1. Here the the volume of between 0 and z (in meters) is ㅠ - - V(z) = (12z – (z − 1)³ — 1) . 3 The barrel is being filled with liquid in such a way that at a certain moment in time (in seconds), the rate of change of the volume occupied by the liquid is 127 m³/s and the rate of increase of the level z is 3 m/s. (a) Find the level z at which this occurs. (b) Find the volume of liquid at that time.

Q: lim ex x 0x = ex lim x-0 1 LHR = 1 1 = 1. Think carefully about the conditions for l'Hôpital's rule…

A:

Q: Given P(x) = 3x5 – 20x² + 118x³ – 530x² + 1075x – 750, and that 5¿ is a zero, write P(x) in factored…

A:

Q: If 8000 dollars is invested at 8% interest, find the value of the investment at the end of 6 years…

A:

Q: Solve for the general solution: Oy 0.25x^2 sin(4x) + cx^2 Oy -0.25x^2 sin(4x) + cx^2 Oy -0.5x^2…

A:

Q: kite 100 ft above the ground moves horizontally at a speed of 2 ft/s. At what rate (in rad/s) is the…

A: We will find the required.

Q: The following is known about f(x): Iim     f(x) = 1 x->2 There is a discontinuity at x = 2 Which…

A:

Q: 6) Prove cos4x -sin+x= cos 2x

A:

Q: If x < 1 (x2 + 1 x - 22 if x 2 1 (a) Find the following limits. (If an answer does not exist, enter…

A: We need to find out the limits.

Q: Find the absolute min and max values of each function on the given interval. f(x) = x³ - 6x² - 15x +…

A: Given function f(x)=x3-6x2-15x+1

Q: 8) Prove sin (x+y) sin (x-y) = tan(x)+tan (y) tan(x)-tan (y)

A:

Q: Find an equation of the plane. The plane that passes through the point (-1, 2, 1) and contains the…

A: Given planes:- P1:x+y-z=5P2: 3x-y+5z=3

Q: Find dy by implicit differentiation. x² x+y dx 11 = y² + 5

A: Given query is to find the derivative.

Q: I find the limit. Use l'Hospital's Rule where appropiste. If l' Hospital's Role does not, find the…

A: limu→0u+u45-u2

Q: Which of the following integrals is the area between the graph of f(x) and the y-axis from b to c…

A: Given graph:-

Q: The following graph shows a rough approximation of historical and projected median home prices for a…

A:

Q: Finding the intercepts, asymptotes, domain, and range from the... OF BOASADRO Shom all asymptotes…

A: Given query is to find characteristics of the function.

Q: Choose the correct answer Find a function f(x, y, z) such that Vf(x, y, z)= F(x, y, z) = (yz, xz,…

A:

Q: Blood Alcohol Level  The percentage of alcohol in a person's bloodstream t hr after drinking 8 fluid…

A: Given:-  The percentage of alcohol in a person's bloodstream t hr after drinking 8 fluid oz of…

Q: y"" - 4y"+y+6y=0

A: Given :y'''-4y''+y'+6y=0

Q: The polynomial of degree 4, P(x) has a root of multiplicity 2 at x = 1 and roots at x = 0 and x =…

A:

Q: 2. Let f(x)= (a) (b) (c) x x+1 and g(x)=2x-1. Find fog and its domain. Find go f and its domain.…

A:

Q: 1≤ 0≤36 arcsin (~1²3/2)

A: The objective of the question is evaluate the value.

Q: 3. f-¹(x) = ± √T 4. None of these 5. f¹(x) = √T Find the inverse of f(x) = x7. 1. f(x) = x 7 2.…

A: Given query is to find the inverse of the function.

Q: Given the function y = Select one alternative: dy dx dy dx dy dx dy f(g(x)) h(x) which of the…

A: Solve the given

Q: A function has a relative maximum at (-1,3). Which of the following could have been the test results…

A:

Q: Find the derivative of the function. f(x) = Upload X-2 Choose a File

A:

Q: Write a function in any form that would match the graph shown below. 10 8 Answer: f(x)= -2 20 16 12…

A: Given query is to find the function of the graph.

Q: Σ(1) A k! μέρος

A:

Q: Evaluate the definite integral. Use a graphing utility to verify your result. fixe- -3x² dx

A: integration

Q: x²-x-6 x² + 4x+4 x +5 +6 + 6-2x a) Factor and determine the non-permissible values of x. 2. Consider…

A: Solve the quadratic equations to find the roots.

Q: 2. y" + 3y + y = (2-6x) cos x - 9 sin x

A:

Q: You are a lifeguard and spot a drowning child 40 meters along the shore and 50 meters from the shore…

A: Distance along the shore= 40m Distance from the shore= 50m Run speed = 4 m/sec  Swim speed = 0.9…

Q: Determine whether the function g(x)=√x+1 is invertible, and find the inverse if it exists.

A: Given query is to find the inverse of the function.

Q: Find poly degree 4. zuos are: 3i, 5 (Multiplicity 2) a

A:

Q: В С -10-2 -6 -2 1 5 13 2 69 3x + 2y = 4 >+ X

A: We have to find out

Q: 2 Let f(x) = √3x² + 3x + 2 f'(x) = ƒ'(1): = OF

A: Topic - Derivative of  a function We are given, f(x)=3x2+3x+2Formulas usedChain rule:…

Q: 10- 8- 6- 4. 2- NY of y = f(x) -2 4 6 -8 Xx 10

A:

Q: 4. A function f has the following verbal description: multiply by 3, add 5, and then take the third…

A:

Q: Differentiate a. Y = y the following 1 x² + x² +1 b. g(u) = √ 24 +√√√3u functions

A:

Q: show me steps on how to get the rational equation: x-int = -2/5, 1/3, y-int 4/15, Horizontal…

A:

Q: 9. We know that 1 ² = n(n+1)(2n+1). Use it to determine the following 26 Σ₁² i=6

A:

Q: ху 1-23 y =

A:

Q: 2. Determine whether the series (a) Converges 00 (b) 5 3/2 converges or diverges. Diverges

A: need to find out the the series converges or diverges.

Q: Write a polynomial with leading coefficient 1, degree 5, zeros at x = i and x = 2 — i, that passes…

A: To write a polynomial with leading coefficient 1, degree 5, zeros at x=i and x=2-i, that passes…

Q: Consider the function f(x) = 2 - 6x on the interval [-5, 5]. Find the average or mean slope of the…

A:

Q: Question A4 and A5 relate to the following information. In a goodness of fit test, the observed and…

A:

Q: e² 82. · [ (v + In u) dv du e In u

A:

Q: 4. The value of a timber forest after t years is V(t) = 4 maximized.

A:

Q: Determine the solution for the following higher-order homogeneous differential equation. Also,…

A:

Q: Write a polynomial with degree 4 that has a zero at x = 3i, and a zero at x = 5 with a multiplicity…

A: