(a) AB-BC (b) projABAC (the vector projection of AC onto AB) (c) the area of AABC

Q: The owner of an orange grove estimates that 150 orange trees per acre will each yield on average 800…

A: Given that the owner of an orange grove estimates that 150 orange treesper acre will each yield on…

Q: Use the method of reduction of order to find another solution of y"−4y'+4y=0 if y₁=e²x is a solution…

A: The given equation is;  y''-4y'+4y=0 and y1=e2x

Q: Question For the following graph of a function, estimate the area under the curve on the interval…

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Q: 24. g(t) = t³ + 4t

A: Solution: g(t)=t3+4t The derivative of g(t) with respect to t is defined as limh→0f(g+h)-f(g)h

Q: 4. ["s 0 sinx + 2 cos x dx

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Q: Evaluate the line integral F. dr, where C is given by the vector function r(t). C F(x, y, z) = 6zi +…

A: Let's evaluate given integral.

Q: 4. Use the Fundamental Theorem of Calculus to evaluate [(-3) -

A: The objective is to find the integral using fundamental theorm.

Q: Partial fraction decomposition can now be used to write L{y}, such that all terms have linear…

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Q: Find the indefinite integral. [Hint: Use some algebra first.] (Use C for the constant of…

A: ∫t-2t+6t2dtExpand:=∫4t-12t2+1dt=4∫1tdt-12∫1t2dt+∫1dtWe know that ∫tndt=tn+1n+1

Q: An even function f(x) for all values of x and x holds a. f(x) = f(-x) b. f(x) = -f(x) c. f(x) =…

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Q: Evaluate the geometric series or state that it diverges. Το 198 Σ k = 0 56 k Select the correct…

A: topic - geometric progreesion

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. S² (t =…

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Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. r =…

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Q: Differentiate parametrically to find X 1 t-1 y=t³+2 dy dx in terms of t:

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Q: Q6. Angle a is acute and COS a = (a) (i) (b) 3|5 Find the value of tan a as a fraction. Hence show…

A: Given problem:-  Angle α is cute and cosα=35Angle β is obtuse and sinβ=12 (i) find the value of…

Q: 28.y= I 4+4

A: We have to find derivative

Q: Find the value of a if the centroid of the region bounded by the parabola y² = 4px and the line x =…

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Q: Find all numbers c that satisfy the conclusion of the mean value theorem. f(x) = 2x2 - 5x + 1, [0,2

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Q: Find the standard form of the equation of the ellipse and give the location of its foci. Ay 6 G Type…

A: Standard form of an ellipse : (x-h)2a2+(y-k)2b2=1 ; where , (h,k) is the center and a>b .

Q: Suppose de cos 0 sin³0. Answer the following. 6) Separate the differential equation, then integrate…

A: answer is in next step.

Q: Use the Laplace transform to solve the following initial value problem: y" - 2y +26y=0 y(0) = 0,…

A: The given initial value problem is y''-2y'+26y=0, y(0)=0, y'(0)=5

Q: Use the Laplace transform to solve the following initial value problem: y" - 6y +9y=0 y(0) = 5, y(0)…

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Q: Q5. (a) (i) (b) (c) (ii) Express sin 2x Express cos 2x Show that in terms of in terms of sin x Solve…

A: Given problem:- (a) (i) Express  sin 2x in terms of sin x and cos X.(ii)  Express cos 2x in terms of…

Q: 3. A wheel has a diameter of 70 cm and completes a revolution in 0.25 seconds at top speed. a.…

A: Angular velocity= θ/t , θ= 2π×number of revolution per unit time  Linear velocity= radius× angular…

Q: 5. The general solution of (D² A. y = (C₁+C₂x)e+C3 C. y = (C₁+C₂x)ex+C3e-2x +2D+1)(D²+4)y=0 A) A cos…

A: To find out the general solution of the differential equation.

Q: I. Given: 3x - y - 2z = 1 -x + 6y -3z = 0 -2x-3y + 6z = 6

A: I am attaching image so that you understand each and every step.

Q: What is the gradient of the curve y = x^3+4x^2-6x+3   at the point where x=-2 ?

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Q: Differentiate parametrically to find x=3t², y=6t dy dx in terms of t:

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Q: Find the indefinite integral. (Use C for the constant of integration. Remember to use absolute…

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Q: dy Find the complete solution of 2 + 4y = 1 dx

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Q: Graph to the image below and find the volume of the area bounded by y = (x^2 - 4)^2 and the x-axis,…

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Q: If f(3) = 5 and f ′(x) ≥ 2 for 3 ≤ x ≤ 7, how small can f(7) possibly be?

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Q: Show in paper. Find the integral of (2xcot(x) csc²(x)) dx.

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Q: question 8 please

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Q: Problem 12. Find the absolute maximum and absolute minimum values of the function over each of the…

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Q: -95A + 20B = 40 -20A- 95B = -190

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Q: 3 A merry-go-round has a radius of 4 m and is spinning at a rate of 0.5π radians/s. Bill is standing…

A: Formula used: Circumference of circle = 2π×radius of circle  velocity =  angular velocity × radius

Q: A region bounded by fly) = 5 - y, y = 1, y = 4, and x = 0 is shown below. Find the volume of the…

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Q: log4 You can write log421 as log21- True False

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Q: Sx cos²xdx

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Q: 4 F(s) = 3s7 (s²+3)

A: First to find the partial fraction decomposition of the function: F(s)=43s7(s2+3) For that let,…

Q: 2. (x+2y-1)dx - (2x + y - 5)dy = 0

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Q: Find the distance between the point P(1, 1, 1) and the surface x² + 2y² + 3x² = 1.

A: Given Point P1, 1, 1 and surface x2+2y2+3z2=1

Q: 7. -In2 2ex ex + 1 - dx

A: As per bartleby guidelines we only give first question answers.  Please repost for other parts.

Q: t is a fact that the function  f(x) = x(161/x − 1) has a limiting value. Use a table of values to…

A: We need to find limiting value.

Q: Find the standard form of the equation of the ellipse satisfying the given conditions. Major axis…

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Q: Let f(x) Then f'(x) = 3 sin x 6 sin x + 2 cos x m = The equation of the tangent line to y = = f(x)…

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Q: Let f(x)= x - 25 (a) Calculate f(x) for each value of x in the following table. (b) Make a…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: here are two regions bounded by the line y=x and the curve y=x^3, one in the first quadrant and…

A: Given problem:- There are two regions bounded by the line y=x and the curve y=x^3, one in the first…

Q: 2 3. Prove: sinx + sinxcot x = cscx.

A: I have stated the used formulas in the solution