Find two positive numbers that satisfy the given requirements. The sum of the first number squared and the second number is 54 and the product is a maximum.

Q: V16-x polar coordinates to evaluate [' [" V16-x 4.) Use y tan™

A: Let's find.

Q: 6. Determine if is con n=1 (3n-1)*

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Q: Solve of the following equation 4 y' +y = x'y? Given by x3 In x – c -x3 In x + c O Option 1 O Option…

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Q: 20-1 to -5 -10 Find the aren et he regpen endosad by Hhan gaco p he serkicd lie X =1 an2 %3D

A: Given the query is to find area enclosed bybthe curves.

Q: Solve for n in permutation 9(n²-1Ps) + 9(7²P6) = n²+1 P7 %3D

A: Let's find.

Q: The volume V of a right circular cylinder is given by the formula V= Tr h, where r is the radius and…

A: Given that the volume V of a right circular cylinder is given by the formula V =(pi)r2h, where r is…

Q: What is the probability you draw two cards of the same color from a standard 52 card deck you are…

A: favourable conidtion is  26C1*25C1 = 26*25 total condition is 52C151 C1 = 52*51 probability =…

Q: A tangent line to the curve c(t) - (- 4t - 5t + 2, t - 15t - 1) has slope 3 at the pointias) 2-1…

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Q: X-1 y-3 Given that L: k and M: 4x + ky – 3 = 0 then find the value(s) 16 of k such that the two…

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Q: Assume the coefficient on Age is -0.052 and the coefficient on Age-Squared is 0.0007. Based on this…

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Q: 2 4

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Q: 2 Compute limx→14-x2 1 + X-1

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Q: 16) Rewrite the integral 10 3(1 – z/10) 7(1 – y/3 – z/10) dx dy dz in the order dz dy dx.

A: To rewrite the integral ∫010∫031-z10∫071-y3-z10 dx dy dz in the order dz dy dx

Q: 9) Determine whether the series is absolutely convergent, conditionally (-1)"n convergent or…

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Q: Find the local linear approximation L (x) of the function f(x) = 5 – x² at =2.

A: To find the linear approximation of given function.

Q: Fina the integral (2x-1) (x+3) a. In 7 (2x-1) + C x+3 b. In 6 (2x-1) + C x+3 3 (2x-1) c. In + C x+3…

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Q: 1. Find the derivative of the following: (Simplify your final answers.) (a³-8)° (Va²+4) g. g(a) =…

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Q: 19x + 900 The average cost for a company to produce x units of a product is given by the function…

A: To find change in average cost as production goes from 150 to 151 units.

Q: "If a function is continuous at some point then it must be differentiable at that point". Do you…

A: To show whether the given statement is true or false .

Q: Let, \(f(x)=4x^2-12x+10\). Find: (a) the X- coordinate of all critical points, b) the open intervals…

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Q: 2. Find the integral 2x+3 dx x2-9 a. In/(x – 3)³(x + 3) + C а. b. In[(x – 3)³(x + 3)] +C c. 2ln[(x –…

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Q: ||r'(t) × r"(t)|| ||r'(t)||³ Use the formula k(t) = to find k(t). r(t) = t²i + t5j 390 t14 K(t) = 3…

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Q: Shown below is a graph of a line in the Cartesian plane. What corresponding polar equation? 2 -1 -1…

A: As we know that; The intercept form of equation of a line; xa+yb=1 Where; The x-intercept is at a,0…

Q: A manufacturer needs to make a cylindrical can that will hold 1500cm3 of liquid. Determine the…

A: Let r be the radius and h be the height of the can.

Q: x- 2 16. What is y' of the function y = arctan x+2 A) y'= C) y'=- x² +4 x* +4 2 B) y'= x² +2 D) y'=-…

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Q: x³+2x-1 (x²+9)² The partial fraction decomposition of has the form None of these Ax+B (x²+9)² A x²+9…

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Q: Question An open-top box is to be made from a 30-inch by 42-inch piece of plastic by removing a…

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Q: Verify Green's Theorem by evaluating both integrals Lv = / an_ aM dA dx + x² dy * ax ay for the…

A: Given problem:-

Q: Find the antiderivative of the function 4x3 - 2x2 +x - 5 dx

A: This question is based on indefinite integral.

Q: Find f. (a) fi" (æ) = sin æ, f(T)= 2, f'(7) = 3. %3D %3D (b) f' (t) = 2 + , f(1) = 1.

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Q: consider a function f (x) vihose derivative f"(x) is continuous as shown belowr. Graph of f'(x), NOT…

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Q: A cylindrical container with a circular base and open top must have a volume of 1000 m³. Find the…

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Q: 5- If Die is rolled find the probability that never appear 2 a) b): d) 3

A: A Die is rolled, the probablity that never appear 2

Q: From the graph below which statement is true? (A) not a function (B) function; domain: R (C)…

A: To determine which of the given options is true for the given function

Q: A ball is thrown vertically upward from the top of the house 112 ft high with 6. an initial velocity…

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Q: The volume of a cantaloupe is approximated by V=za. The radius is growing at the rate of 0.8…

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Q: dy Use an appropriate technique to find dx from x² + y² = (2x² + 2y² -x)*.

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Q: What is the probability you draw two cards of the same color from a standard 52 card deck you are…

A: we know that  The deck has cards in two colours red and black

Q: x³ +2x2-3x 2) Evaluate lim -6-1. x² +4x+3 X-3 Show every step.

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Q: Given the two vectors: å = 2ỉ -j+k, b = i + 2k and d = 3ỉ + 5j in 3D. a) Determine the dot product…

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Q: -3 -2 -1 1 2 4 8 16 32 64

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Q: y" + y" – 4y' – 4 = 8x + 8 + 6e™

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Q: Using the substitution u = x + 1 / Væ +1 dæ is equivalent to 1 u +1 -1/2 du /2 1/2 du (4 – 1) /…

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Q: B: .A card is drawn from a well shuffled pack of 52 cards. Find the probability of: (i) '2' of…

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Q: 1. Identify the type of conic section whose equation is given, then find the vertices and foci.…

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Q: The evaluation of S S 3y³e*ydxdy is e - 1 O

A: Given: ∫01∫0y2 3y3exydxdy

Q: Find a unit vector in the direction of the given vector

A: Follow the procedure given below.

Q: Find the local linear approximation L (x) of the function f(æ) = 5 – a² at x= 2.

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Q: Question 7 Find the volume of the solid that results when the region enclosed by the given curves is…

A: We need to find volume of enclosed region.

Q: 1. Jx cos 3x dx

A: Question 1 is solved. Solving more than 1 is against the policy.