Draw a cone that is inscribed in a regular pyramid whose altitude is 5 inches less than 3 times a base edge and whose base central angle is. If the base perimeter is 18 inches, find the total area and volume of the cone and the pyramid respectively.

Q: Use Lagrange multipliers z = f(x, y) = x² - xy + y² to find the absolute maximum and minimum values…

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Q: The half-life of chemical substance is approximately 9 years. Initially there is 80 grams of the…

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Q: 2. Find the volume generated by revolving the area bounded by the parabola y² = 8x and its latus…

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Q: 4. Classify the following differential equations according to whether they are linear or nonlinear.…

A: For (A), The above differential equation is linear. For (B), It is the same as dydt+1=0. So, the…

Q: 20- 18 16- 14- 12 10 Co 8 6 4 2 1 Estimate the instantaneous rate of change at x = 1

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Q: An ice cube is freezing in such a way that the side length s, in inches, is s(t)=t+6, where tis in…

A: Write down the equation of the volume.

Q: 05/ Giving the following data: X 0 1 2 4 5 f(x) 1 0 1 3 8 16 Evaluate the integral [f(x)]³dx by…

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Q: The slope of tangent lines to a curve y=f(x) is given by f'(x)=1/√√x +4x^3-1. If the point (1,6) is…

A: Equation of curve

Q: 11. Describe as many equivalent conditions as possible for a given vector field F is a conservative…

A: Given : F→ is conservative.

Q: 4) x(xdy - yox) = y² lnx dx

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Q: Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and…

A: Given problem:- Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a…

Q: D Question 5 If y = 7³/2, then True False dy = ¹/2

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Q: (2y^2 + 3x)dx+2xydy=0 Solve using integrating factor

A: To solve the following differential equation by using the integrating factor.2y2+3x dx+2xy dy=0

Q: A farmer plans to enclose a 200 ft^2 rectangular field that borders a straight river. He needs no…

A: The solution is given in the next steps.

Q: Find the angle between two vectors: A=31+4j-5k, (1) Scalar product. (2) vector product. B = 3i+4j+5k…

A: To find the angle between two vectors: A→=3i^+4j^-5k^, B→=3i^+4j^+5k^ by using: 1 Scalar product2…

Q: Find the Taylor polynomials of orders n = 0, 1, 2, 3, and 4 about x = xo and then find the nth…

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Q: Question 20 sin t Dz 20 sin T I COS T sin r I COS I I Cos I sin z 2x² COS T 2 JORNAL 27² MAN dabiskt

A: Here, to find the derivative of sin x2x which is a rational function. So, we use the quotient rule…

Q: A tank initially contains 50 gal. of fresh water. Brine (water in which a certain number of pounds…

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Q: x.e²ydy + 12 dx = 0

A: Follow the procedure given below.

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

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Q: 2) 2xydy + (x² + y²) dy : > 0

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Q: In a particular town, all of the streets run north-south or east west. A student lives 3 blocks west…

A: Here, to reach school, the student has to move 3 blocks west and 15 blocks south of a school.

Q: Consider the initial-value problem y' + exy = f(x), y(0) = 1. Express the solution of the IVP for x…

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Q: If y = (3 + 2x), what is y"? 00 48(3 + 2)2 © 12(3+2r)? O24(3 + 2)²

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Q: Q.2)(A) Determine (215) ² Σ (5)(2+1) of each point convergens or diverges: 13.0

A: Given

Q: Find an equation of a plane containing the following 3 given points P, Q, and M: P (3,-1, 2) and Q…

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Q: Graph the function. f(x) = √√x+5 Plot four points on the graph of the function: the leftmost point…

A: Given problem:- f(x)=√x + 5

Q: Given the function z = f(x,y) = x²y + 2y² + 4xy-2, find the following: a) Find all of its critical…

A: Here, we need to find the critical points.

Q: Given the matrices A ING B 3 4 the matrix X in the equation A (X + 3B) = C. 148.9 X = 9 and C= - [-3…

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Q: If a force of 128 lbs is required to stretch a 10-ft spring by 4 ft. How much work is done by…

A: Here we have to use the concept of integral calculus

Q: The logarithmic equation 2 log c = b, where a > 1, expressed in exponential form could be Oa² = bc…

A: Given

Q: 2. The subspace in R3 is a plane whose equation is x+y+z=0 x-2=0 x-2y+z=0 (a) (b) 2-0 (c) y-2--0…

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Q: (X^1/2 + 6) (X^3/2 -32)

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Q: Carlos surveyed 50 students about their favourite subjects in school. He recorded his results.…

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Q: using determination of integrating factors y (y^3-x) dx + x(y^3+x) dy=0 Attpemt only you can solve…

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Q: Solve the differential equation. 11.    ( 2xy – tan y) dx + (x2 – xsec^2y) dy = 0

A: The given differential equation is; (2xy-tany)dx+(x2-xsec2y)dy=0.

Q: The domain of the logarithmic function y = log4 (x + 3) is Ox>0, XER Ox-3, x=R Oxz-3,TER OX>0, XER

A: Let's find domain of given logarithmic function.

Q: Solve for C in the solution for dx/dy = xy^3/(2y^4+x^4) ; y(2)=4 Use 2 decimal places

A: Here we have to solve the given differential equation

Q: € G x² y" + (y²)² = ں

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Q: 51 b. Determine the gradient of the following function at Po h(x, y, z) cos xy + e + ln zx, Po(1, 0,…

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Q: Determine whether the series converges. Σk³ e-k4 k=1 The series >

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Q: Find f'(a) using the definition of the derivative at a point for: f(x). 1 = √x at a = 4.

A: Find derivative using  definition of f(x)=1x at a=4

Q: ed at (2,1) is Assuming that y is defined implicitly by the equation ²-2-58, the derivative

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Q: An inverted conical tank is being filled with water at the rate of 2ft3 per minute. If the tank has…

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Q: If y = (6x)¹/2, what is

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Q: Find the volume of the solids generated by revolving the region bounded by the curves y = 7r² and y…

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Q: Q2: Find the following limits 1-√x²+1 1. lim X-0

A: Given, limx→ 01-x2+1x2

Q: Use the difference an+1 an to show that the sequence {n - 5"} is strictly increasing or strictly…

A: To find whether given sequence is strictly increasing or decreasing.

Q: y=? € x ² y² + (y²) ² = 11 - U

A: see below the solution and calculation

Q: Prove the identity sin(-0)- cos (+0)

A: