1) Write a differential equation that models this situation. Let V represent the volume (in gallons) in the tank and t represent the time (in minutes). 2) Solve for the general solution (do not solve for V). 3) Use the initial condition to find the constant of integration, then write the particular solution (do not solve for V).

Q: Q6) Find the Area bounded by the curves y = √x and x = 2y-y² ,with sketch.

A: The objective of the question is determine the area bounded by the given curves.

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A: Let's find t for the given  terminal points.

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A: We have to solve a part 6 and 7.

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A: The Price wise function  is given below.

Q: = X ¹0 = 1 8 = = 0 ay!!

A:

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A:

Q: Determine the area, in square units, of the region bounded by f(x)=−7x3−4x2+2x−1 and…

A: To find the area bounded first find the intersection of f(x) and g(x)

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A: Recall:., To find Average,  Ave=1b-a∫abS(t)dt We have, S(t)=600 et, a=1, b=5

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A: We need to find dy/dx.

Q: (6) Using suitable transformations, evaluate closed region in the first octant bounded by the…

A: We have to solve given Questions.

Q: Suppose that the polynomial function fis defined as follows. f(x)=(x-13)²(x-8)³(x+4)³ List each zero…

A:

Q: on with a nonremovable discontinuity at x=4 on with a removable discontinuity at x=-4 on that has…

A: Answer is in next step . please give a like !!

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A: To find a function Fx satisfying the given conditions.1 F'x=2x; F1=22 F'x=3x2+2; F-3=-323…

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A:

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A:

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A:

Q: Find the formula for a cubic polynomial, ax³ + bx² + cx + d, with a critical point at x = 2, an…

A: Use double derivative concept

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A: To find out f-1(-1).

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A: Solve the following

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A: Topic = Derivative

Q: Solve for x: |x+5| < |X-71

A: Follow the procedure given below.

Q: Q2: Fill the blank: 1) lim (1+)52 x48 4x 2) lim x.e-3x = X-80 3) (csch¯¹x³) = . dx 5x =...

A:

Q: volume Find the about the given a) sketch the graph 6) Find the limit and 6 OF c) Complete volution…

A:

Q: Use Newton's method to approximate a root of the equation 3x² + 7x² + 2 = 0 as follows. 1 Let x₁ = 3…

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Q: Q4) Find dy /dx for the following functions : a) y².cotx= [sin(x.y)]-¹

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

Q: Consider the following function. Function f(x) = 8x4 - 6x³ - 165x² - 37x + 60 (a) Verify the given…

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Q: In the following table the values series y are consecutive terms of a series which the number 31 is…

A: Concept: Newtons forward difference interpolation method: Extrapolation is the process of computing…

Q: Graph the rational function. -5x-15 f(x)=- x²+2x-15

A: Graph the rational function :      f(x)=-5x-15x2+2x-15 Start by drawing vertical and horizontal…

Q: Q3)Evaluate the following integral by using Trigonometric Substitutions Method. dx y = S₂ 9x² +9

A:

Q: (a) Given functions f(x) = 3x+2 and g(x) = x³ - 1, find fog and the inverse of fog. 4. (b) Use the…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the…

Q: generated by revolving the given plome area line uning the dirc method. (answers ore in cubic a.)…

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Q: // لاح - لا - لا -4

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A:

Q: Solve the given initial value problem. x³y² - y³ = 45 ³y² + xy³ = 18 x²y² + xy³ = 90 x¹ y² + y² =…

A: Here we have to solve the differential equation.

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Q: The value of integral (cos(4x)+cos(81)) dx

A: We have to determine the integral

Q: Which of the following is the graph of the piecewise function f (x) - 7 f(x) -2-1 2 1 √-x-1 if XS-1…

A: To plot the piecewise continuous functions: f(x)=-x-1 if x≤-1xx2-x-2 if -1&lt;x&lt;2log2(x-1) if x≥2

Q: is: The value of the following limit Lim (cos(x))ou(x)

A: The value of the limit is when x tends to 0 for the function (cos(x))cotx

Q: 5. Find parametric equations for the line through the points (1, 3, 0) and (2, 4, 4).

A: 5. Given that, the points are 1,3,0 and 2,4,4. Note that, the symmetric equation of the a straight…

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Q: 2a)Use triple scalar to verify that the following vectors are not coplanar. a=[-2,1,0], 5=[-3,4,5],…

A: Given problem:- 2a)Use triple scalar to verify that the following vectors are not coplanar.…

Q: Use Newton's method to approximate a root of the equation 4 sin(x) = x as follows. Let ₁ 2 be the…

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Q: The number of bacteria in a culture is given by the function n(t) = 940e 0.1t where t is measured in…

A: To find out the relative growth rate.

Q: 1. For the curve given by R(t) = (cost + tsin t)i + (sin t − t cost)j + (t^2)k, find a. the length…

A:

Q: (i) Find the shortest distance from the origin to the line 3x + y = 6 and give the coordinate of the…

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Q: A utilities company wants to deliver gas from a source S to plant P located across a straight river…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…