Find two numbers differing by 42 whose product is as small as possible. Enter your two numbers as a comma separated list, e.g. 2, 3. The two numbers are

Q: A bookstore sells 96 history textbooks per month at $120 each. The owners estimate that for each $10…

A: let number of $10 price increase is x

Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

A: Using Trapezoidal rule

Q: 10. Find the indefinite integral J dx (3+5)2 dx

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Q: Find the equations for the lines through the point (a, c) that are parallel to and perpendicular to…

A: Given query is to find the equation of the lines

Q: roasted turkey is taken from an oven when its temperature has reached 185 Fahrenheit and is placed…

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Q: What is the relative minimum value of the function f(x) = 5-6x - x²? Of(x) has a relative maximum…

A: Since you have asked multiple questions, As per the guidelines we have to solve the first question.…

Q: This function: 24 4 -4 -2 0 -2 -4 has a jump disco has an infinite di

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Q: Find the average height of the paraboloid z = x² + y² over the square 0≤x≤3, 0≤ y ≤3. The average…

A: Given data The equation of paraboloid is, z=x2+y2. The limits of the square is 0≤x≤3, 0≤y≤3.

Q: Problem 1 A large pizza of radius 15 in. is sliced into 8 delicious equal pieces (the normal way a…

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Q: Consider the graph of Ax + By = C where A, B, and C are positive constants and A B. If the value of…

A: Solution: Given data, Ax + By = C where A, B, C are positive constants Ax+ By = C → (i)   X-…

Q: x3 The function f is defined by f(x) = x-2 Find the x-coordinates of all local extreme values of f.

A:

Q: A certain magical substance that is used to make solid magical spheres costs $600 per cubic foot.…

A: As we know that Area of sphere( A ) = 4πr2Volume of sphere( V ) = 43πr3

Q: Find (without using a calculator) the absolute extreme values of the function on the given interval.…

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Q: The line ℓ is given by the equations x −2y + z = 2 and x + y −3z = 4. That is, ℓ consists of all…

A:

Q: 1. An open box (no lid) with a square base has a volume of 4 cubic feet. What dimensions will…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 4. How much work is required to fill a spherical tank with a radius of 1m with water (1000 kg/m³)…

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Q: how do you determine it's a quarter circle?

A: Question is ∫-100100-x2dx is quarter circle

Q: Integrate the following using MISCELLANEOUS SUBSTITUTION ∫secxdx

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Q: You go to the doctor and he gives you 17 milligrams of radioactive dye. After 16 minutes, 5.25…

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Q: +P от 2+1дет акт гр

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Q: 1. For the function y = 2x²-3x use a simplified algebraic expression in terms of a and h to estimate…

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Q: Integrate the following using To xox $1+2x miscellaneas substitution:

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Q: No written by hand solution

A: Consider the following equations. a1x+b1y+c1=0a2x+b2y+c2=0 The system has unique solution if…

Q: A restaurant purchased kitchen equipment on January 1, 2017. On January 1, 2019, the value of the…

A: The given modeled is: Vt=14550 e-0.161t On January 1, 2019, the value of the equipment was $14,550.

Q: 14. Find all the critical points of the function f(x, y) = sin(x + y) and determine if they are…

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Q: Find the directional derivative of the function at the point P in the direction of the point Q. f(x,…

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Q: Let f(x) = 6x65x5. (If an answer does not exist, enter DNE.) (a) Find all critical values of f(x).…

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Q: If 3x2 + yx = 9, what is -? dx dx dx = = = 11 -6x-y² 2.xy -6x+y² 2x -6x-y2 2x² 6x-y2 2y 59

A:

Q: 7. Let E be the ball of radius 1 centered at the point (0, 0, -1). (a) Show that E is given in…

A: The solution is shown below-

Q: Let 6 sin x + 3 cos y = 4. dy dx d²y dx² -0

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Q: Let r(t) = (t², 1 — t, 4t). Calculate the derivative of r(t) · a(t) at t = 2, assuming that a(2) =…

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Q: Use the graph M of the derivative of f to locate the critical points zo at which has neither a local…

A: see below the answer and explanation

Q: Find all the zeroes of the function f(x) = 5x³-54x² + 170x-104; given 5 + ✓ is a zero

A: Given: f(x) =5x3-54x2+170x-104 One of the zeroes of the the given function f(x) is 5+i

Q: 1. Find the linearization of f(x) = (x³ + 1)¹/² at x = 2 and use this to estimate f(2.05).

A: Please see the below picture for detailed solution.

Q: the following theorem. Theorem If f is integrable on [a, b], then b [ºr(x) dx f(x) dx = lim f(x₁)AX…

A: Given query is to find the integral.

Q: Express these decimals in short form using the bar to designate the repeating part. Find the…

A: We can solve this as follows:

Q: An isotope of a radioactive element has decay constant equal to 0.06 per year. Initially, there are…

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Q: .) Find the volume of the solid whose base is the region bounded between the curve y=secx and the…

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Q: Suppose that f(x) 13x - 3 In(x), x > 0. (If an answer does not exist, enter DNE.) (a) Find all…

A: Here we have to apply the application of differentiation.

Q: Average Life Span One reason for the increase in human life span over the years has been the…

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Q: Determine whether the series is convergent or divergent. n = 1 5 n² + n³

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Q: A company that makes bicycles has determined that a new employee can assemble M(d), where M(d) =…

A:

Q: 9. At time t= 0 a particle is at the origin. It then begins moving along the positive x- axis so…

A: For part (a):

Q: 4. By changing the order of integration, evaluate IS rdx) a rdra parccos(y)

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Q: For each problem, sketch the region bounded by the graphs of the functions and find the area of the…

A: Integration means to find the area under any curve. Use the formula ∫xn dx=xn+1n+1 Area of a square…

Q: If 46 +3ƒ(x) + 5x²(ƒ(x))³ = 0 and ƒ(-1) = −2, find f'(-1). ƒ'(-1) =¯

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Consider the region R bounded by y=1-x² x = 0 and y=0 [This region is used to answer questions a -…

A: Given curve, y=(1-x2) and x=0 , y=0 The region R is by the curves,  y=(1-x2) , x=0 , y=0

Q: The equation A(t) = 2000e0.045t gives the balance after t years of an initial investment of 2000…

A: Equation given A(t) = 2000e0.045t Find - (1)  dA/dt(2) Find and intepret A'(5)(3)  compare the…

Q: Find all values of z at which the graph of f(x) = 2³² +42² +7 has a point of inflection.

A: