A variable plane lx +my+nz = p (where 1, m, n are direction cosines of normal) intersects the coordinate axes at points A, B and C, respectively. Show that the foot of the normal on the plane from the origin is the orthocentre of triangle ABC and hence find the coordinates of the circumcentre of triangle ABC.

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Q: 3 Look at the boxed result on page 417. Now determine which of the following improper integrals…

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Q: a = 3 iff N(a) = G. also show that if G is finite, then a € 3 iff o(N E

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Q: 2.15 Find a graph G with 10 vertices, 24 edges and Y(G) = 4. 10 2193

A: Please find the attached solution

Q: Prove that every minimal dominating set in a graph G 26. is a maximal irredundant set of G.

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Q: Question 2 system: a) form; Consider the following linear (−2x₁ + 4 x₂ + 3x₂ = − 3 - 4 x₁ + 3 x ₂ −…

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Q: a) Let 3-4 5 B-2 4-1 00 S be a nonsingular matrix. Then find the values of s using row operations.…

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Q: So the maximum is (-0.5, -16e^(-1))? And the minimum is (0.5, 16e^(-1))? I need the answer in…

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Q: Question 1 Assume that a sequence (fn)n of integrable functions converges strongly to an integrable…

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Q: 2. Using the function f(x) = 2x+cos³ (x) - sin(x) bounded by x = 4 to x = 10 Find the area using…

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Q: 6-7:

A: 6-7=-1

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Q: 6. Consider the sequence defined recursively by 1 2 an+1 = an + N an If ao = 1, does the sequence…

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Q: Prove that pork = pur in O₂ if and only if 0 w = 2m for some m€ Z and k = 1 (mod 2)

A: To prove that ρθrk=ρωrl in Ο2 if and only if θ-ω=2πm for some m∈ℤ  and k¯≡ l¯mod 2.

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Q: g your calculator. (b) {(1,98)+(2,01)4+1}¹/4

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Q: 24. Using the CAD drawing below, calculate the measures of angles C and E in degrees and minutes if…

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Q: If G is a group and H is a subgroup of index 2 in G show that H is a normal subgroup of G.

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Q: find x, y € Z such that 2261x + 1275y = gcd(2261,1275).

A: we want to find the greatest common factor  we will use Euclid's algorithm 2261=1275×1+986 -----1)…

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Q: x + 2 x+5-x + 5 (a) lim Calculate the following limits, or explain why they diverge. 1-n-n² n→∞ 1-2n…

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Q: Prove that every minimal dominating set in a graph G is a maximal irredundant set of G.

A: Given that, Every minimal dominating set in a graph G is a maximal irredundant set of G. We have to…

Q: In a probability experiment, G and H are independent events. The probability that G will occur is r,…

A: Probability that G will occur = r Probability that H will occur = s Since G and H are independent,…