In a world where people's happiness is the product of the square of the amount of one's food which costs 200 pesos per kilogram and number of BTS collectibles that cost 50 pesos per piece, determine how many pieces of BTS collectibles will maximize the happiness of a person whose budget is 3000 pesos. Use the method of Lagrange multipliers.

Q: Change the Cartesian integral into an equivalent polar integral. 2 2 a -x 00 S SO dy dx = dr de 2 2 ...

A:

Q: 4 dx J (3+12x?)arctan 2x

A:

Q: Question Find an algebraic expression equal to csc(cot (4x)). (You may assume that - < cot-" (4x) < ...

A: First we let cot-1 (4x) =thetha Then we using csc2 x=1+cot2 x

Q: Find (f-1)'(a) for f(x) = ーX-3 when a = 3x +2 (Enter an exact answer.) Provide your answer below: ((...

A:

Q: Calculate the amount of money​ you'll have at the end of the indicated time period. You invest ​$400...

A: Given query is to find the amount after 8 years.

Q: -6 -5 4 The plot above is created with the parametric equations S¤(t) = a cos(bt) y(t) = c sin(dt) T...

A: Solve the following

Q: 1. f (х) — 5ӕ -4

A:

Q: I Find the second derivative(y") of the following functions and simplify the final results. 1. y = x...

A: Product  Rule of differentiation: du.vdx = u.dvdx +dudx.v dcos(x)dx = -sin(x) dsin(x)dx = cos(x) dxn...

Q: ly Find tue indefinive intgrel by making ful frebstitution x = 4sin O. de (16-x²) %

A:

Q: Find the area of the region bounded by the given curves. Decide whether to integrate with respect to...

A: According to our guidelines we can solve only three question. (1)y=3x2, y=0 and x=3Area=∫033x2dx    ...

Q: Consider f(x)=ax+xln⁡(bx) for a>0a>0, b>1b>1, and x>1x>1. Find f′(x)f′(x): f′(x)=f′(x)= ------- Bas...

A:

Q: If u = e3x. du = 2 cos 2x dx then du = 3e* dx, v = sin 2x. Select one: True O False

A: Differentiate the equation u=e3x with respect to x.                                                 ...

Q: What Mclaurin Series this function represents: En=1(-1)n+1 =" = ¤ n 3 O a. In(1+x) b. cosx c. sinx O...

A:

Q: 2.) Find 1st derivative of y = e-'In (x-1)

A:

Q: dx sin? - cos 2

A: Here, the given integral is: I=∫0πsin2x2cos7x2dx Substitute x2=t⇒x=2t⇒dx=2dt as x→0⇒t→0 &amp; as x→π...

Q: Ísin^8 (3z) cos^5 (3z) dz * O 1/27 cos^9 (3z) - 2/33 cos^11 (3z) + 1/39 cos^13 (3z) + C O 1/27 sin^9...

A: Given integral I=∫ sin8(3z) cos5(3z)  dz

Q: 9 y = Arctan(+x, 1- 2x

A:

Q: Find a differential equation whose general solution is -4t y = cjet + cze¬4.

A:

Q: Question 3 If lim an = 0, then the series a, is convergent. n=1 True False

A: Note: According to our expert guidelines only first individual question is to be answered kindly rep...

Q: A cuboid has a square base of side (2 + 3)cm and a volume of (16 + 9 3)cm³. Without using a calculat...

A: It is given that, A cuboid has a square base of the side 2+3 cm and Volume of 16+93 cm3. Without usi...

Q: 8. Using (4.6), find the polynomial P2(x) that interpolates the following data. In each case, simpli...

A:

Q: Related Rates - Rectangles Mar 20, 9:02:57 PM Watch help video A rectangle has a length of 7 inches ...

A:

Q: n=0

A:

Q: IV. Exercises: Find y', y", y'", and y"" for the following expressions: 1. y = x* 2. y = 2x2 + 3x - ...

A:

Q: - y = (2x² – 4x + 1)60

A: Since you have asked multiple questions in a single request we would be answering only the first que...

Q: Using f (x) = In(3 – 2x), find the value of L and calculate the radius of convergence of the series....

A:

Q: С. 1 Evaluate the following limits x2 +6x+5 1) lim x-5 x²+2x-15 x(х-5)-24 2) lim x→8 x2-8x (2+x)3-8 ...

A:

Q: (a) Graph the function f(x) = 1/x (b) Hence, using translations, reflections etc., graph 1 f(x) = -1...

A: We have to draw the graph of the given functions according to the given information 

Q: . Sketch the graph h(x) = x2 -x-12. Then, a.) Determine the line tangent to h(x) at x=c. What is it...

A:

Q: Letting I répresent the grams of salt in Tank A, and y represent the grams of salt in Tank B, set up...

A: Rate of change of salt concentration = difference of inflow salt concentration and outflow salt conc...

Q: n=0 n!

A: This is series problem

Q: A. Determine the derivative of the following using the Four-Step Rule 1. f (x) = 5x – 4

A: Note:- These are multiple questions and according to our company guideline we can do maximum 1 quest...

Q: (a) f(x) = (3x² – 1)/T +x/4 (b) y(x) = r-1 r³+2 (c) g(t) = [(t³ + 4)(t² – 1)]/

A:

Q: X- 3/ = 12

A:

Q: [ a(x+y) - xty]dy = (x+xy²- 2y +3)d« when x-1, yal 3. %3D (9xy - 2y²) dx - ( 6x²_ xy) dy =0 4.

A: I have authority to answer one question only, if you want another question to be solved then upload ...

Q: Using the integration bay parts formula with u = x- dv = cos x dx, the integral x cos x dx becomes

A: The given integral can be solved as follows:

Q: y' + 3y = 5e2x – 6; y(0) = 2

A: since you have posted multiple question in this question which are not interlinked so i have solved ...

Q: find the second derivative of y = x In x A 1/x в) 1/2х D) 2x

A:

Q: sin? - cos' 2 2 zdx 2.

A:

Q: 2x-3 dx J9x2-12x+4

A:

Q: Find dy/dx by implicit differentiation. 4. x²- 2xy + y = c 5. x'y + xy² =3x 6. y +x°y =1+ ye?

A: This question is based on differentiating equation both side with respect to x.

Q: Exercise 2 Find symmetric equations of the normal line to the surface 4 + y – 162 = 0 at (2,4,2). (a...

A: Given surface is     4x2+y2-16z = 0We will find the symmetric equation of the normal line to the sur...

Q: +00 2 -1)"+1(3n)! 3n+1

A:

Q: Find the area of the surface obtained by rotating the curve y = 5x° from x = 0 to x = 9 about the x-...

A: Let's find. 

Q: If lim an = 0, then the series an is convergent. n=1 O True O False Question 4 For Item 4, determine...

A:

Q: -6 -5 -4 -5- The plot above is created with the parametric equations S¤(t) = a cos(bt) ly(t) = c sin...

A:

Q: +00 El-1)nInn- n=2 n2

A: The given series,        ∑n=2+∞-1nln nn2

Q: The points P and Q have position vectors, relative to the origin O, given by OP = 7i + 7j - 5k and o...

A: We have to find equation of plane and distance AB

Q: How to solve the following ordinary differential equation (ODE) xy' – 2y + y² = x“.

A:

Q: X X sin². sin? - cos' ,dx CoS 2 2 2.

A: x2=u → dx=2 duI=2 ∫ sin2u cos7u duI=2 ∫ sin2u cos u cos6u duI=2 ∫ -sin2u cos u (sin2u-1)3 dusin u =v...