A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure). Find the dimensions of a Norman window of maximum area if the total perimeter is 8 feet. X = ft y = ft

Q: Given the polor coordinate U, write it as a rectonguicr coordinate, anc write three other coordinate...

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Q: Determine the x-intercept(s) of the graph visually. Then find the x-intercept(s) algebraically to co...

A: In this question we have to find x-intercepts.

Q: -3x + 4 a) lim x-2- x2 - 4 x2 b) lim x-3* x2 + 2x – 15 2x4 + 5x3 - 2х- 3 9x + 10 c) lim 5x7 + 2x6 – ...

A: a) limx→2--3x+4x2-4=-3(2)+422-4=-6+44-4=-20=-∞limx→2--3x+4x2-4=-∞

Q: 8. ye = In(xy) 9. (y- 5)? = 8(x – 3) _10. 2x – xy +y = 0

A: We can solve this as follows:

Q: 1. Differentiate. Do not simplify. а. f(0) = 3cos(0*)sin(0³ – 2) b. f(x) = 4x + 25-x² + 2x-1

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Q: Calculate the derivative using implicit differentiation: dw x'w + wt + wz² + 4yz = C dz ||

A: Given problem:-

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Q: A baseball diamond is a square with side 90 feet. A batter hits the ball and runs toward first base ...

A: Here we have to use the application of derivatives

Q: y” − 10y’ + 50y = 0, y(0) = −3, y’ (0) = 1

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Q: a power series representation (Give yo power series representation centered at x 8 + X f(x) 1 -X f(x...

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Q: y" – 2y' + y = -3 – x + x², y(0) = –2, y'(0) = 1. %3D %3D

A: Given: y''-2y'+y=-3-x+x2 ; y0=-2, y'0=1 So, We can also write as; D2-2D+1y=-3-x+x2   The auxiliary e...

Q: Write the equations in spherical coordinates 3x+4y+7z=1

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Q: 1. Evaluate these integrals either by substitution or by integration by parts: cln 2 et a sin(2r) dr...

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for yo...

Q: 2 y = 2x – x¯, y=2x¯ – 4x

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Q: Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0), (4...

A: [ x-0  y-0  z-0] [4-0  0-0  4-0]      = 0 [-1-0  -1-0  8-0] [x  y  z] [4  0  4]      = 0 [-1  -1  8]...

Q: J E1 = (J – 2) i = 3

A: This question can be solved using the concept of series.

Q: PROBLEM [ B6 (a) ]: Obtain the differential equation whose general solution is y=a sin 7x – bcos 7z,...

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Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the...

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Q: Sketch the region enclosed by the given curves. y = 3x, y = 3x

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Q: Complete the following tables of values to investigate. Write your answer in the space provided afte...

A: To evaluate the given limit using the tabular method. Let, f(x)=x2-2x+4

Q: xsin-1(x) is If x =0.1 and y = 0.11, then value of C in the antiderivative of F(x) = V1- x?

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Q: Find a polynomial of degree n that has the given zero. (There are many correct answers.) Zero Degree...

A: To find : A polynomial of degree n that has the given zero. Given information: Zero: x=9, Degree: n=...

Q: Directions: Evaluate the following limits. 3. lim ) 4. lim ) x-1 x2 X+4

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Q: Find length of curve y= 2/3 (1+x^2)^3/2,  0<= x<=1

A: Let's find. 

Q: Find the indefinite integral and check the result by differentiation. (Use C for the constant of int...

A: Use property of polynomial for evaluating the integral.

Q: Use vectors to determine whether the points are collinear. (0, –2, –5), (15, 8, 0), (6, 2, –3) The p...

A: The given points are 0,-2,-5, 15, 8, 0, 6, 2,-3

Q: Solve the stated IVP using the method of undetermined coefficients. y” – y’ − 12y = 10e^5t , y(0) =...

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Q: 1. Determine whether the following series conv. or div. (n+4)! a. Ln=1 4! n! 4n 1 1 b. En=1 4n 2" co...

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Q: The position function of a particle is giyen by s(t) = (t – 1)²(t – 3) , where t is measured is seco...

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Q: Give two other polar coordinate representations of the point, one with r 0. (r, 0) = ( 3, – 2.14 X ...

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Q: dP to find the solution to the problem dt K 7. Use P = 4P Р() — 4. 1 - 1+ Ce-at 20

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Q: e² sin® (e²) cos' (e²)dx

A: According to question,Given Integral,Let I = ∫ ex sin6ex cos7ex dx

Q: Suppose f(x) = [ 6t² /1+t° dt .

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Q: Find a polynomial function that has the given zeros. (There are many correct answers.) 0, -8, –9 f(x...

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Q: kx +5, g(x)={ 2 x<-2 4. If the function 3x+x², x2-2 is continious at x=-2, then find the value of k.

A: Given query is to find the value of k.

Q: Find the directional derivative of the function h at the point (1,1,1) in the direction of vector v....

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Q: 6. f(16) = 63. VX Find f such that f'(x) = %3D %3D

A: Topic = Integration

Q: Sketch the region bounded by the given curves, then find the centroid of its area. x = 8 - y², x = y...

A: Let's find. 

Q: Find the point of diminishing returns (x,y) for the function R(x), where R(x) represents revenue (in...

A: Given: R(x)=10000-x3+45x2+700x, 0≤x≤20

Q: Find a set of parametric equations of the line with the given characteristics. (Enter your answers a...

A: Given,            The line passes through the point -1,4,-8 and is parallel to v=4i-j.To find : Find...

Q: e5x cos e5x dx sin²e5x

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Q: Q1.Find the general solution of following PDE equation (a) (5z+ R)uz + (7x+ R)u, R (b) (z + R)u, + (...

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Q: Let a = ci + jand b = 5i + 35j. Find c so that a and b are orthogonal. C = i eTextbook and Media Hin...

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Q: C.Logarithmic and Exponential Functions

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Q: 1 determine whether it converges or whether it diverges. As part of your 6. For the series k3' k=0 s...

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Q: Determine the interval of convergence I and radius of convergence R for the following series: En=1 (...

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Q: Use the alternative form of the dot product to find u · v. |lu|| = 50, ||v|| = 20, and the angle bet...

A: Given: u=50, v=20 and angle between u and v is 5π6 We know that u·v = uvcosθ, where θ is the angle b...

Q: dav dyt if va (x*+y*+z) Show that d'v

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Q: Given that log(2) ≈ 0.3010, find the value of the logarithm. log(√2)

A: Given query is to find the value of logarithm.

Q: f"(x) = 13r- (x²-1)a 2.f(x) = f'(x) = r* +1) 4x (x²-1)2 Determine the intercepts. Determine the equa...

A: f(x) =2x2x2-1Intercepts:x=0, y=0(0, 0),y=0, x=0X and Y-intercept: (0, 0)Asymptotes:x2-1=0x=1, x=-1  ...