4. a) Find the entire are length of the curve r = 2a cos³ (0/3).

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Q: How may chords are there in the figure? [1] (134°-50°1/2-42" 4AFC-134* 4EFD-50*

A: chords are the line segment whose  both end points lie on the circle.

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A: Please see the attachment

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Q: 12 Two towers AB and PQ stand on level ground. The angles of elevation of the top of the taller…

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Q: al P(x) = (x - emainder is -7.

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

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Q: n (2) Find the derivative of the function f(x)= e at 2= 2 by using numerical affronsmation for the…

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A: Solution

Q: PROBLEM S Prove that in any bi-right quadrilateral DABDC, LC> LD if and only if BD > AC. (Assume ZA…

A: Given , In any bi-right quadrilateral  ABCD ∠A and ∠B are two right angles .Let ∠C > ∠D   now…

Q: 2- 2 X dy dx dy d x +34 x/2 e Sinx X2

A:

Q: 7. Find the exact x-value where the function f(x) = x + ln (x² − 1) attains a maximum value. An…

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Q: 7) Find the Volume and Surface Area of the following figure: Tetang 1 ft 4 ft SALE a tom totum od) 8…

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Q: sketch the surface 2² 16 11 -1

A: Given:x29+y24-z216 = -1

Q: Find the general solution of the equation д и 2 ди 3 ди 3 + дхду х-у x-y ду (x - y)2 дх u = 0).

A: The solution is given below

Q: 4. An n x n matrix A is persymmetric if Jn AJn = AT and skew persymmetric if JnAJn = AT, where Jn is…

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Q: 8. Using the Mean Value Theorem and Rolle's Theorem, show that³+x-1=0 has exactly one real root.

A: We are entitled to solve only one question at a time. Please post another questions separately. To…

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Q: f(x) = x²+1, if x < 2 7-x, if x ≥ 2

A: Given: f(x)=x2+1,if x&lt;27-x,if x≥2 To find: Critical numbers of given function.

Q: (i) 8 #=1 Σ (-1)"-1 6n (ii) (n+1)( − 1) 3n³2n +1 series below. n=1 00 5(-4)"+2 Σ (3)2n+1 n=1 (a)…

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Q: Finding a probability density function A continuous random variable X, with mean unity, has…

A: Given a continuous random variable X, with mean unity, has probability density function fX(x) given…

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Q: If A and B are bounded subsets of R, then prove that AUB and AB are bounded.

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Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(2,0,2) on the…

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Q: Consider y' - 2y = 3e²x with y(0) = 2. Using Runge-Kutta method with h=0.1, approximate y'(0.2). (a)…

A: Given y′=2y+3e2x,   y(0)=2,   h=0.1Forth order R-K methodk1=h f(x0,y0) = (0.1) f(0,2) = (0.1)⋅(7) =…

Q: 12 Two towers AB and PQ stand on level ground. The angles of elevation of the top of the taller…

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Q: When approximating f(x) dx using Romberg integration, R4,4 gives an approximation of order:

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Q: Determine the result of the Ratio Test on the series: (2n)! Σ 1.4 7.10.13. . .. (3n-2) n=1 Converges…

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Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: Given, the surfaces:               x+y2+2z=4,   x=1  Point: (1, 1, 1) Let         z = 1-2t

Q: Use the binomial ser a. f(x)=√√(+X- ..b.....fo.x

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Q: let FC k be a Galois extension with Gal

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Q: Use a triple integral to determine the volume V of the region below z = 6 - x, -2√x² + y² inside the…

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Q: V. En el siguiente ejercicio obtenga la derivada de la función brindada. 5, y = In (2e¹ sen 1)

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Q: × ➜ TO Use the short truth table method to determine whether the following argument is valid. (p →q)…

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Q: Use centered finite differences to solve the ordinary differential equation for 0≤x≤6 d² u du +3…

A: We will use the basic knowledge of ordinary differential calculus to answer this question.

Q: Romberg integration for approximating ff(x) dx gives R21 = 5 and R22 = 3 then f(1) = 3.815 4.01 O…

A: Given : ∫02f(x)dxSo , given Interval , [a,b] = [0,2]Then  a =0 , b = 2For Calculating R11n = 1 , h =…

Q: Solve the differential equation using 3rd order RK method dy/dx = yx3 – 1.5y, y(0) = 1 find y when…

A: The solution of given differential equation using third order rk method.

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Q: Consider the following lines. r(t) = (4t-1,4t - 1,2t+3), for -∞<t<∞ R(s) = (s +3, 4s+3, -2s+5), for…

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Q: air balloon rising vertically is tracked by an observer located 4 km from the lift-off point. At a…

A: In this question, the concept of the derivative is applied. Derivative A derivative can be used to…

Q: Consider the following lines. r(t) = (4t+4,2t+2, 3t+4), for oo<t<0⁰0 R(s) = (s +3,3s-1, -4s+8), for…

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Q: 3. Consider the vector field F(x, y) = (2xy, x² - sin y). Evaluate F.ds π where is the curve c(t) =…

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Q: need the answer qu

A: Introduction: The volume of the right circular cone of radius r and height h is given by, V=πr2h3

Q: Solve the following PDE problem using the separation of variables Ꭷ2Ꭲ . Ꭷ2Ꭲ + = 0 ax² ay² T(L, y) =…

A: ∂2T∂x2+∂2T∂y2=0----------(1) T(L,y)=160∘C T(x,0)=60∘C ∂T∂x(0,y)=0 T(x,h)=60∘C let T=V(x)U(y)

Q: B. Find the area of the region bounded by the following: 18. common to 7 = 3 cos and r=1+ cos

A: 18. The given curves are r=3cosθ and r=1+cosθ. To find: The area under the curves . Please post the…

Q: SOLVE IN HANDWRITTEN   Find the equation of the line if it passes through the points (4,−3) and…

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Q: 2. Consider the function 2r²-9r-18 f(x) r²-r-2 (a) Sketch the curve y = f(r). (b) Find the area of…

A: Given: f(x)=2x2-9x-18x2-x-2 To find: (a) Sketch the graph of function. (b) The area of the region…

Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.