Question

Q: Find the height of a circular cylinder of max. volume that can be cut from a spherical wood of…

A: Let the radius of the cylinder is = r and the radius of the sphere = R  Let the height of the…

Q: dx ex√4-e²x the integrand is transformed into? (a) cos² 0 (c) sin² 0 (b) sec²0 (d) csc²0 When the…

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Q: Find the derivative of the following functions. Use long method. a. f(x) = 3x² + 5x - 100 b. f(x) =…

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Q: pair of parametr quations is given. x = e4t y = et (a) Sketch the curve represented by the…

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Q: State the initial value theorem. Verify the theorem for the functions: (a) 3-4 sin t (b) (t-4)² and…

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Q: x-4 x²+2x-15 Inx+51-Inx-31+ C 8 Option 1 S: dx 1 (x + 5)⁹1 Je In + C + x-3 -100 1 9 In|x + 5|ln|x −…

A: We can find the answer as below

Q: A projectile is fired vertically upward with an initial velocity of 210 m/sec from a point 2 m above…

A: topic- algebra

Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

A: I have shaded the area green which is to be calculated

Q: Find the area of the surface generated by revolving x=√(8y-y2) on the interval 2≤y≤5 about the…

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Q: How long did it take for an investment of $25,000 to grow to at least $28,000 at 2.75% compounded…

A: Given: A = $28000 P = $25000 r = 2.75% We know the quarterly compound interest formula as A=P1+r44t.…

Q: Find the area of the region bounded by y² = 4ax and x² = 4ay.

A: We have to find the area of the region bounded by y2=4ax and x2=4ay.

Q: As you are walking in the forest you look up just as a boulder becomes dislodged from the side of a…

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Q: 4. Evaluate the line integral along the path C given by x = 2t, y = 10t, where 0 ≤ t ≤ 1. I (a) √(x…

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Q: 2-1 4s - 4 s² - 16/

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Q: Find the area bounded by the curves y = x(x − 1)², y — axis, and the line y = 12.

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Q: What integration technique can be used to integrate: O Integration Formulas O Trigonometric…

A: The given integration is I=∫53+x2dx

Q: If z is a function of x and y implicitly defined by əz əz find and əx ду at (x, y, z) = (0, 2, -1).…

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Q: xdy = (5y + x + 1)dx Ans: y

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Q: Find the volume of the solid generated by the region bounded by x² + y = 6, y = x, y = -2 and x = -2…

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Q: Given: planes Π1 : 2x − 5y + z = −1 and Π2 : x + 5y + z = 5 intersecting on a line ℓ. (a) Compute…

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Q: Find the transition points. f(x) = = x(5 - x)¹/3 (Use symbolic notation and fractions where needed.…

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Q: Evaluate the y' and Simplify the answers I Direct trigo functions y = x² sinx + 2xcosx - 2sinx

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Q: 5. (4xdy+3ydx) + x³y² (xdy + ydx) = 0 Ans: 6x³y² + x6y6 = c

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Q: Consider the vector-valued function R(t) = 1. Find the domain of R. 2. Show that R is continuous at…

A: All three questions are solved.

Q: √√7 - t³, cos t³) t³, c 3 R(t) = (sin t³,-

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Q: A bucket that has a mass of 25 kg when filled with sand needs to be lifted to the top of a 20 meter…

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Q: ds Find the complete solution of = 8t³√√s. dt

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Q: 1 Find the arclength of the curve x = 3 1 ',v = 22 -t³ t2 with 7 ≤ t ≤ 8.

A: The arc length of a curve in parametric form x=f(t) ; y=g(t) for b≤t≤a is given by,…

Q: 5. Find the limit, if it exists. If the limit does not exist, explain why. sin x- cos x (a) lim x/4…

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

Q: Find the area bounded by the curves x² + y = 6, y = x, y = -2 and x = -2.

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Q: Solve ²₂(x + 1)(x + 2)²(x² − 1)dx with and without the even-odd theorems (show both solutions).

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, −12t) (a) If R(0) = (-1,4,-5),…

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Q: q4

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Q: i can't understand your solution

A: We have to explain the solution.

Q: Find the area bounded by the parabolas (x - 1)² = 4ay and y² + 4a = 4ax.

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Q: In a certain bacterial culture where the rate of growth of bacteria is proportional to the number…

A: Let's find initially present bacteria.

Q: dy Find the complete solution of 2e-2 cosx- dx Note: fedu=e" + C - sin² x = 0.

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Q: True or false √2 If cosh x = V, then sinh x = 2. It is possible for a function to have an absolute…

A: To determine whether the following statements are True or False.1 If cosh x=62, then sinh x=22.2 It…

Q: Write the complex number in polar form with argument between 0 and 2. 5/(1 + i)

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Q: 3 [² [v³ – y³]³ª a Jo ² dy

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Q: Assuming that a 360-foot tall giant redwood grows vertically, if I walk a certain distance from the…

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Q: o - 23 dy

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Q: A projectile is fired vertically upward with an initial velocity of 210 m/sec from a point 2 m above…

A: projectile motion

Q: 4 35₂² In evaluating 2 dx x√√x²-4 is same as evaluating lim cos-¹(f(x)). Determine the value of f(x)…

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Q: 7. ydx-xdy + xydy = 0 Ans: In²+ y = c

A: We have to solve differential equations

Q: Find the area that are bounded by: y=x²+5x and y=3-x² from x=-2 to x=0.

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Q: 3. The region bounded by the curve y=sec x, the x axis, the y axis and the line x=0.25pi is revolved…

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Q: Consider the points K(-1,0, 7) and M(1, -2,5), the vector MN = (1,4, -3), and the line with symmetr…

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

Q: Find the intercepts and the vertical asymptote of x²-2x-3 4 Enter the intercepts as points. (a, b),…

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Q: ←…

A: Given