Find the solution of the given initial value problem in explicit form. 1 y' = (1-7x)y², y(0) = 6 y(x): =

Q: What is the center of gravity of the solid formed when the plane region bounded by y^2 = 4x in the…

A: First we sketch the given region using a graphing calculator as shown below:   The shaded region…

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Q: 4. Which of the following lines is parallel to y = 6x 18? 3x+6y=2 ○ 2x + 3y = −2 -6x -6x - 2y 2y =…

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Q: III. Let f(x) = e2 sinz 2. Find the absolute extremum values of f on the interval [

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Q: TU Evaluate a sec²20d0 8 a. 00.33 b. 0.5 c. 0.67 d. 0.25 e. NONE OF THE ABOVE

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Q: So x² (a²-x²) ³¹/2² dx

A: A detailed solution is given below.

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Q: 6. A family wants to build a fence in their backyard for their dogs, Charlie and Linus. The enclosed…

A: Given:     Area = 4000 sq meter

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Q: Perform the integration. 3 [² (13² - 11 + 13* - 31) dx

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Q: The integral of 3^4x dx is equal to A^AY Ing+ 0

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Q: A study indicates that the population of a certain town will be growing at the rate of p' (t) = 5 +…

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Q: 1-coth² (log₂x) dx x cosh(log₂x) 1. 11/20

A: We have to find the integral.

Q: Determine the following integrals: 1.1.1 ļ (cos2x+sin x) dx x+1 .1.2 1₁ JF dx x + 2x+1 2 1.1.3 | ₁…

A: ∫ sin(ax) dx =-cos(ax)a+C       and     ∫cos(ax) dx =sin(ax)a+C ∫xn dx = xn+1n+1+C Note : As per our…

Q: What is the the x-axis and the semicircle y = (4 - x^2)^1/2? O 0 02 Ο ΝΑ x-coordinate of the…

A: Solution is given below:

Q: The total cost of producing 1 unit of a product is given by C(x, y) = 80+ 0.3x² + 50y - xy dollars…

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Q: Stan5 x sec³ x dx

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Q: Set up the double integral that will find the volume of a solid bounded by z = 1- y²x² and the xy-…

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Q: Integrate the following (3x + 5)dx 1. S (x - 1)(x² - 1) -

A: Given:∫(3x+5)dx(x-1)(x2-1)Perform Partial…

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Q: The following differential equation is a Bernoulli equation: 2 dy + 27/ y3 where y = f(t) dt By…

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Q: I. Evaluate the following limits x-tanx 1. lim x-sinx x-0

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Q: S 1 C=S²x + Sin'x

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Q: Life expectancy in the United States has been rising since the nineteenth century. The table shows…

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Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: The solid generated by x+y=5, y=0 and x=0, about y=0

Q: Evaluate the integral of e^x^3 x^2 dx from 0 to 2. * 973.10 O999.40 876.56 993.32 Final rated…

A: As per guidelines,  we support one question in one request . Kindly repost next question in next…

Q: (Requires a short but nontrivial geometric Let ABC be a triangle argument.). with angles…

A: Using sine rule, length of other two side are evaluated.

Q: ab c Pq r U V W a. det (2B¹) where B = 4u 2a 4v 2b -q 4w 2c <-r 2p -a+u 3u b. det (20¹) where C =…

A: Given problem:-

Q: Evaluate the improper integral or state that it diverges. P -dx Select the correct choice below and…

A: The given integral is: I=∫2∞32x2dx   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1 And…

Q: Solve the differential equation of order one.  (x4 + 2y)dx - xdy=0 STEPS: a. Put the equation in…

A: Separate the equation to form standard form then solve

Q: The joint cost (in dollars) for two products is given by C(x, y) = 24 + x² + 3y + 2xy where x…

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Q: yı y' = 2x +2y +1 3x +y -2

A: We can solve the given differential equation .

Q: 1. Let B = {. What is A. C. B. ( D. cannot identify } and the operation * is defined by the table…

A: To find what element we get after operating the given elements.

Q: dy dx = x+1 2(y+3)

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Q: A small business determined that the price-demand and cost functions for producing and selling x…

A: We have to find the marginal profit.

Q: Perform the integration. 3 (13 (|3* − 1| + |3* − 3|) dx 0

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Q: The area bounded by the graphs of y = 2 - x^2 and y = x^2 revolves about the x-axis. Determine the…

A: The given curves are y=2-x2 and y=x2   Now find the point of intersection between the given curves.…

Q: Find the area (in square units) bounded by the parabolas x² + 2y - 8 = 0. a. 7.10 sq. units b. 7.01…

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Q: y-coordinate of the centroid of the plane region bounded by 17 What is the the x-axis and the…

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Q: Find the formula for the sequence below: -5,15,-45,180,...   a an=-3(-5)n-1 b an=5(3)n-1 c…

A: We have to find the formula

Q: Let h(x) = f(x) = g(x). If f(x) = 9x² and g(x) = 8x, what is h'(-5)? - Do not include "h' (-5) =" in…

A: SOLUTION-

Q: Find fx (x,y) and f, (x,y). Then, find fx(1, -2) and fy (-3,3). f(x,y) = -2xy +9y² + 10 fx(x,y)=

A: We can find the answer as below.

Q: 2.) Obtain the solution of the following initial value problem! (t-2)x' - x = 2(t - 2)², x(0) = 1.

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Q: The tenth term of an arithmetic sequence is 23, and the second term is. Find the first term. X

A: Let's find first term of arithmetic sequence.  Tenth term = 73/2 Second term = 9/2

Q: 5) Find the Maclaurin Series for f(x) = ²² +₂²²²₁ exte tex 2

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

Q: 2. Find the interval of convergence of the power series & 3x गय

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Q: P(x, y) = 10x + 6.1y-0.007x² -0.035² where x is the number of pounds of Kisses and y is the number…

A: ∂P/∂y is the derivative of P with respect to y taking x as a constant..

Q: 3x² - 6x² + x (36²-6x² x)]d² X

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Q: 1. (2x6x5 +7x³-3x² - 11) dx 2. f(9y2 +6y-4-y-5+1) dy (12x-x+x) dx 3.

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Q: Find the area bounded by the curve 2x² + 4x + y - 0 and the line y+x=0 a. 1.000 b. 1.125 c. 1.525 d.…

A: We will first sketch the curve and the line.