If an object travels in the xy-plane along the curve traced out by 
the vector function r(t) = (t 3/2, -t) for t ≥ 0, then the total distance traveled by the object from t = 0 to t = 4 is

Q: Question 2. The second order linear homogeneous differential equation y" + 2y' = 0, has a general…

A: The given differential equation is: y''+2y'=0 We can also write as: D2+2Dy=0   So, the auxiliary…

Q: Evaluate √²+√2+1 dz. T3/2

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Q: Find the limit. x+2)(x+61) lim (x+2) X→-6* O A. 8 OB. 4 OC. -4 OD. The limit does not exist.

A: Topic = Limits Correct option = C

Q: Given the following graph of f, find the limit or quantity if it exists. If it does not exist,…

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Q: If f(x) = 4x² - 2x + 3, find f'(4). Use this to find the equation of the tangent line to the…

A: To Find Equation of tangent line to the parabola.

Q: >/ 2(2x + 4 2(2x + 4)5 dx, u = 2x + 4

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Q: If log (95) + log(y) = log(z), then 95 + y = z. ---Select--- If In(95x) = In (y), then 95x = y.…

A: (1)  given  log95+logy=logzfrom properties of log loga.b=loga+logbif loga=logb, than a=b

Q: Integrate the following. Reduce answers to its simplest form if possible. (b) Stan* ydy

A: Topic = Integration As per guidelines , at a time only one question can be solved out of different…

Q: Determine if each is correct or incorrect (a) In(2) + In(x) – In(y) = - ---Select--- ✓ (b) 104log(x)…

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Q: 4. If cot(B) = = -and 7 and sin(B) < 0, determine the exact value of cos(B).

A: If cotβ=-27 and sinβ&lt;0, then to determine the exact value of cosβ.

Q: What expression can I use for this question

A: need to write down the expression that can be used for the given question.

Q: Find the solution to the differential equation (dy/dx)=(14xy)/(ln(y))8 which passes through the…

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Q: 10. Which one is the arc length of the given f(x)= c)1 + √2 A) 2 + √2 11. Which one is the…

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Q: 8 2/7 4/7 5/9 3/5 x² - 4x +3 x+3x²+x-12° Calculate lim

A: Given that a limit problem and we solve this problem by using L'Hospital's rule. We know that…

Q: The graphs of the vector-valued functions r(t) = (t², t³, 2t³) and s(t) = (t², t, 2t) intersect…

A: Please see the below picture for detailed solution.

Q: can you please rewrite the resultant acceleration equation.

A: We need to write the expression of resultant acceleration.

Q: Use l'Hôpital's Rule to find the following limit. sin (x) - X lim X→0 2x³

A: Please refer to the image below

Q: A 50-gallon barrel is filled completely with pure water. Salt water with a concentration of 0.3…

A: given  Q(t)=15(1-e-kt)where k&gt;0given  Q(t)=15(1-e-kt)where k&gt;0

Q: 3) Before you leave for your trip, you have to finish your last task at work: build a slide at for…

A: To find the horizontal length of the slide.

Q: Determine whether the improper integral converges or diverges. dx 6 √5x+1 O Converges O Diverges

A: Given integral:- ∫-∞∞dx5x6+1

Q: f(x) = x² + 8. (a) Find the value of y when x is zero. Let y = f(0) = (b) What is f (4)? ƒ (4) i X =…

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Q: Obtain the general solution of the following differential equations. 2. (D2-4D + 3)y = 20 cosx

A: Given; The characteristic equation is m2-4m+3=0. So,                  m2-4m+3=0⇒m=--4±-42-4· 1· 32·…

Q: Consider the initial value problem y² = e(x²-x), y(0) = 1. (a) Find the intervals on the x-axis…

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Q: Q2: Calculate the shortest distance between the two lines: (2) a-L Zo z+1 and a

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Q: Let C(x) be the cost to produce x batches of widgets, and let R(x) be the revenue in thousands of…

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Q: 7. Determine values of a, b, and c such that the graph of y = ax³ +bx² + c has a local extremum at…

A: To determine the values of a, b, and c such that the graph of y=ax3+bx2+c has a local exremum at 2,…

Q: Suppose s(t) is the position of an object moving along a line at time t20. What is the average…

A: The average velocity of an object between the times t=a and  t= b is given by Vav=final postion…

Q: dy/dx = -3x2y y = ___

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Q: Find the average rate of change of the function between the given values of x. y = 5 + 5x + 0.5×2…

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Q: Find the maximum and minimum values of the function f(x, y) = 2x² + 3y² − 4x - 5 on the domain x² +…

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Q: Evaluate f(x + 3) when f(x) = 3x² + 4x − 4

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Q: )= -5 √2+1 A. D: [0,∞), R: (-∞,∞) B. D: [1,00), R: (-∞0,00) C. D: (-1,00), R: (-∞0,0) D. D: (-∞,…

A: Topic:- function      Definition:-  The domain of a function f(z) is the set of all values for which…

Q: Evaluate the integrals below by interpreting them in terms of areas: (a) ƒ5 √√25 – x²dx = (0) (5 +…

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Q: There is a linear relationship between how many times a cricket will chirp per minute and the local…

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Q: 1₁) GINEN f(x,y)=-e-X FIND af af xe & he ?

A: We can answer both the question in the below steps by finding the partial derivative.

Q: 3 Find the equation of a plane that passes has normal vector through (-1,4, 1) and that is Parallel…

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Q: = f(x): (1) The graph of y = f (x + 4) + 5 is obtained by translating the graph of y (B) Left 4…

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Q: 3. Find the Standard and General Equation and other parts of the Ellipse given the Center (2,0), one…

A: Topic = Geometry

Q: 4. (x²-1 f(x)=2x-1 3 Domain: Function: Yes No Continuous: Yes No f(-2)= f(0) = x≤0 05 Range: f(5)=

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Q: A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the…

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Q: Use calculus to find the area A of the triangle with the given vertices. (0, 0), (5, 3), (1,4) A = |…

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Q: 04 * (ii) (√3+j) ³. O-16√3+16j O-16√3-16j O 16√3-16j O 16√3+16j

A: Given query is to find the value of the expression.

Q: 6. 2 a. Solve the equation 3(3x² + y2)x - 2xydy = 0. x² = c(9x² + y²) x² = c(3x² + y²) b. C. d. x³ =…

A: The given differential equation is a homogeneous differential equation. We can solve the given…

Q: A rock moves along the parabola x = y² + 2 under the force field F = (x², yeª). Find the work moving…

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Q: ector Operations) Given vectors =, √ = and =, show (√x) = ( x )

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Q: Consider the curve given by x(t) = acos³ (t), y(t) = asin³ (t) for a > 0 and 0 ≤ t < 2π. ind the…

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Q: The escape velocity is the minimum velocity with which an object must be propelled in order to…

A: Escape velocity is defined as the minimum velocity that is required by a moving body to escape the…

Q: K Construct a table and find the indicated limit. √x+2 X-5 If h(x)=- Complete the table below. X…

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Q: Find the derivative y = (10 – 100) tanh of y with respect to the appropriate variable. 0

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Q: Example: Sketch the following graphs, state any types of discontinuity and any values not in the…

A: The given functions, a) y=2x-2 b) y=xx+22x c) fx=x3,x&lt;0-x+2,x&gt;0 We have to sketch the each of…