A 42 cm piece of string whose length is given below is cut into two pieces. One piece is used to form an equilateral triangle and the other to form a circle. What should be the perimeter of the equilateral triangle and the circumference of the circle so that the sum of the areas is a minimum? Find the minimum sum of the areas. Express the answer in terms of pi.

Q: Which of the following is the Taylor series expansion of the function (x) =ex? with center at 0. 00…

A: Taylor Series representation of e-x about x=0 is given by, e-x=∑n=0∞-1nxnn!....(i)

Q: Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, from the…

A:

Q: determine which statement is true   x + 2y^2 + 20 = 0 (A) not a function (B) function; domain: R…

A:

Q: Find the center of x 2 + y 2 - 10x - 8y + 1 = 0. (5, 4) (-5, -4) (-10, -8)

A:

Q: 4. If the marginal cost for a product is MC = 2x +9 and the production of 10 units results in a…

A:

Q: Let R(x), C(x), and P(x) be, respectively, the revenue, cost, and profit, in dollars, from the…

A:

Q: 7. Evaluate (5 – x)dA where R {(x, y) : 0 < x < 5,0 < y < 3}

A: Double integral

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: 6. sin v- -2 cos Va + C %3D 4x2 1. Ja-8 dx = 18 (1-8x)4 (1-8x3)4 8. Se*dx =+ %3D In e

A: As per the instruction, we will be answering only the first three subparts. For (6),    ∫sinxxdxLet…

Q: suppose f(x)= x^3+ax+b where a<0 and has stationary points at (-2,3) find a and b and find position…

A:

Q: Solve the differential equation dy 1 dx Зу3 By the method of separating the variables

A: To solve the given differential equation.

Q: Find the n-th Taylor polynomials for 1 about x = 3 and express it in f(x) = x+ 2 sigma notation.

A: Taylor polynomial of nth degree of f(x) centered at 'a' :          f(x) = f(a)…

Q: 1. Sketch the graph of r = 6/ (3 + 3 cose).

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: dr

A:

Q: d 31. Evaluate et ht dt 1 ((1+ Int) dx 1 A) x(1 + Inx) C) x+1 xe* B) 1+x D)

A:

Q: (5) Find the volume of the wedge in the first octant that cut from the solid cylinder x² + y? < 4 by…

A:

Q: Q1// Find the Area bounded by: x = -y2 and x = y-2

A:

Q: {In (n+10) – In (n+5)}°

A: an =ln(n+10)-ln(n+5)an =lnn+10n+5limn→∞ an =LIf the limit exists and finite, then the sequence is…

Q: A triangle is inscribed in a parabola such that the first vertex (point A) is at the origin and the…

A: This question can be solved using the concept of maxima and minima.

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…

A:

Q: Given that å = i+ 53 -3k and b = 3ỉ – 23 +k are vectors in 3D. Find the value of ả x b and b xả…

A: Given; a→=i→+5j→-3k→, b→=3i→-2j→+k→

Q: Differentiate the following, and simplify: a) y = x'e* b) f(x) = 2" + 7** evi c) g(1) = 1+ev

A:

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

A:

Q: F(rn) f(In) for f'(En)] For the function f(r)- tan(z), write Newton's formula as , 1 = In solving…

A:

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

A:

Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z = 10xe…

A:

Q: The non-homogenous solution of the following equation by using variation of parameter method y" + y…

A: Given

Q: x-2 lim 3x+5+2x' +2*

A:

Q: 2 Compute limx→16; 1-x2 1 X-1

A:

Q: g Ca) : -8) (uring logarithmic differentiation) 2 +4 11

A: We can find the derivative using logarithmic differentiation as below.

Q: Sketch the graph the integrands and use areas to evaluate the integrals. LV16 – x² dx

A: Here we have to use areas to evaluate the integrals.

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

A:

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

A:

Q: Show that whether x5 + 10x3 + x + 1 is O(x4) or not?

A:

Q: Area: 7A square centimeters

A: The length is 7/3 cm and breadth is 3 cm or vice-versa for the perimeter to be minimum

Q: Vector Calculus Given, A = 2? zi – 2y32j+ x} zk. Find divA at the point (1, –1, 1).

A:

Q: r(0) = tanh-1(cos 0) + cosh(0º)

A:

Q: . Consider the polar curves C1:r= 3 sin20 and C2 :r = 3 cose, and let R be the shaded region as…

A: r=3 sin 2θ and r=3 cos θ R is the shaded region: To Find:a. Find all points of intersection of C1…

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

A: As per guidelines we can answer only three subparts questions at a time, if you need more answers…

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: 2. Find the area of the region bounded by the curve r = 2 cos 30 .

A: Given problem:- Find the area of the region bounded by the curve r = 2cos(3θ)

Q: 5. A reservoir is 80m long and its cross section is an isosceles trapezoid having equal sides of…

A: We need to find rate of water leaking.

Q: 8. Determine if 2n-1 [5 -1 is cont 7n n=1

A: Given

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

A: This question is based on indefinite integral.

Q: Integrate the following using partial fraction decomposition: integral sign  [(3x2+4x+56)  /…

A:

Q: 4–x? c1-a²-y² x dz dy dx = -7+x?+y?

A:

Q: Sketch the graph the integrands and use areas to evaluate the integrals. 1. Llx| dx

A: As per our guidelines, we can help you in solving only first problem, rest of the problems you have…

Q: x³+2x? -3x x²+4x+3 2) Evaluate lim -6-1. x→-3

A: Use l-hospital rule.

Q: per ale hey sepalating 4. A line passes thru (5, 11) and cuts a right triangle with the coordinate…

A:

Q: A teacher has prepared 20 mathematic and 30 geometric and 25 physics questions for a test he can…

A: This question can be solved using the concept of combination.