The base of a solid is the region in the xy-plane bounded by the lines x = a and x = b, the graph of y = f(x) and the x-axis. The cross-sections of this solid perpendicular to the x-axis (and the xy-plane) are squares: a y=f(x) each slice is a square b X

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Q: 1 12. f(x) = -3x -9, g(x) = -x-3

A: Verify that f and g are inverse functions

Q: Consider the position function s(t) = 7 sint that describes a block bouncing vertically on a spring.…

A: Given position function s( t ) = 7sin( t )Average velocity ( Vavg ) = ∆s∆t

Q: The equation r(t) = (4t+9) i+ (5t² − 1) j + (3t) k is the position of a particle in space at time t.…

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

Q: Determine the point at which the line passing through the points P(1, 0, 6) and Q(2, -1, 2)…

A: Topic = 3D-Geometry

Q: The graph below is comprised of transformation of tool kit functions. 16 -5 -4 -3 -2 f(x)= -1 = 6 4…

A: A detailed solution is given below.

Q: The profit function of Brackets Inc, LLC for 3 inch steel brackets is P(x) = 127x – x² – 2626. Find…

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Q: Determine the infinite limit. lim¸In(x² – 36) x→6+

A: Given that a limit problem and we solve this by using general property of limit.     Here i attached…

Q: Change from rectangular to spherical coordinates. (a) (9, 3√3, 6) (p, 0, 9) = ( (p, 0, 4) = ( ) (b)…

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Q: For the following function, make a table of slopes of secant lines and make a conjecture about the…

A: Given f( x ) = 7cosxat point x = π2

Q: Three fire observation towers are located at points A(-10, -14), B(7, 13), and C-7, 13), on a map…

A: Given: A(-10,-14)   B=7,13    and C-7,13.   Distance 17 km , 15km , 13 km

Q: The graph of a function y = f(x) is shown below. The function is constructed using line segments and…

A: We can graph the given function by using the transformation rules.

Q: What does x = 4 represent in xy-plane? Sketch this 2D representation. What does x = 4 represent in…

A: Given: What does x = 4 represent in xy-plane? Sketch this 2D representation. What does x = 4…

Q: Question 1 Let g(t) be the population (in thousands of people) of Calculus City, as a function the…

A: Given g( t ) be the population t = time t = 0 corresponds to 2020 In 2020 , the population was 10000…

Q: Given that f(x) = 8x + 7 and g(x) = 4x², calculate (a) f(g(0))= (b) g(f(0))=

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Q: The quantity demanded each month of Russo Espresso Makers is 250 when the unit price is $140. The…

A: Let p denote unit price and x be the number of units As we know slope of linear function passes…

Q: Company A xx 0 5 10 50 100 200 CC 60 61.25 62.5 72.5 85 110   Company B xx 0 100 150 175 190 200…

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Q: So whats the answer?

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Q: Find the general solution of the given second-order differential equation 3y" + 2y' + y = 0 y(x): =

A: The given differential equation is;  3y''+2y'+y=0

Q: The function s(t) represents the position of an object at time t moving along a line. Suppose s(3) =…

A: Given that s(3)=150, s(5)=190, where s(t) represent the position of an object at time t.

Q: Find the area of the shaded region. f(x) = -x³ + x² + 16x 3) g(x) = 4x (-3,-12) 30+ 20 10- -20- -30-…

A: Given curves equations:- fx=-x3+x2+16x , gx=4x

Q: 3, 0≤t≤1 f(t)=3-4t, 1 ≤ t ≤ 3 -t², t≥ 3 = {3-

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Q: Find the volume of the solid by rotating the region bounded by the given curves about the specified…

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Q: HOMEWORK NO. 3.2: Find the general solution. 3. (D² +6D+1)y = 0 4. (2D³ - D² + 36D - 18)y=0

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Q: Compute the area of the parallelogram with vertices A(2 1), B(5,0), -2) and D(4, -1).

A: We are asked to find the area of the parallelogram

Q: Find the volume of the solid generated in the following situation. The region R in the first…

A: To find the volume of the solid generated in the following situation. The region R in the first…

Q: Eliana is flying a kite tethered to the ground at the end of 117 meters of string. If the a of…

A: Question - Eliana is flying a kite tethered to the ground at the end of 117 meters of string. If the…

Q: Suppose the number of subscribers, S, to a YouTube channel increases according to S(t) = k(1.13)t,…

A: A detailed solution is given below.

Q: Evaluate the difference quotient for the given function. Simplify your answer. f(x) = 1 + 4x-x²,…

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Q: Evaluate the function f(x)=x²+x for the given value of x. F(2)=

A: To find f(2) , substitute x=2 in f(x).

Q: Find an equation of the sphere with center C(3, 4, 5) that passes through the point A(1, 3, 3).

A: Question - Find an equation of the sphere with center C(3, 4, 5) that passes through the point A(1,…

Q: Determine the slope of the tangent line, then find the equation of the tangent line at the given…

A: We have given parametric equations x=6t y=3t3 When t=-1 x=6-1=-6 y=3-13=-3 Say,  x1,y1=-6,-3…

Q: Compute the derivative of the vector-valued function. r(t) = et i + 5et j + k

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Q: John works for the local used car dealership. His weekly salary is $375 plus a commission based on…

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Q: World population¹ is about P = 7.68(1.0103)', with P in billions and t in years since 2020. (a) What…

A: Let's solve given population problem.

Q: Your college newspaper, The Collegiate Investigator, has fixed production costs of $60 per edition…

A: Givenfixed cost( F ) = 60 variable cost( V ) = 0.4 per copySelling cost( S ) = 0.6 per copy

Q: Find the rules for the composite functions f. g and g. f. 1 f(x)=√x+10; g(x) = x-10

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Q: Perform the following calculations and report the answers to the correct number of significant…

A: Solving the following problems

Q: (a) Find a simplified form of the difference quotient and (b) complete the following table. f(x)=2x²…

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Q: State the region enclosed by the given curves and find its area. x = y¹, y = √√√2 — x, y = 0

A: To state the region enclosed by the given curves and to find its area. x=y4, y=2-x, y=0

Q: Problem #5: In the process of solving the differential equation x³y - 6x²y = cos(6x), x > 0, which…

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Q: Find the derivative of f(x) =-2x + 10x8 f'(x) =

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Q: In AABC, side a=23, side b= 12, and m<A=20°. What is m<B to the nearest degree?

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Q: sin 57 a sin 37 127

A: given  sin(57°)a=sin(37°)127

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Q: # 1-7 Give the name of the parent function and describe the transformation represented. 1. g(x)=x²-1…

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Q: ii) If the initial charge in the capacitor is zero, determine a formula to calculate the voltage.…

A: General expression for the voltage in a capacitor is Vc=3t210+C1Capacitor is a storing element in…

Q: I can not see the whole answer

A: Given,            Your college newspaper, The Collegiate Investgator, has fixed production cost of…