...

Q: Suppose that a fourth order differential equation has a solution y = -6e5* sin(x). (a) Find such a…

A: (b) General solution for this differential equation is

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Q: Let F(t) = ( Find 1 t +4 i fr(t)dt ( )dt (don't include the +C) fr (t) dt = {{ -, 4 sin(-2t), √2t…

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Q: Find the absolute extrema of the function f(t)=2cos(t)+sin(2t) on the interval [0,1/2] using the…

A: We want to find absolute minimum and maximum

Q: Evaluate the following integral π/2 S π/3 sin x √√1 + cos x -dx

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Q: Find the area of the region that is bounded by the given curve and lies in the spect r-eº, 37 ≤0≤ 31…

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Q: Determine all values of x that satisfy the equation: 3x-2 = 27x+5 b. Use the properties of…

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Q: the short test distanse between the two curves y=sinx² and x² + y² = 2. where the interset oregen…

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Q: The length of one square is 70% larger than the length of another square. The perimeter of the…

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Q: Optimal Chapter-Flight Fare  If exactly 196 people sign up for a charter flight, Leisure World…

A: need to find out the maximum revenue and fare per passenger.

Q: What are the solutions to sine -- {픔쯤} 아픔 2 4 3 3 5개 66 {} 6 ,where 0 ≤ 0 ≤ 2πT?

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Q: When the cost of producing a VCRS is given by C(x) the average cost for each VCR is C(x) x =…

A: To find minimum average cost

Q: Find a particular solution for y" + 4y = 8 sin(2t)

A: To find a particular solution for the following differential equation.y''+y=8 sin2t

Q: In each of Exercises 1-14, D(x) is the price, in dollars per unit, that consumers are willing to pay…

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Q: Let f(x) 07 O O 11 - S x² + 1 4x – 1 - if x ≤ 1, Determine the value of (ƒ o f)(1). if x > 1.

A: The answer is in step 2.

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: Consider the initial value problem Suppose we know that y(t) → 0 as t→∞o. Determine the solution and…

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Q: Part III. Find the 53rd derivative of sin x. Show your solution. I

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Q: To calculate the integral 3 /VR²³116 dr dx x² + 16 we want to make the trigonometric substitution

A: To solve the given integral.

Q: Consider the graph 2 6 2 2 f(x)=√x² - 4 Where is the function positive?

A: function is given  this is the question of function we have to find domain of function where it is…

Q: find the first derivative for :Y=8-7x-7x^2+4x3

A: Given query is to find first derivative.

Q: Consider the function h(x) = f(x² - 1). Give the formula for the derivative h'(x).

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Q: Which of the following shows the simplified function of cscxsin 01 -1 tan x O cotx

A: Topic - Trigonometry We are given, csc x sinπ2-xWe know that,sinπ2-x=cos(x)