Basic Mathematical formulae (original) (raw)
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LI < 0 Semisolid 0 < LI < 1 Plastic LI > 1 Liquid Volume e = V v V s n = V v V S = V w V v Weight ω = W w W s 0 < e < ∞ e = n 1 − n 0 < n < 1 n = e 1 + e Se = G s ω ɤ = W V ɤ d = W S
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This paper proposes a solution for merging the measurements from two perpendicular profiling sonars with different beam-widths, in the context of underwater karst (cave) exploration and mapping. This work is a key step towards the development of a full 6D pose SLAM framework adapted to karst aquifer, where potential water turbidity disqualifies vision-based methods, hence relying on acoustic sonar measurements. Those environments have complex geometries which require 3D sensing. Wide-beam sonars are mandatory to cover previously seen surfaces but do not provide 3D measurements as the elevation angles are unknown. The approach proposed in this paper leverages the narrow-beam sonar measurements to estimate local karst surface with Gaussian process regression. The estimated surface is then further exploited to infer scaled-beta distributions of elevation angles from a wide-beam sonar. The pertinence of the method was validated through experiments on simulated environments. As a result,...
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The dastardly approach to the teaching of mathematics has resulted in attendance poor performance and stigmatization of the subject. Obviously, mathematics is styled a difficult subject everyway in the globe; not withstanding so many methodological changes that have taken place in the teaching and learning of the subject, the public views, classroom activities aftermath, teachers’ comments, all paint mathematics as hard, complex and difficult. The situation spells doom but is not incorrigible. The fact is that the teachers’ preoccupation before class includes enriching knowledge of content material, assembling appropriate instructional materials, procuring suitable assessment and evaluation tool for learners achievement and is satisfied that the delivery will be successful after the class what ever happened is rarely the teachers business,of course mathematics is not an easy subject, let the learners go home and work hard. This have been the bend in the teaching of mathematics over the years, the teacher lacks a reappraisal mechanism, the tools to assess the success or failure of his delivery is unavailable hence is unable to measure at each stage or at the end of the class how well the work has been done. Axiomatic approach emphasize principled techniques of evaluating teaching, subject matter, materials and deliverability of the content as the class activities progresses, using formula where numerical constants and variables are imputed to obtain deliverability indices that are capable of giving indication for the success or failure of a learning activity. The formula include instrument for measuring the effectiveness of the instructional materials in promoting learning, adequacy of teachers mastery of the content material in terms convertibility, versatility and communicability of the required skills and also formula for measuring the level of acceptability and receptivity of the instruction by the learners.
UNEB UACE MATHEMATICS QUESTION BANK 1993-
Solve the simultaneous equations x + 2y − 3z = 0 3x + 3y − z = 5 x − 2y + 2z = 1 Ans: (a) x =-1, x = 0; (b) x = 1, y = 1, z = 1 2. When the quadratic expression ap 2 + bp + c is divided by p − 1, p − 2 and p + 1, the remainders are 1, 1 and 25 respectively. Determine the values of a, b and c. Hence the factors of the expression. (Ans: a = 4, b =-12, c = 9; factors: (2p-3) and (2p-3) b) Express 2x 3 + 5x 2 − 4x − 3 in the form (x 2 + x − 2) Q(x) + Ax + B; where Q(x) is a polynomial in x and A and B are constants. Determine the values of A and B and the expression Q(x). (Ans: A =-3, B = 3), Q(x) = 2x + 3 3. i) Show that ln2 r , r = 1, 2, 3 is an arithmetic progression. ii) Find the sum of the first 10 terms of the progression. (Ans: 38.1231) iii) Determine the least value of m for which the sum of the first 2m terms exceeds 883.7. (Ans: m = 25) b) Given that the equations y 2 + py + q = 0 and y 2 + my + k = 0 have a common root. Show that (q − k) 2 = (m − p)(pk − mq). 4. Solve the simultaneous equations z1 + z2 = 8 4z1 − 3iz2 = 26 + 8i Using the values of z1 and z2, find the modulus and argument of z1 + z2 − z1z2 (Ans: z1 = 8 + 2i; z2 =-2i) 5. Use the Maclaurin's theorem to show that the expansion e-x sin x up to the term in x 3 is 2 33 3 x xx .