the length of a child's square-based jewellery box is 5 cm more than its height. the box has the capacity of 500 cm3.solve the polynomial equation to determine the dimensions of the box

Q: 7. (D+ 3)'y = 15x'e-3* 8. (D- 4)'y 15x²e**. 9. D (D – 2)²y = 16e2 10. D2(D + 3)²y = 9e-3x 11. (D² –…

A:

Q: Consider the following planes. 3x + 2y - z = 42 x - 4y + 2z = 0 (a) Find the angle between the two…

A:

Q: 2. y = loga(x³ + 2x – 2)

A:

Q: Integral Calculus: Integration by Parts (Original method

A:

Q: Find sets of parametric equations and symmetric equations of the line that passes through the two…

A:

Q: Calculate L4 for f(x) = 24 cos () %3D L4

A:

Q: Derivatives of trigonometric functions Find the derivative. 1. y = 3sin x +3 cos x - tan x

A:

Q: e* +e* –x? - 2 Lim sin? x– x? 2

A: To solve the given limit of the function

Q: (x) = sin(x) ompute (5) + * (5 ) + x" (;) IT 2

A:

Q: Find dy and simplify whenever possible. dx sec x+tan x 1. у 3 sec x-tan x 2. у 3 е * соs e * — sin e…

A:

Q: An ice cream cone is filled with ice cream and surmounted ice cream in the formof a hemisphere on…

A: Given problem:- An ice cream cone is filled with ice cream and surmounted ice cream in the form of a…

Q: r(3x² x + 8x – 12)d: .3 x' +7x +12x

A: Given:          ∫3x2+8x-12x3+7x2+12xdx Factor the denominator:       =∫3x2+8x-12xx+3x+4dx The form…

Q: (8) 2xy = x2 + 2y² = x² dx

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Evaluate by using homogeneous D.E. 3 (3x? + y) dx – 2xydy = 0 03 In(x2 + y?) + 4 = C O a = C(9x³ +…

A: To evaluate by using homogeneous D.E.33x2+y2 dx-2xy dy=0

Q: tan x dx sec x+4 cosx 5.

A:

Q: After its fastest rate of growth ever during the 1980s and 1990s, the rate of growth of world…

A: I am attaching image so that you understand each and every step.

Q: y = |x|, y = x² – 1, x = -1, x = 1 - г2 — 1,

A:

Q: Which of the following is not equivalent to sin 0?

A: We are asked to find which is not equivalent to sinθ

Q: Direction: Solve the following equations using separation of variables. 1. y' =- y(1) = 1

A:

Q: Verify that the two planes are parallel, and find the distance between the planes. (Round your…

A:

Q: 3. Scse*x dx

A: The objective of the question is evaluate the indefinite integral.

Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

A:

Q: Direction: Solve the following equations using separation of variables. 4. sin(x)dx + ydy = 0, y(0)…

A: Given

Q: Find dy and simplify whenever possible. dx 1. y = arcsin + 4-x2 2. y = In(e¯* + xe¯*) sin x cos x…

A: To find derivative of given function.

Q: Find a) any critical values and b) any relative extrema. f(x) = x -2x +2 ... a) Select the correct…

A: We need to find critical points for maxima or minima.

Q: Learning Task 4: Given the equation x2 +y² =9. 1. Differentiate using implicit differentiation. 2.…

A: Since, the student has mentioned to solve only part numbers (4) and (5), so we are solving part…

Q: sin 2x (1 - 2 cos 2x)? dx 6.

A:

Q: Solve the differential equation with the appropriate method. Finalize answer equated to ky^n.…

A:

Q: Find the volume of the solid generated by revolving the area of a circle. (x-3)²+y²=9; about the…

A:

Q: 11 2

A: We can solve this as follows:

Q: Determine the Riemann sum that represents the illustration below. The function is Ax) = /x +1. 4- 3-…

A:

Q: Direction: Find the differential equation of the family of curves described. 5. Circles with fixed…

A:

Q: Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y =…

A:

Q: (b) Draw the graphs of the solution and of the forcing function; explain how they are related. [1, 0…

A: Given

Q: 4. Solve the second order differential equation given by 2 dt2 3z = 4c", z(0) = 0, dt dr(0) 0. dt

A: We will solve the second order differential equation.

Q: y^2=(x^2 - 9)/(x - 4) find the x and y intercept, symmetry, region/scope, asymptotes, critical…

A:

Q: 5 If csc² A = ;, what is the value of 1- cos? A? 2 5 5 2 2 Option 1 O Option 2 2 2 D Option 3 O…

A:

Q: (b) If a > b and c > 0, then ac > bc.

A:

Q: (x² + y² ) dx – xydy = 0 O 2y = x In cx² O y? = x² In cx²

A:

Q: Consider the following function. f(x) = x2 – 6x %3D (a) Find the critical numbers of f. (Enter your…

A:

Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction ||v|| =…

A: We can solve the given problem as follows:

Q: What is the magnitude of the vector cos 0 i + sin 0j+ 1? 01 O2

A:

Q: onsider the following planes. -4x + y + z = 4 12x – 3y + 4z = 16 a) Find the angle between the two…

A:

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) =

A:

Q: what is the minimum value of f(x)=3x2-18x+25 a. -2 b. 3 c. 6 d. -18

A: Given  f(x)=3x2-18x+25

Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations that are…

A: Given: Here, M=2x-2y2, N=12y2-4xy. Notice that ∂N∂x=-4y=∂M∂y. So, the function is exact.

Q: For an integral of the form f sin™(x)cos"(x)dx, saving one sine factor and converting the rest to…

A: Given data÷

Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations that are…

A: use the definition  of exact or non exact.

Q: E. Determine which equations are exact and not exact. Afterwards, solve for the equations that are…

A:

Q: VECTOR DIFFERENTIATION: If R = e^(−t) i + ln(t^2+ 1) j - tant k. Find: (a) dR/dt, (b)…

A: R=e-ti+ln(t2+1) j-tant k