fla) compute T [ f 77E] t.

Q: Find a mat rixP such that P-1 I 0 2 1 0 0 2 1 0 P = OA. 1 0 P = O B. 1 1 -1 0 P = OC. 1 1 OD. 1-1 P…

A:

Q: x+y uis = 1 n upi = no • prove that x-+ y-

A:

Q: Q3: Prove that Σ(y₁ - y) = 0 AND Σfi(y₁ - y) = 0

A: The question is about proving given equation. To prove : ∑ ( yi - y¯ ) = 0∑ fi ( yi - y¯ ) = 0

Q: Prove Theorem (A + B )T = AT + B T

A: Prove Theorem (A + B )T = AT + B T

Q: Let f (L, K ) = 32LK. Find df/dL.

A: Differentiate the function f with respect to L.

Q: dt (e2t + 8et + 7)ā et+4 a) 9ezt +8et+7 +C b) In(e2t + 8et + 7) + c 2 c) 5Ve2t+8e*+7 +c e4t d)…

A:

Q: ハジ nd the exact lkength of the wnve र 4=1n(seccx)),

A:

Q: Show that (A − B )T = AT − B T .

A: Given  (A − B )T = AT − B T

Q: Prove that the quartic function q(z) = r* - 16 has only

A: Given that: q(x)=x4-16

Q: prove the ged (atb,a?+b³) =16Y2 assuming that gcd (a,b) =1 •

A: It is given that gcd(a,b)=1

Q: Complete the proof that AUVX ATWX. U V T. W

A: Given:  WX=VX and UX=TX. In △UVX and △TWX WX=VX                  (Given) UX=TX…

Q: Prove in detail that Q(/3+ v7) = Q(V3, v7) %3D

A: According to guidelines we solve one question.

Q: Given u(x, t) = t-²e¯, 2 , compute:

A: We can find the required answer as below.

Q: Find the d. c. of T from definition.

A:

Q: verify that (A + B)T = AT + BT

A:

Q: Find f"() if fx) = 2e* - %3D e* In 2 Ob) 20 2e* O c) 2e O d)

A: Recall:     d(eax)dx=a.eax

Q: is the gropt Q whch of Hhe of followring

A: Given that: 1. y=x2ex2. Graph of f(x)

Q: Let r(t) = ⟨t, t, t⟩. Compute r'(t) and interpret the result.

A: rt=t, t, t

Q: J prove that for 0 <r<R

A:

Q: Use Cramer's ru;e to fins a solution: 5x+4y=12 3x-6y=24

A: System of equations are 5x+4y=123x-6y=24

Q: IS T-dist prove o E(T)=0 QvarしT)=て %3D V-2

A:

Q: (b) Use part (a) to show that f (T) is either a transposition disjoint transpositions. or a product…

A:

Q: Q4 Prove that E(",") = ("::)- () .n 2mzr. %3D +1 +1

A: we have to prove that                                                   ∑k=0mn-kr=n+1r+1-n-mr+1 now,…

Q: Prove the following statements: d (a) [u(t) · v(t)] = u'(t) · v(t) + u(t) · v'(t). dt

A:

Q: Is 1z = 1 for all z ∈ C?

A:

Q: al HL b7 SAS C) NOt Co ng ruent

A: We will prove what relationship these two triangles have.

Q: nd C such that AC=E

A:

Q: Find e² in the form of u + jv and le²| for z = 2 + 3nj

A:

Q: Let F I2). Evaluate JJaw as z² + y? 0

A: In the given question, the concept of the Divergence Theorem is applied. Divergence Theorem Assume S…

Q: a) Let Z = 7 – 13i, find: i) Im ) ii) (Re Z)?

A: Complex Numbers: The complex number is basically the combination of a real number and an imaginary…

Q: Prove that dv du 2 – u? + v² 18

A:

Q: Let fo find t

A:

Q: Calculate A and B so that t B %3D 1+1 (1-z²)

A:

Q: Q2// A :- Compute for the following at t=1 z = re²", x = t², y =t-1

A: # We are entitled to solve one question at a time , please resubmit the other question , if you wish…

Q: So So t² etu du dt

A: Given, ∫03∫0tt2etududt

Q: T: M22 ---&gt;M22 defined by T(A) = AB,

A: Given, a matrix B, and defined a map T(A) = AB, where T: M2×2  ---&gt; M2×2. We have to find the…

Q: find he querage vallwe of he fanction z-cor ox m De mternal ( )

A: fx=x-cos26x,   0, π6.

Q: Use the diagram shown. В C 主 G 丰 Which is a needed step to prove that AABF EAEDG

A:

Q: 2. Use the met hod of undet er mined coefficients to solve t he syst em x' = Ax+f, where - -] b. A =…

A:

Q: Write a in the fom a = a7T + ax N att 0 for R(t) =t?i+ (t+);+(t -)*

A: We have given R(t)=t2i+(t+13t2)j+(t-13t2)kV(t)=derivative of…

Q: Show that the dyfferential equatian IS exact x(スt5in t) do + cast -2tu) abe +x² dt-

A: We will show that the given differential equation is exact.

Q: Find a mat rixP such that P [1 2 1 0 | 1 0 P = O A. -1 1 1 - ОВ. 1 P= OC. 0 1 -1 0 P = O D. 1 1 1 0…

A: Just multiply both sides by P from left side and set P as 2×2 matrix.

Q: Find T, N, B, K and t for r(t) = ti +÷e2'j when t = In 2. 2

A: answer is in next step

Q: c- Verify Clairaut’s Therom f(s,t) = s²t + In(t²-s)

A: In the question it is asked to verify Clairaut's theorem for the following function given in…

Q: The IHiplicative in verse of 2° tX -I in Zs [x] /is; mu d. nune of

A: Ring Theory.

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!