1) Find the volume of the prism whose base is the triangle in the xy-plane bounded by the x-axis and the lines y=x &x= 1 with top that lies in the plane z = 3-x-y by evaluating 1 x SS (3 - x - y) dy dx. 00

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Q: Convert 591 to base 5.

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Q: Prove by contrapositive. Let k be an integer. If 5k+9 is odd then k is even.

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A: Sol:- ∫π4π22sinxdxTake the constant out:  ∫a·fxdx=a·∫fxdx=2·∫π4π2sinxdx

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A: Sol:- Here f(x)=x2-31st iteration :Here f(1)=-2&lt;0 and f(2)=1&gt;0∴ Now, Root lies between 1 and…

Q: 5 1 5 4 Let T be a linear transformation from R³ to R² such that [T] (0,2,3)} is a base of R³ and C…

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Q: 8. Let A be an m x n matrix. Prove that if n is an odd number, then rank(A) = nullity(A).

A: Rank nullity Theorem : Nullity (A) + Rank(A)=Dim (Domain) =n

Q: all 2 ا ی ہے ony Fil 20 کے لیے ( Q) Evaluate the following integrati ) ) - (1) đ sinh con đối 5² √…

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Q: Find the Laplace transform f(t) = cosh³3x. s²-18 s($²-36) s²+4 s² (s²+16) O $²-9 s²-36 2 O $² 5²-9

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Q: Find the solution of the equation In(2-1) + cos(-1) = 1.7 using Newton-Raphson method with an error…

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A: Some of the Properties of Laplace transformation  Lsint=as2+a2Lu5(t)=e-5ssLf(t)*g(t)=Lf(t)·Lg(t)

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Q: 2- Evaluate sin x dx using i. Trapezoidal rule ii. Simpson's rule iii. Simpson's rule, taking n = 6

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Q: 1. Let T: M2x2→→ P₂ be a linear transformation such that Find T()=1-x T₁=1+x+x² T(₁¹)=2x-x² TG1 T₁₁₁…

A: You will use the property of linear transformation to find the transformation in part (a) and (b).

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Q: USE SPHERICAL COORDINATES TO EVALUATE 2π 2 r+z 1² 1² 1² 1² +7 273/27 dz dr do -r (r² z²)3/2

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Q: Prove by contrapositive. Let k be an integer. If 5k+9 is odd then k is even.

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Q: 2. According to postal regulations, a carton is classified as "oversize" if the sum of its height…

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Q: b) [-- Determine whether the series Σπορ" n=1 is convergent or divergent.

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Q: Use the Monotone Convergence Theorem to show that the sequence n! - --- +∞o (1.3.5 (2n-1)) :D)},…

A: Solution: