Find an explicit solution of the given initial-value problem. 1 y(4) = 4 y = dy dx = y² x² - - 1

Q: 9/ Approximate the follwoing integrals using The Simpson's ruls @ 0-25 b (Cosx) dx -0-25 Š 0-5…

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Q: A conical tank has height 3 m and radius 2 m at the base. Water flows in at a rate of 2 m³/min. How…

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Q: F(x)=5cos(3x) on [-pi, pi] What intervals is f increasing and decreasing?

A: F(x)=5cos(3x) on [-pi, pi] What intervals is f increasing and decreasing?

Q: 1. Determine the vector and parametric equations of the line passing through P(-2, 3, 5) and Q(−2,…

A: According to our guidelines we can only solve the first question and rest of the questions can be…

Q: The Maclaurin series of the function f(x) = 8x² sin(6x) can be written as f(x) = Σ₂² n=0 where a few…

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Q: Use the Limit Comparison Test to determine if the series converges. k³ +7 k(k+ 3) (k − 2) (k+1) k=1…

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Q: 46×12

A: Find value of 46×12

Q: Find the area between x-axis and the curve defined by   y=2·x2−6·x on the interval [0‍,4].

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Q: Find the vector projection of OA = (4, 3) on OB = (4, −1).

A: This is a basic vector problem

Q: Given the series: 1 1+ + + 9 27 does this series converge or diverge? diverges converges 00 If the…

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Q: Evaluate the indefinite integral Select one: O a. 1 (1 - √√x)4 1 O b.. O c. - + C (1 - √√x)² 1 + C +…

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Q: If w = f(r,s,t), r = x-y, s = y - z, t = z − x then aw дw ?x + О O -1 -2 Əw дz 1 2 (

A: It is given that, w=fr,s,t, r=x-y,s=y-z,t=z-x.   The objective is to find the value of…

Q: Nedian Sf = = = -0-1 a So 0.9062 Cos (1-√3x) dx = 1/2 How? a=0.5968

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Q: Use the washer method to determine the volume of the solid formed when the region bounded by y = x…

A: Solution given below

Q: Complete the parametric equations of the line through the point (-3,1,-4) and perpendicular to the…

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Q: 18. 19. 20. The curve y = x³ + 3x² − 2 has an inflection point at the point: a) P(-1, -2) b) P(-1,2)…

A: Use inflection point concept

Q: Make the indicated trigonometric substitution in the given algebraic expression and simplify (see…

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Q: The equation of plane through (3,-1,7) and perpendicular to the vector n(4,2,-5) is 4x + 2y5z-25 =…

A: we know that if a plane is  perpendicular to a vector then the  normal of the plane is parallel to…

Q: A curve has an equation y = 2√x which intersects the line x = y. What is the volume generated by…

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: A triangle is placed in a semicircle with a radius of 6ft, as shown below. Find the area of the…

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Q: 1. Determine the domain of the real function f. 2+x a. f(x) = log b. f(x) = √2+x-x² c. f(x) = cos d.…

A: According to the company rule we can answer only first question and rest can be reposted.

Q: 1 4. First, make a substitution and then use integration by parts to evaluate [Hint: Use the fact…

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Q: If [ f(x) dx = 18, then √ (f(x) + 4) da is equal to: A B с D 20 22 25 30

A: Evaluating the given definite integral

Q: a) Find a and c so that (a, 1, c) is a point on the line through (0, 2, 3) and Justify your answer.…

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Q: 1. Find a result by using variable separation 101 b- y³y+x³=0

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Q: The radius of a circle is increased from 2cm to 2.03cm find approximately increase in area

A: Solving using differentiation

Q: La longitud de un rectángulo es tres veces su ancho. Si el perímetro del rectángulo es 72 in, ¿cuál…

A: Length of rectangle be l

Q: Evaluate [cos² ydy a. 1/2y + 1/4sin2y + c c. 1/2y + 1/2sin2y + c b. 1/4y + 1/2sin2y + c d. 1/9y +…

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Q: find the general solution (x - 2y + 3) dx + (x-3) dy=0

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Q: INTEGRATION OF 1/1+TANX

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Q: Find an algebraic expression equal to sec (csc-¹ (3x + 2)). T (You may assume that — < csc¯¹ (3x +…

A: The expression is  seccsc-13x+2

Q: Docking a Boat A boat is pulled toward a dock by means of a rope wound on a drum that is located 3…

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Q: b.) Draw the projection on a xz plane Show solution for the equation 4 اس -2 7 z 3 2 0 -2 1 2 c.)…

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Q: find the are 2y² + 3x² = K family of orthoganał to the when κ>0 y >0. choose your answer from the…

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Q: S²³ x² e ²x ly and numerically. For the luations use (a) single application of I rule; Compute…

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Q: The length of the curve r = sin² for the period 0 ≤0 ≤π is 6 O 2 O 8 O 4 O O None of them

A: Use derivative and length of curve formula for polar curve.

Q: Hos solv the step? ₁0.9062cos (1-√3x) d x [sin (1-√√3x) -√√3 √³x)] -0.1 -0.1 sin (1-√√3a) - sin…

A: We have to solve the step  sin(1-√3a)= -0.9556+0.9210

Q: Find an algebraic expression equal to sin (cos-¹ (5x-3)). (You may assume that − <cos-¹ (5x − 3) <…

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Q: What is the difference between quadratic and logarithm functions? a. The effect of x on y never…

A: Concept: Polynomial function: A polynomial function with one or more variables, where the largest…

Q: Find the general solution of the given differential equation. x²y + x(x + 2)y = ex y(x) = Give the…

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Q: Evaluate the following integral: f²f₂f²x+yz dxdydz 24

A: Due to some technical inconvenience I cannot type this answer in Math type I am providing you the…

Q: Consider the function f : [-1, √10] → R defined by { 10 8 6 T 2 0 -1 f(x) = r², r>2; x≤ 2. I Answer…

A: Disclamier: Since you have posted multiple a question with multiple sub- parts , we will solve first…

Q: The length of the curve r = sin² for the period 0 ≤ 0 ≤ π is 8 O 6 None of them O 2 O 4 O

A: In this question, we want to compute the length of the curve.

Q: 7 Given the geometric sequence: 35,7 3' 45 Find an explicit formula for an, where the first term is…

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Q: √1+4x4 x3 dx

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Q: Evaluate the following integral: 2² ²₂ 2² x+yz dædydz

A: Solution given below

Q: The marginal cost for a company to produce q items is given by MC(q)=0.004q^2−0.9q+625. The​…

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Q: 2. If F and G are differentiable functions such that F'(x) = G'(x), which of the following is true…

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Q: Two-thirds of Ariadne’s money together with five-sevenths of Brian’s money is equal to three-fifths…

A: given:-Person A has $2.40Person C has $11.25To calculate the person B's money.

Q: 4. Let the universal set U, and the subsets of U are A = {x|x is a letter of your first name}, B =…

A: Disclamier: Since you have posted a question with multiple sub-parts, we will solve first three sub…