Consider a closed rectangular box with a square base with side x and height y. a. Find an equation for the surface area of the rectangular box. S(x, y) = 20 (x + 2y) dy when x = 3 feet and y = 5 feet. dx b. If the surface area of the rectangular box is 78 square feet, find dy dx

Q: . Find an equation for the surface area of the rectangular box. =(x, y) dy = . If the surface area…

A: We will solve the surface area problem.

Q: For the equation, 2y(x^2 - y + x)dx + (x^2 - 2y)dy = 0, what is dM/dy - dN/dx?

A: 2y(x2-y+x)dx+(x2-2y) dy =0M.dx+N dy =0M = 2y(x2-y+x)N = x2-2yNow.            dmdy =…

Q: dy c) Hence find the solution when x = 0, y = 0 and 1. dx

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Q: A. y II

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

Q: Consider a closed rectangular box with a square base with side x and height y. a. Find an equation…

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Q: Consider a closed rectangular box with a square base with side x and height y. a. Find an equation…

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A: The objective is to find the derivative.

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A: The solution is given as

Q: dy = y? – 4 dx

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Q: NOTE: Enter the exact answer. yz dx dz dy -180 J–120

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Q: Given x = 4 In(t) and y = 16 t² then find dy dx d²y dx?

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Q: dx

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Q: Consider a closed rectangular box with a square base with side x and height y. a. Find an equation…

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Q: d?y -5dy + 6y = 0 dx2 Find the constant m if y = emx satisfies %3D dx

A: Given,d2ydx2-5dydx+6y=0A second order linear, homogeneous ODE has the form of   ay''+by'+cy=0For an…

Q: d'y If xy + y' = 1, find the value of at 2 dx (0,1). %3D

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Q: M(x,y) + N(x,y)*dy/dx = 0 ? is it Exact Equation?

A: Consider the equationMx,y+Nx,y×dydx=0provided that there exists a function ψ(x,y) such that∂ψ∂x=Mx,y…

Q: Find d?y/dx? implicitly in terms of x and y. x?y - 3x = 8 dx2

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Q: Find d^2y/dx^2 x=5(t+sint), y=5(t-cost)

A: To determine the derivative of the parametric equation.

Q: NOTE: Enter the exact answer. r3-y 5y dx dy

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Q: Given that y = (a + bx)e¯* where a and b are constants, show that d²y + 2 + y = 0 dx2 dx

A: Given equation is  y=(a+bx)e^-x

Q: Consider a closed rectangular box with a square base with side x and height y. a. Find an equation…

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Q: Find dy/dx fc (1) y = x³ Inx ,,2

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Q: Shows : 1 Vi- e2x dx = aresin(e") + ;e'v *V1- e²* + C (9) e*

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Q: Consider a closed rectangular box with a square base with side x and height y. a. Find an equation…

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Q: Question 10(both parts)

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Q: culate dy/dx.

A: Given that : The equation is x = e 2t + t3 , y = t2 e- t .

Q: Given x = 75 sint + 30 and y= 75 cost +4 dx (i) dt dy (ii) dt dy (iii) dx || ||

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Q: Consider a closed rectangular box with a square base with side x and height y. a. Find an equation…

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Q: (бх + у?)dx + (2ху — Зу?)dy %3D 0 уз 3.

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Q: Consider a closed rectangular box with a square base with side x and height y. a. Find an equation…

A: Since base is the square : So   Length(l) = x  width(w) = x Height(h) = y

Q: For the equation, y(x+y+1)dx + x(x+3y+2)dy = 0, what is dM/dy - dN/dx?

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Q: Given z = 1le lle*y® , find 10 dz dz dy

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Q: The value of [ yx? +y? dx dy %3D

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Q: Consider a closed rectangular box with a square base with side x and height y. a. Find an equation…

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Q: V1-x² e-(x²+y²) dy dx

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Q: Find the solution of dy X. +y.Inx y.lny dx Show all your calculations.

A: Given equation is as below :

Q: For the equation, find dy/dx evaluated at the given values. x2 + y2 = xy + 28  at  x = 6, y = 4…

A: Given : x2+ y2 = xy + 28

Q: dy If x=sin y, find the value of at the point dx 2 3

A: Since we have been given that x=sin y -(i) and our aim is to find the value of dydx at the point…

Q: Consider a closed rectangular box with a square base with side z and height y. a. Find an equation…

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Q: } Identify (write down) the type of DE, and find the general solution. (у - 3x)dy %3D (x + Зy)dx

A: Type of DE is, homogeneous & linear and order is 1.   The solution is provided below :

Q: Given y=ae" +Be where a and B are constants. Show that d'y Ay. dx

A: Given that: y=αe2x+βe-2x…

Q: Given a = 12 ln(t) and y = 144 t2 then find %3D dy dz &y dz2

A: x=12ln(t)y=144t2

Q: The volume of a right circular cone of radius a and height y is given by V = dy volume of the cone…

A: Explained below

Q: Find for the indicated function y. dx y=15* + e7 (Type an exact answer.) dy dx

A: y=15x+e7Differentiate w.r.t x

Q: Consider a closed rectangular box with à quare height y. a. Find an equation for the surface area of…

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Q: NOTE: Enter the exact answer. c6 V36–z² xy dy dx dz | 0. 0,

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Q: Find the value of d-y/dx at the point defined by the given value of t. x- 6t 2 -3, y= t 5, t=1 3D1…

A: Take the derivative than eliminate the extra terms as required.

Q: Consider a closed rectangular box with a square base with side x and height y. a. Find an equation…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.