A fireplace arch must be constructed in the shape of a semi-ellipse. The opening must be 60 cm high in the center and a base of 1.5 m in length attached to two small nails. Where should you put the nails?? 30- 30 60 -60-30

Q: Prove or disprove: If R and S are partial orderings on A, then R ∩ S is also a partial ordering on…

A: Partial order relation of intersection of two partial order set

Q: F (ƒ') - {¹(- Ji(- (-5w+4w2), (a) Find an expression for f (w) in terms of unit step functions u w…

A: Let us start solving the problem step by step  We must find the values of f(w) F(x) and g(x)

Q: Question 1 (Subspaces) For (a) and (b), show that these sets are subspaces of IR¹. (a) {(a,b,c):…

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Q: Problem 3. Let VCR³ be the region bounded by the planes z = 0, z = 1, and the surface defined by…

A: Solution :

Q: e of ne nded by

A: We have to find the volume of solid generated by revolving the region bounded by 2y = e-(x^2) , the…

Q: Consider the following two player bi-matrix game 19 6 19 1 -10 21 B = 0 -8 -5 A = 7 12 6 2 14 16/ -9…

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Q: 2n+2 Σ (3k + 2n) + k=0 =

A: The given summation is                          ∑k=02n+2(3k+2n)

Q: 4. Suppose a 12th-order homogeneous linear differential equation with constant coefficients yields…

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Q: A linear time-invariant system (A, b, c) is modelled by the state-space equations x(t) = Ax(t) +…

A: Here we need to show that wether system is controllable and observable.

Q: 4 Evaluate: ₁₂ (4x²y – z³) dz dy dx

A: We can evaluate the integral  ∫13∫-24∫10(4x2y-z3)dzdydx.

Q: eigenvalues and eigenvectors a) Solve the following differential equations: x₁ = y1+3y2 y₂ = 4y1+5y2…

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Q: II. Solve the non-linear equation: 1.) x2 - xy + 2y2 = 16 x - y = 2

A: Since x - y = 2 => x= 2+ y Therefore  x^2 -xy + 2y^2 =16 becomes (2+y)^2 -(2+y)y + 2y^2 =16 =>…

Q: 2″ Given f(x) = xr-¹e-λx, x > 0, r, λ > 0. Γ(r) 2. Evaluate etx f(x) dx. HINT: Express f etx f(x) dx…

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Q: ! (5) If f(x) Option 1 =.. Option 2 then f(x) is reducible in Z5 [x]. x² + 3 x² +1 x² + 2

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Q: 4Z is prime ideal of 2Z, but it is not Maximal ideal of Z. To fo

A: To identify given statement is true or false.

Q: Evaluate ¬⇒(PV¬q) if p and r are True and q is False. Select one: O True O False

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Q: Determine the total solution of the differential equation (D2+5D+6)y=6e(-3x)-100e2x O A. y =…

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Q: (4) Let K be integer ring module 12 and let I=([4]) and J=([6]) be ideals of K. Then [2] belong to…

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Q: 4 Find the area of the region bounded by x = = 2y²+1 and the y-axis using the horizontal strip.

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Q: (1) Let I be a proper ideal of the commutative ring R with identity. Then I is a ........ if and…

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Q: F L (a) Given A = use the Cayley-Hamilton theorem to find (1) A¹-3A6 + A¹+ 3A³ - 2A² +31 (ii) A*,…

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Q: Determine the magnitude of the vector difference V' = V₂ - V₁ and the angle 0x which V' makes with…

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Q: 5. Use Cartesian coordinates to evaluate Jff ² av D where D is the tetrahedron in the first octant…

A: 2x+3y+z=6 z= 6-2x-3y When z = 0 6-2x= 3y y= (6-2x)/3

Q: 3. Determine if b is a linear combination of a₁, a2, and a3 2 1 2 3 a1 = 1 a2 = 2 , az 1 4 1 0 9 - =…

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Q: Evaluate: ³4²₁²[z³(x + y)³] dz dy dx

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Q: Solve the following differential equations, giving y in terms of x. dy (iii) cotx + 2y = sin 2x. dx

A: Let us consider a differential equation of the form dydx+Py=Q where P and Q are function of x  To…

Q: Show that in any collection of 7 or more natural numbers there are ALWAYS TWO numbers whose sum or…

A: Here we use Pigeonhole principle to prove the statement.

Q: The volume of the solid E that lies above the cone = sphere p = 2 cos is 21 T 2 C050 (a) dp da de p²…

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Q: Let F(x,y)=ln(x² + y²), then answer the following (1) Find the function's domain (2) Find the…

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Q: determine the general solution of y''-y=0 given y1(x)=e-2x using reduction of orders

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Q: 6. Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: As per the policy we are allowed to answer only one question at a time. So, I am answering the first…

Q: 6. Determine the values of C₁ = 922 @ +923 and C₂ = 924 @ +925 if y(t) = e2¹ (C₁cos(1) + C₂sin(t))+…

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Q: Find the area of the region bounded by x = and the y-axis using the horizontal strip. 2y²+1

A: Given curves are x=42y2+1 and y-axis.

Q: A moving sidewalk in the Atlanta airport moves people between gates. It takes Molly's 8-year-old son…

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Q: 2. อใน at2 a อริน 0x2

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Q: f₁ = x² - 6x f₂ = x² + 6x f3=x²-3

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Q: Find the general Solution of the following PDES ди ди ay 9 2 -5х = 3e + 2e +u ucx;o) = > -5х-3у…

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Q: 4Z is prime ideal of 2Z, but it is not Maximal ideal of Z. To fo

A:

Q: 2. Evaluate the double integral that will find the volume of a solid bounded by z = 1-2y² - 3x2 and…

A: Solution :-

Q: Evaluate: ³₁¹[z³(x + y)³] dz dy dx

A: We have to solve given problems:

Q: Find the area of the region bounded by the curves 1 y y = 4 and the x-axis using vertical strip.…

A: We have to solve given problems:

Q: 5. In determining the particular solution to 2x" + 3x' = 3 sin(t), you must solve 2(-M sin(t)- N…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: 1. Identify the surfaces of the following equations by converting them into equations in the…

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Q: To illustrate the Mean Value Theorem with a specific function, let's consider f(x) = x3 - x, a = 0,…

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Q: Find the area of the region bounded by the curves 1 y = y = 4 and the x-axis using vertical strip.…

A: We have to solve given problems:

Q: Evaluate: ₂₁(4x²y - z³) dz dy dx

A: We can solve this using Given information

Q: 02u 0t2 = аг 02u ?x2

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Q: Classify the following quadratic forms: (a) 2x² + y² +22² - 2xy - 2yz (b) 3x² + 7y² +22² - 4xy - 4xz…

A: As per our guidelines we are supposed to answer only first question. Kindly repost other parts in…

Q: 24. A point is moving along a curve that is given as: R(!) = (cos 3!)i + (sin 31) j + (31)k. Find:…

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Q: 1. Find the Inverse Laplace Transforms of the following. 3s 2) -335-4 s²-4 2

A: Solution :  Given that  3ss2-4