The volume of a cylindrical canister is given by the formula V=nr^2h Part1. Write a function f(V) to express the radius of the canister as a function of the volume. Part 2. Suppose a certain type of canister must have a height of 32 centimeters (cm), so the quantity nh is about 100 cm. Write an updated version of the function f(V), using 100 for nh, to determine the radius of the canister that would result in certain volumes. Complete the table to find the values of f(V) for V = 25; 100; 625; 900; 2,500; and 10,000. Part 3. Plot the points from your table on the grid and sketch the graph. Part 4. If the graph were rotated 90° counterclockwise about the origin, which function would the result resemble? Explain your answers, including relating the two functions

Q: Let T :P2(R) → P3(R) be defined by T(f) = f(t)dt. Show that T is linear, find the nullspace and…

A:

Q: Find the general solution to the following problems: 1. (D² + 4D + 5)y 2. (D² - 1)y = 50x + 13 e³x 2…

A:

Q: That solution was incorrect

A:

Q: 1. Find the general solution of: dx dy _y+xy²+x² x+x²y+y³

A:

Q: Consider the DE y' = (5x + y + 7)², y(0) = 1 Solve it numerically using Euler's method (n=4) to…

A: Given y'=5x+y+72

Q: The figure shows a semicircle with radius 1, horizontal diameter PQ, and tangent lines at P and Q.…

A: As per the question we are given a circle of radius 1 and a horizontal line above the x-axis. Now we…

Q: Show complete solution

A: According to guidelines we can solved only first three subparts..thank you.

Q: Given: 30KN/m A 9m GOKN VV B Solve for the reactions

A:

Q: (a) Solve the first order equation for 2 and substitute into the second equ thereby obtaining a…

A: Given the system                   x'1=-2x1+x2                 ...(1)x'2=x1-2x2…

Q: ≤m for all FEF. subset of X. Then |||| ≤a for all & E nd F € F, ||F((rx/a)+a) || ≤m, so all /TI

A:

Q: 4. A thin homogeneous bar of thermal diffusivity 9, length 2 cms and its left end maintained at…

A: Given that a thin homogeneous bar of thermal diffusivity 9, length 2cms and its left end maintained…

Q: 6. Prove or disprove the following statement: (x E Z. x < 0) (3y E N. x-2y). Translate the statement…

A:

Q: compute the mass along the x-axis, the moment (M) around x=0, and the center of mass given the data…

A:

Q: Evaluate 11 2 By (+³+1)2 dx dy 24 by reversing the order of integration

A:

Q: 8.xy² If u = and error in x, y, z be 0.001, compute the maximum absolute and relative z³ error, when…

A: Given equation be u=8xy2z3 error in x, y, z be 0.001 Now ∂u∂x=8y2z3, ∂u∂y=16xyz3, ∂u∂z=-24xy2z4  and…

Q: We assume that in a village there are farmers, carpenters, and tailors, who provide the three…

A: We have to calculate the production of farmer and carpenter seperately

Q: . Obtain a solution to the following differential equation valid near the origin: y" + 3xy' + 7y = 0

A:

Q: The formula a. What was the population of the state in 2000? b. When will the population of the…

A: We have to find the solution for given problem.

Q: Find the largest interval of existence and uniqueness of solution for the IVP 1 x'+ (sec t)x t-1 *…

A: Here given the differential equation as x'+sec tx=1t-1 where xπ4=1

Q: If October of a certain year has 5 Wednesdays, on what days of the week could Halloween fall?

A: We know that there are 31 days in the month of october and Halloween's day falls on 31st of the…

Q: The equation f(x, y, z) = exyz+z=1 + e implicitly defines z as a function z = g(x,y) of x and y.…

A:

Q: Consider the initial value problem yty + 0.03y³, y(0) = a, where a is a given number. Draw a…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Find the solution of the given initial value problem: y (4) + 2y" +y = 3t+4; y(0) = y'(0) = 0, y"(0)…

A: It is provided that: y4+2y''+y=3t+4 and the initial conditions are: y(0)=y'(0)=0, y''(0)=y3(0)=1.

Q: u(x ) = 2 − 2x + 5x ª + 7x ³ + ſ', (x − t)u(t)dt

A: Consider the given Fredholm integral equation, ux=2-2x+5x4+7x5+∫-11x-tutdt So, it can be expand as,…

Q: 70 P is a point on a straight line with position vector r=a + tb. Show that 7=a+2a-bt+ B² By…

A:

Q: A bungee jumper leaps from a bridge. Velocity is determined by the given differential equation. dv…

A: Consider the given differential equation, dvdt=g-cDmv2 Since, we have given that g=9.81, cD=0.25,…

Q: H.w: Use the bisection method to determine the drag coefficient c needed for a parachutist of mass m…

A: It is provided that: f(c)=gmc1-e-cmt-40, m=68.1, t=10, g=9.81.

Q: D dz |z|=1 |z-a|² 2

A:

Q: EVALUATE THE FOLLOWING ITERATED 2TT √²H SS₁² p²sin y d p de do INTEGRAL. 4 ד

A:

Q: Question 4 All rational functions have at least one vertical asymptote. True False Question 5 A…

A:

Q: 2x = 1+ sint, y = cost-2, 0≤t≤n

A:

Q: Show your solution. Given the differential equation: x(x+3)y'' - 9y' - 6y = 0 Question: Which of…

A: We can solve the given problem by Frobenius method.  In this method we consider the series solution…

Q: Do the functions y₁ = cos5t and y2 = sin5t constitute a fundamental set of solutions of the…

A:

Q: (a) |([10]² – {1,3} × {2, 5, 6}) — {5, 7, 9} × {8, 10}|.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 3 "(x) = -x + x ²₁² = 1 √ ₁ ( x −t)³u(t)dt, u (0) = 0,u'(0) = 1.

A:

Q: Find the centroid of a lamina enclosed between the circles of radius 1 and 2 centred at the origin,…

A: Consider the diagram of the lamina as per given information, The centriod of the lamina is defined…

Q: 2П u(x) = ( ²5 - Ln (2+√3)) x 3 x + Sec (x )Tan (x) - [³ x t u(t)dt

A:

Q: Find the solution of the initial value problem 1 6y" - 7y + y = 0, y(0) = 6, y'(0); 6 Then determine…

A:

Q: Use cylindrical coordinates to find the volume of the solid. Solid bounded by the graphs of the…

A: Sol:-  The volume of the solid bounded by the graphs of the sphere r2 + z2 = 25 and the cylinder r =…

Q: The function f: RR defined by f(x) = 5x3 + 3x2-x + 7 is O(x). True False

A:

Q: Question 10 What is true about the function ) - A))→0 from above B) Ax) →∞ OC)) →0 from below D) x)…

A:

Q: Explain Mathematical modeling of anomalous diffusion.

A:

Q: Find all integers that leave a reminder of 3 when divided by 5,5 when divided by 7 and 7 when…

A: The given problem is to find all the integers that satisfies the given conditions. We have to…

Q: .3 4 1 1) dzdxdy S² S³ S1²3 S₁ 0 1 z(y4+1)

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 3 3 1. The function y = x² has undergone the following sets of transformations. If y = x²³ passes…

A:

Q: (a) r ≤ 4 case (b) r = 1+ cosa (c) r = 1-sinf

A: "Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: 3. For each of the functions below, decide whether the function is injective and surjective (i.e.,…

A: 3. (d) Given f:P([5]×P([8]) →P([5]×[8]) defined by f(S1, S2)=S1×S2   (e) Given…

Q: Find the general solution to the equation y(4) — 4y" + 4y″ = 0. NOTE: Use C₁, C2, C3, and c4 as…

A: Given differential equation is y(4) - 4y''' + 4y'' = 0

Q: Given the following linear problem Minimize z = 5x1 + 2x2 + 6x3, subject to: 4X1 + 2x2 + x3 ≥ 12 3x1…

A: Introduction: The pivot variable is crucial to the conversion of the unit value since it is used in…

Q: A weight is oscillating on the end of a spring (see figure). The displacement from equilibrium of…

A: To find the time when the weight is at the point of equilibrium.

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: