A car is slowing down at the rate 0.8 ft/sec². How far will the car move before it stops if its speed is initially 15 mi/hr?

Q: Find in the parametric equation d'y dx² x = 5 sin² t y = 2 cost 0≤t≤ 2π.

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Q: Derive implicitly—Implicit differentiation. Please show a detailed solution. Also, comprehensive and…

A: In this question, we want to differentiate the given expression implicitly.

Q: What is the exact value of sin(67.5°)cos(22.5°)?

A: Solution-

Q: Typewritten for an upvote. No upvote for handwritten. Please skip if you have already done this

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Q: SET-UP a triple integral that will solve for volume of the solid S bounded by the sphere x² + y² +…

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Q: the Following differential equation ²²=1+ P²

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Q: Determine the x - y coordinates of the points where the parametric equation x = 5 sin²t y = 2 cost 0…

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Q: You deposit $1500 in an account with 5% annual compound interest. Complete the following, assuming…

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Q: Find the linearization f(x) = √x, L(x) = L(x) of the function at a. a=4

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Q: e the differential equation e2x dy +2e²x y = 2x

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Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

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Q: 2 Find the area bounded by the parabola y = 4x and the line y = 2x - 4.

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Q: Differentiate. f'(x) = f(x) = 8x7-9 cos(x)

A: As per our guidelines we are supposed to answer only one question. Kindly repost other questions as…

Q: I. 1.) Simplify. Write "undefined" for expressions that are undefined. 2 4 4 [169 -6 -3 -5

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Q: Find the equation of tangent line to Graph of f(x)=3 x In(5x-4) at point where x=.1

A: Solution:

Q: a. Find an equation of the tangent line at x = a b. Use a graphing utility to graph the curve and…

A: Equation of the line :         y-y1 = m (x-x1) ; where , 'm' is the slope of the line .

Q: f(x)-f(a) a. Use the definition mtan = lim x-a x→a b. Determine an equation of the tangent line at…

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Q: 2. Use the graphs of y=f(x) and y= g(x) to sketch the graph of y=h(x). Hint: Estimate the function…

A: answer is in next step.

Q: Find the volume of the solid generated by revolving the region bounded by the lines and curves y=√x,…

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Q: (5x)" . Given the power series Σ(-1)", , find and justify its interval of 4n In(n)' n=2 onvergence…

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Q: Let F(x) = - [² 2 √t dt. Find F" (2).

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Q: dy 1. If (x + y)² = x² + y² prove that 11 I Alx y

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: limits

A: L'Hospital's rule apply only when there is 0/0 for ∞/∞ form.

Q: af axdy of f (x, y) = xy(x+y — 1) — x² Find-

A: The given function is: fx,y=xyx+y-1+x2   As we know that; The Power Law: ddxxn=nxn-1 The Product…

Q: Find the area of the region enclosed by the given curves. y = 2√√√√x, y = x - 3,x=0, x=4

A: Given y=2x, y=x-3 x=0, x=4To find area of region enclosed between two curves:

Q: Find dy/dx, if y= (3+cos x) ^(2x+1)

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Q: Use Cartesian coordinates to set up the iterated double integral given by [[[ y² dV D where D is the…

A: Given problem:-

Q: Find the solution of the following IVP. * (yexy) dx + (xexy + sin(y))dy = 0, exy + cosy - 1 = 0 O…

A: The differential equation Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x. The solution is: ∫Mdx⏟Take y…

Q: Find the general Solution of the complement of the following differential equation y" - yy) +y =oy=0

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Q: Use a double integral to find the area inside one leaf of r=3sin2*theta

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Q: onvert the point p = (2,7) in the polar coordinate system to its artesian coordinate equivalent, and…

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Q: 1) If y = (x-a)√2ax-x² + + a is constant. x- -1(*-ª) ,then y' = 2√2ax - x² a² sin-¹ a²

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Q: What is the general solution of the following ODE * (x² + xy − y²)dx + (²x² − 2xy) dy = 0 1 1 x³ +…

A: We know that the equation is of the form of  Mdx+ Ndy = 0  We will check whether the equation is…

Q: 3. y= x²-3x-4 x+2

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Q: Find the area contained between the two curves y = 3x - x² and y=x+x². 71/6 81/5 91/4 62/3 None of…

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Q: Q3) Assume A = [4 6 3 11 7 2 [32] and B = 1 14 5 show that (AB)' = B' A' 31

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Q: 6 F 0 28inx Cask ex

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Q: The integral of sin x³ dx is cos x + Option 1 cos³ x 3 + C cos x + Option 2 cos² x 2 + C

A: Given ∫(sinx)3dx=∫sin3xdx

Q: It is known that for a function f(x), f'(1) = 0 and f" (1) = -0.5. What does the Second Derivative…

A: This question can be solved using the concept of second derivative test.

Q: Find an equation for the hyperbola that satisfies the given conditions. Foci: (0, ±7), vertices: (0,…

A: We have to solve above hypobola question

Q: 11. Given f(x, y) = 6r² - 2r³ + 3y² + 6ry. Determine any local maxima, local minima, and saddle…

A: To find out the local maxima, local minima and saddle points.

Q: Find the average value of the function on the given interval. f(x)=x²-7: [0, 1] Set up the integral…

A: Average value of a function f(x) on [a,b] is given by, V=1b-a∫abf(x)dx

Q: Set up the iterated double integral in polar coordinates that gives the volume of the solid enclosed…

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Q: Solve using Variation of Parameters (D² + 1) y = tan x O y = c₁ cos x + c₂ sin x − cos x ln(secx +…

A: The objective is to find the general solution using variation of parameter.

Q: The given integral is equal to cos 3t dt 5 + 3 sin 3t O (1/3) In 15 + 3 sin 3t| + C O (1/9) In 15 +…

A: To find out the integration.

Q: Determine the constants c and d in the equation of the curve y = at (0, -1) and an inflection point…

A: This question can be solved using the concept of functions and derivatives.

Q: Evaluate SSA, dA, where R is the region bounded by y=x2 and x = y² in the first quadrant. X

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Q: A population grows according to the model, 1400 e 0.06t where A is the population t years after the…

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Q: The Physics Club at Foothill College sells Physics Show sweatshirts at the yearly Physics Show…

A: Solution

Q: Solve the linear ODE using an Integrating Factor. dy dx - 3y = 8e5x

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