1. Find the height of a circular cylinder of maximum volume, which can be inscribed in a sphere of radius 10 cm. 10 h/2 a. 11.55 cm b. 12.55 cm c. 14.55 cm d. 15.55 cm

Q: Consider the cone shown below. If the height of the cone is 3 and the base radius is 2, write a…

A: We have to parameterization of  the cone.

Q: what is the basic concept of a derivative? How is this derivative calculated? What techniques/rules…

A: Use the definition of derivative

Q: A tumor is injected with 0.6 grams of Iodine-125, which has a decay rate of 1.15% per day. Write an…

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Q: π 3π The region bounded by y = cos x - 1 and the x-axis in the interval is revolved about the line x…

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Q: 3. Reduce 9x² +9y2 - 12x - 24y - 5 = 0 to the standard form of the equation of a circle.

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Q: y"-2y'-8y = 0 if y(0) = 3; y'(0) = 6

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: Solution is here

Q: 81-2 da Evaluate the integral: √√81 (A) Which trig substitution is correct for this integral? Ox = 9…

A: Solve the following

Q: 10- 7- A. 3 О А О в О с D 12√3 √9 B. V3 11 С. 1 D -1

A: Use the basic property og exponents

Q: 11. x² +1 Find +3x+1 -dx

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Q: Q3/ Evaluate four of the following integrals. a. S sinx cosx 1+cos2x dx_b. f*¹ dx c x²

A: INTEGRATION

Q: Using Simpson's method off, no spaces) Blank 1 0.66 √√x dx for n= 4 is equal to 0.66 (use 2 decimal…

A: As we know from the Simpson's Rule: ∫abfxdx=∆x3fx0+4x1+2fx2+4fx3+2fx4+...+4fxn-3+2fxn-1+4fxn-1+fxn…

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: An employee's monthly productivity M, in number of units produced, is found to be a function of the…

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Q: Evaluate 3 (9x² - (0x+6) dx 2

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

Q: ! If 2* ((4x-1)/5) =3 then x = 1 17/8 O 0.1 O -0.1 * 5 100 160 500 25 O +1 O -1 O +1,-1 O None of…

A: We have to find the values of the following equation.

Q: 4) x² (1-8)² + 100 25 =1

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Q: 3. Let there be some a, b ER such that f(a)f'(a) = f(b) f'(b) + 1. Show that f f(x)f"(x)dx ≤ 1.

A: This is a problem related to integration. Based on the general formula and concept we will prove the…

Q: Condense the expression to a single logarithm using the properties of logarithms. log (x) - log (y)…

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Q: SUBJECT

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Q: A contractor wanted to buy equipment; current price of it is ($50,000). So, he requested the help of…

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Q: a) Use the Quotient Rule to find the derivative of the given function. b) Find the derivative by…

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Q: Draw a graph to match the description given. G(x) is decreasing over (-∞0,0) and (8,00) and…

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Q: 1. How do you think will the infrastructures be, if area in solving the plane region using definite…

A: 1) in that case there would be some standard object with a specified area which can be used to scale…

Q: All continuous functions have antiderivatives. (A) True B) False

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Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

A: Form the graph first then see maxima and minima

Q: (x² + 3xy + y²) dx − x² dy = 0 -

A: As equation is an homogeneous differential equation then put y =vx and solve.

Q: For the function, find the points on the graph at which the tangent line is horizontal. If none…

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Q: Find integral sec^2(2θ) dθ

A: Use substitution method for solving the integral.

Q: IF y = u+ + 3u2 & u = 2x Find dx

A: Chain Rule of differentiation : If y=f(u) and u= g(x) , then         dydx =dydu.dudx

Q: 2) If the function of is odd function (i.e. f(-x) = - f (x)) then, the Fourier transform of f(x) is…

A: Please see the below picture for detailed solution.

Q: 1) 3) (x-3)² (v-4)² + 16 196 (x + 1)² (y-8)² + 9 81 = 1 = 1

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Q: 10) (x + 7)²_ (y + 4)² = 1 + 81 36

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Q: For the given function, find (a) the equation of the secant line through the points where x has the…

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Q: The volume of a cylinder of height 12 inches and radius 7 inches is given by the formula V = 12π².…

A: We have to slove the derivative

Q: B-Soive the Differential equation : Y 1 x√√x+x = 0, y(9)=1.

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Q: Which of the following is equal to da? In(x) + c +c 20 +0 с

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Q: A balloon, leaving the ground 60 ft from an observer, rises 10 ft/s. How fast is the angle of…

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Q: D Question 2 An aircraft is flying horizontally at a speed of 600 km/h. How fast is the distance…

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Q: Determine the area of the triangle bounded by the coordinate axes and the tangent to x² - y = 0 at x…

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Q: The graph of a derivative f' is shown to the right. Use the information in the graph to determine…

A: The graph of the f'(x) is given as

Q: Let y = f(x). Which of the following statement is TRUE? O None of the above O Let f(x) = -2x + 4. If…

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Q: SUBJECT: DIFFERENTIAL CALCULUS NOTE: Make the solution detailed and clear in a sheet of paper.…

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Q: ator of a sphere, parameterized by spherical coordinates 0, and p. Let "north" point to the top

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Q: Find the area of the region above the x-axis bounded by the function y = 4x - x2 – 3

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Q: lim (3x - 5) x--1

A: limx→-1(3x-5) = limx→-13x - limx→-15  [ lim(a - b) = lim a - lim b ]                         = 3…

Q: 6x-1 b) f(x) = (3x+5)*

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Q: 3] [1 2 Find A¹ of The Matrix A = 3 2 -1 3 1 2]

A: As per the instruction, we will be answering the first one. Given: Now,…

Q: What are the applications of these derivatives?

A: First derivative tells the rate at which the original function changes.  Second derivative tells the…

Q: Differentiate. g(t) = 24¹ g'(t) =

A: g(t)=24ttake log both sideslng(t)=ln24tlng(t)=t·ln24by property of loglnab=blnaalso…