Solve the area bounded by the parabola y2 = 4x and the line y = 2x - 4 in two ways. Answer: 2 sq. units

Q: One version of the Folium of Descartes is given by x³ + y² = 1.4xy for what value(s) of x is the…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Click the best answer -1 -0.5 5 4 y = (x² + 1)² 24 0 0 0.5 1.5

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Q: Compute the area of S. f(x) dx for f(x) = 4x if x < 1, and f(x) = 1 ifx≥ 1. Area =

A: To find the integral, split the limit of integral in two parts

Q: Let the position of a swinging pendulum in simple harmonic motion be given by s(t) = cos(t) + sin(t)…

A: Given:- st=cost+sint

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Q: A sheet of paper 84 cm-by-64 cm is made into an open box (i.e. there's no top), by cutting x-cm…

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Q: ) Find the equation of the tangent plane to the surface x² + y² − z = 4 at the point (2,2,0)

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Q: What does it mean for f to be concave down on an interval (a,b)? Select all answers that apply.

A: Solution: Given data, f is concave down on an interval (a,b)

Q: (... The curve C consists of the line segment from the point (5,5) to the point (3,0). Write -")…

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Q: 25. Birth and death rates If the birth rate of a population 0.024t is b(t) = 2200eº people per year…

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Q: Time left 0:53:15 e population of a city is tripling every 13.9 years. If its current population is…

A: Given query is to find population after 5.8 years

Q: Question 2 Given the IVP: y" - 5y + 6y = 80, y(0) = 0, A) Use the Laplace transform to find Y(s). B)…

A: To solve IVP.

Q: Use mathematical induction to prove that the statement is true for every positive integer n.…

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Q: Obtain the general solution. (HOMOGENOUS EQUATION) 1. 2(2x² + y²)dx - xydy

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Q: Find in sin (1 + 2x) + xy = ecosy dy d.x

A: Find derivative

Q: √ d (268)6 This can be transformed into a basic integral by letting Consider the indefinite integral…

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Q: population of a city is tripling every 15.8 years. If its current population is 35.2, in thousands,…

A: Given query is to find the population after 2.6 years

Q: Find the derivative of y with respect to x if y = In (7x) S 0 sin (4e¹) dt.

A: ∫sinxdx=-cosx+cwe know  elnx=x and  lnxn=nlnx

Q: What do you think is lim→∞ (x³ - x)? 01 0.2 O Definitely, none of the choices is correct. 8880

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Q: Find the area under the given curve over the indicated interval.   y=x2+5x+4​; [4,6

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Q: Find f ◦ g and g ◦ f, and their domains. f(x) = √x − 4, g(x) = x^2

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Q: (y² cosx - 3x²y - 2x)dx + (2ysinx − x³ + lny)dy = 0; y(0) = = e

A: Solve this given differential equation.   We will compare the given differential equation with M dx…

Q: = f(x + Find +6)(x − 2)dx + C

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Q: 4. Use the graphing guidelines (see below) to make a complete graph of f. f(x) = 3x - x³. (Graphing…

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Q: The traffic flow rate (cars per hour) across an intersection is r(t) = 400 + 900t – 150t², where t…

A: Rate

Q: According to the Principle of Mathematical Induction, to prove a statement that is asserted about…

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Q: A) Find the Laplace transform of the following function: f(t) = 0, 1 - t, G(s) = B) Find the inverse…

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Q: ber of al real s) ber of qual/unique root(s) ber of ginary roots ber of s the graph ses the x- ber…

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Q: Suppose that sin(a) = 2/8 and cos(b) =1/8 define in the first quadrant, determine cos(a+b). (round…

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Q: Consider the following table, and assume that f(x) and g(x) are differentiable fund as given. X 1 2…

A: Given query is to find indicated derivative.

Q: Given: z = x² + xy¹, x = uv² + w³, y = u + vew Find дz dv when u = 3, v = -2, w=0

A: Given that z=x2+xy4, x=uv2+w3, y=u+vew We have to find the value of ∂z∂v, when u=-3, v=-2, w=0.

Q: What should be multiplied to an angle in radians to convert it into degrees? 180° π 180° T 360° π…

A: What should be multiplied to an angle in radians to convert it into degrees?

Q: df (3.2² Find ³x² + 6x³) dx + C

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Q: A ball is dropped from a height of 121.3 meters. Its height above ground (in meters) t seconds later…

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Q: Consider the function f(x) whose second derivative is f''(x) = 7x + 7 sin(x). If f(0) = 4 and ƒ'(0)…

A: Given: f''(x)=7x+7sin(x), f(0)=4 and f'(0)=3

Q: If we have a formula for f(x) , then using the central difference is a better way to estimate ƒ'(a)…

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Q: What are the domains and ranges of the following functions? Function y = secx y = sinx y = tanx…

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Q: Evaluate the following integral using integration by parts. Ste A. -221 dt Use the integration by…

A: Let's solve given integration.

Q: Evaluate the derivative of the following function. f(x) = (2x)³x f'(x) = (Simplify your answer.)

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Q: 5. Using n = 4 rectangles, estimate the area under f(x) = 2x² +5 to the x-axis on the closed…

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Q: 1. Find the area bounded by the parabolas y = 6x-x² and y = x² - 2x. Answer: 64/3 sq. units

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Q: Find the area between the curve y = x3 - 6x2 + 8x and the x-axis. Answer: 8 sq. units

A: Given y = x3 - 6x2 + 8x

Q: Suppose that 0=arcsin(2/6) in the first quadrant. What is sin(0/2)? (round to 4 decimals) Your…

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Q: Find the area of the shaded region. Enter your answer as a reduced fraction. 1.5 1 0.5 -0.5 AT 25 6…

A: To find the area of the shaded region

Q: The zeros of  f(x) = x2 − 2x − 15 are −3 and 5.  What are the coordinates of the x-intercepts of…

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Q: An object moves with velocity as given in the graph below (in ft/sec). How far did the object travel…

A: Given is the graph of velocity. Total distance can  be found by calculating area under the curve

Q: For what does the function f(x) = x² +50-100, 0≤x≤25, have its minimum value?

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Q: Find length of the cardioid r = 2(1 + cos 0)

A: Length of the cardioid, L=2∫0π r2+drdθ2dθ

Q: Show that if an = 5n3 - 14n2 + 7n - 3, then an = Θ(n3)

A: Given:  if an = 5n3 - 14n2 + 7n - 3,

Q: Find an equation of the tangent line at the given value of x. y = S ²² y = sin 8t + ,x=0

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