One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 15 hours. How long will it take the pipe to fill the pool if the drain is left open? (Enter the exact value as an improper fraction if needed.) hours

Q: a = 6i + 4j + 8k and b = 9i – 6j + 12k. a) [ 3] Determine whether the vectors a and b are…

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Q: Q3: A: Solve the following differential equation Ỳ – (sinx) y = 2 sinx

A: We can solve the given differential equation by using the variable separable method.

Q: [Q1] From the letters {A, B, C, D, E, F, G}, how many: (a) 3-distinct-letters codes can be…

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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. 3…

A: Given: Rate of inflow of water, dVdt=2 m3/min Height, h= 3m Radius, r=2m

Q: If u = 4j - 2k and v = 27 − j + 7k, find ū. v. Select one: √110 O -18 O √18 O 18

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Q: Compute dy if y=U³₁, V= dx 4x+1

A: Differential

Q: Find an equation of the line tangent to the graph of f(x) = (5x − 9)(x + 6) at (2,8). The equation…

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Q: me following limit, identify f(x), a, and L. elect the correct answer below: Of(x) = -x + 2; a = -1;…

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Q: Refer to functions m and q. Evaluate (qm) (x) and write the domain in interval notation. Write your…

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Q: Evaluate √t (3t-t²) dt

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Q: In problems 1 and 2, list both the order of the DE and state whether the DE is linear of nonlinear.…

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Q: Find the derivative of f(x) = (-x³ - 2x² - 2x) sin (x). Do not include "f'(x) =" in your answer.…

A: Topic = Derivative

Q: DIFFERENTIAL

A: Please refer to the image below

Q: Let f(x)=x²+3 ifx<1 3x+1 ifx21 lim f(x) b) d) lim f(x) lim f(x) ƒ(1) Find

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

A: Note:- These are multiple questions and acording to our company guideline we can do maximum 1…

Q: Show that the polynomial interpolating the following data has degree 3. 비 f(x) 1 4 11 16 13 X -2 0 1…

A: using the dummy equation ax3+bx2+cx+d =0 and finding the value of a,b,c,d.

Q: [3tan(x)² dx 2

A: Concept: Integration: The Sum of discrete data is denoted by Integration. The integral is calculated…

Q: 2. Determine the modulus and the principle argument of the following complex number: (2 + 4i) (2 +…

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Q: 1. 6 2x² =dx 1 + x

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Q: e Transform of f(t) = sin²t By Rule.

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Q: solve the system of equations by Grammer Method. 3x₁ −2x₂ + 4x3 = 19 x₁ +5x₂ −x3 = -12 2 x₁ + 2x₂ +…

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Q: 3 4. S (x+3) z²+1 5 dx dar.

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

Q: Find the area of the region bounded by the curves, x = −6 ,  x = 6 , the x−axis  and the parabola…

A: Follow the procedure given below.

Q: If f(x, y) = x²y + x sin y, then is af dx Select one: 2xy + sin y x² + x cos y ₂2 O O x² + sin y O…

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Q: Using the two points (x,y) and (x₁,51) to find Lagrange interpolating polynomial, L.(x1) is always…

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Q: Assume that the radius r of a sphere is expanding at a rate of 30 cm/min. The volume of a sphere is…

A: This question is based on derivative.

Q: Use the graph to find the following limits. a. lim f(x) b. lim f(x) X-3 X-1 a. Find lim f(x) or…

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Q: Evaluate the given function for f(x) = x² +1 and g(x) = x - 4. a) f(4)-g(3) _ ƒ(2) b) g(-1+h)-g(-1)…

A: Solution: f(x)=x2+1 g(x)=x-4

Q: Solve the following differential equation Ỳ – (sinx) y = 2 sinx

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Q: 11) S₁0 x ³ lnx dx

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Q: 2 4-2² √√4-x²-2² z=0 x=-- -4-2² y=0 Z dydxdz ||

A: We can solve problem as follows

Q: Let f(x) = 5x² - 4 to find the following value. f(t+1) f(t+1)=

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Q: [(x+1)e(x²+2x dx

A: The given integral,         ∫x+1ex2+2xdx

Q: Find the indicated derivative and simplify. 2x-3 2 x + 9x y' for y=- y'=0

A: To find the derivative.

Q: Given f(x) below, find f'(x). Do not include "f'(x) =" in your answer. f(x) = (3x³ + 3x² - 4).x²

A: Given, f(x)=(3x3+3x2-4)x2

Q: If y, and y₂ are linearly independent solutions of ty" + 2y + tey = 0 and if W(y₁, y₂)(1) = 6, find…

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Q: a) [ Show that the equation 6x + 6y-6z + 3x² + 3y² + 3z² = 18 represents a sphere, and find its…

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Q: IF B = By using the result of det(A) (A) Find the value of det(B) (B) without use the def (det) if…

A: Let's find determinant of given matrix.

Q: n 1: Given the function f(x) (b) find fl 1) ( = : 3x² − x, then (a) find the derivative function…

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Q: Use sigma notation to write the Taylor series about x = 3 for the function. ON X 1

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Q: The vectors a (4, -10,8) is perpendicular to the vector b (8,-8, -14). Select one: True False

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Q: 9. Let R be the region bounded by r=1-y²₁ x=2 + y²₁ y=-1, and y = 1. Find the volume of the solid…

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Q: Fundamental

A: We have to explain the Fundamental theorem of calculus

Q: (15) Use the divergence theorem to evaluate SSF. ds, where S 3 F(x, y, z) = and 5 is the surface of…

A: To evaluate the given integral using divergence theorem.

Q: Ex Gen If dy = y cost and y = 3 when t = 0, then y = dt 56. A. esint +3 C. sint + 3 B. 3e sint D.…

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Q: If a substance decomposes at a rate proportional to the amount of the substance present, and the…

A: This question is based on application of diffrential equation.

Q: Find the directional derivative of the function at the point P in the direction of the point Q. f(x,…

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Q: 4. The volume V of a rectangular box is given by V = LWH where L is the length, W is the width and H…

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Q: Assume that all variables are implicit functions of time t. Find the indicated rate dy dy dt x² +…

A: topic- implicit differentiation

Q: Find the absolute extreme values of each function on the interval. 1 F(x) = - 0.5 ≤ x ≤2 x2, =…

A: Topic:- application of derivatives