Question 1: A teacher told her class to write an equation of a line. Jack wrote down the equation 4x + 6y = 8 and Mary wrote down the equation 3x - 7y= 10. The students begin to discuss which line is steeper. Which line is steeper and why?

Q: 2. S sin√3x V3x -dx

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Q: Cost, revenue, and profit are in dollars and x is the number of units. The average cost of a product…

A: c'(x)=-30x2+110formula for average cost is  c=∫c'(x)dx∫xndx=xn+1n+1+c

Q: (อ) 00 n=1 el/n น

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Q: A farmer wants to fence an area of 6 million square feet in a rectangular field and then divide it…

A: We need to find out the dimensions of the rectangular field that will minimize the cost of fencing.…

Q: Find the domain of the function. (Enter your answer using interval notation.) f(x) = log5 (82x)

A: doamin of logx  is  x>0f(x)=log5(8-2x)for domain  8-2x>0

Q: Let Then f'(x) = f(x) = √2+ sin²x

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Q: Evaluate the following integral: 2x²-1 (3x-1) (x²+1) dx S

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Q: 1) Given that csc A = -25 and cot B = where - <A <0 and 0 < B < , find the value of each of the…

A: To find the values of given trigonometric functions

Q: Consider the following infinite series. Complete parts (a) through (c) below. k=1 4k a. Find the…

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Q: 3. 1+x 1+x² dx

A: Topic = Integration

Q: Consider the following function. F(x) = x4/5(x - 1)² Find the derivative of the function. F'(x) =…

A: Given:     Fx=x4/5x-12   Derivative of the function:     F'x=ddxx4/5x-12 Apply product rule:…

Q: Given sec 8= - 15 O 5 10 2 √10 5 2 what is cos?

A: Given query is to find the measure of the Indicated angle.

Q: Find the domain of the function. (Enter your answer using interval notation.) g(x) = log4(x2 - 1)

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Q: 7. Solve the DE shown below using Exponential Shift; m = 2 & n =4 y" + 2y' + y = menx

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Q: Given: (x is number of items) Demand function: d(x) = 308.7 -0.2x² Supply function: s(x) = 0.5x²…

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Q: Determine if the following series is absolutely convergent, conditionally convergent, or divergent.…

A: Given the series is  ∑n=1∞ -1n+1n3+1.

Q: A company sells square carpets for $3 per square foot It has a simplified manufacturing process for…

A: From given statement

Q: If there is more than one solution, use a comma to separate your answers. Express your answer(s) in…

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Q: Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x² + y² = 36 and…

A: we need to find the volume of the wedge-shaped region.

Q: Find the most general antiderivative of the function. (Check your answer by differentiation. Use C…

A: The Function is given that: fx=3ex+4sec2x              on the interval -π2,π2

Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 1,…

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Q: Draw the graph of y = 4*, then use it to draw the graph of y= log4(x). y

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Q: y 1-CDS 2X 1+ cas 2x

A: I have solved step by step in detail...go through the solution

Q: Given y = 4z and y = 2² +3, describe the region for Type I and Type II.

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Q: Let log₂ (5t + 8) - 4 (a) Find the domain. 0 (-00, 0) u (0,00) 0(0,00) 0 (-∞, - §) U (₁00) 0…

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Q: Find f(x) such that f'(x) = e7x - 6x and f(0) = 10.

A: f'(x)=e7x-6xf(0)=10f(x)=∫(e7x-6x)dx∫xndx=xn+1n+1+c

Q: 1.f x√3x + 2dx

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Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

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Q: Consider the function f(x) this interval. 1 on the interval [1, 12]. Find the average or mean slope…

A: f(x)=1xformula for average value is  favg=f(b)-f(a)b-afrommean value therrom…

Q: In this question, we will find the degree n Taylor polynomial for the function f(x) = ln(1+x)…

A: Given: fx=ln1+xTo Find: a To find f1, f'1, f''1, f31, and fk1 where k is any positive integer.b To…

Q: Consider the function f(x) = 8 + 5 21 Find the instantaneous rate of change of the function at the…

A: Since, you have posted multiple questions, as per guidelines we are supposed to answer only first…

Q: A car travels down a highway at 25 m/s. An observer stands 100 m from the highway. (a) How fast is…

A: Car speed=25  m/s

Q: 5. y = √x² - 1

A: We need to find extreme values.

Q: Calculate the approximation M4 for the given function and interval. f(x) = 7*, [1,3]

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Q: If a rock is dropped from a height of 220 ft, its poistion t seconds after it is dropped until it…

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Q: X Find the values of x where the following function attains its absolute extrema, the interval [-1,…

A: Given function f(x)=x3+x2x+13

Q: 3 4. f(x³-4)6x²dx

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Q: A car, 15 kilometers directly east of a bus, moves west at 80 km/hr. At the same moment, the bus…

A: Distance between bus and car is:  15 kmSpeed of car which moves in west direction is:  80 km/hSpeed…

Q: 1) If Q=L0.75K what type of returns to scale does this function have? 0.75 2

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Q: Prove whether the following integral converges or diverges: 1 S₁Ⓡ dx In(x) x

A: ∫xndx=xn+1n+1+cd dx(lnx=1x

Q: 4. f sin² cosdx 2 2

A: ∫sin2(x2)cos(x2)dxd dx(sinx)=cosx∫xndx=xn+1n+1+c

Q: Solve the DE shown below using the Exponential Shift (m = 2 & n = 5) y" + 2y' + y = menx

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Q: In order to find the area of an ellipse, we may make use of the idea of transformations and our…

A: The region R is given by:(x-5)29+(y-1)225=1

Q: .x²y = 4x² + 7xy + 2y²

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Q: A particle moves along the x-axis with velocity given by v(t) = cos (t) for time t > 0. If the…

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Q: Use the limit definition of the integral to evaluate the following integral:  ∫50 (4 − 2x)dx, You…

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Q: Rewrite the following logarithms in expanded form by applying the properties of logarithms. a. log…

A: We can expand the logarithemic expression in the below steps.

Q: 3-Solve fx lnx dx

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Q: 4.) 9x² + 4y² + 324. +3826

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Q: Question 5: A sine curve is shown on the graph below. y -5- -4 -2 0 -5- -10- 2 P 4 6 8 10 12 2

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