1) (i+2)i + (i+4)i
= (2+2)2 + (2+4)2 + (3+2)3 + (3+4)3
= 16 + 36 + 125 + 343
= 520.
Show that for a material element subjected to principal stresses σ1, σ2 and σ3 (triaxial stress state), the shear stress that develops along the octahedral plane with direction cosines-,-,-in the system of axes 1, 2, 3 is given by
Two very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities σ1, σ2, σ3 and σ4 on their surfaces, as shown in the following figure (Figure 1) . These surface charge densities have the values σ1 = -7.50 μC/m2 , σ2=5.00μC/m2, σ3 = 1.30μC/m2 , and σ4=4.00μC/m2. Use Gauss's law to find the magnitude and direction of the electric field at the following points, far from the edges of these sheets.What is the magnitude of the electric field at...
Considering two Gaussian distributions N1~(μ1,σ1^2) and N2~(μ2,σ2^2), we pick two random variables x1 and x2 in order to compute the sum x3=x1+x2. We want to prove that: a) x3 follows a gaussian distribution b) estimate mean value μ3 and variance σ3^2 c) repeat the above steps for multivariate Gaussian distributions N1~(μ1,Σ1) and N2~(μ2,Σ2)
design a PDA for this language し-(012kl i = 2j or i = k, where ij,k2 1} し-(012kl i = 2j or i = k, where ij,k2 1}
.1. Write a Python script for compute P50 k=1 P100 j=−2 (k − 2j) 2. It is clear that the cardinality of the Natural numbers is no more than the cardinality of the Rational numbers. Show that Rational numbers have cardinality no greater than the natural numbers (and therefore they have the same cardinality). 3. Prove (by contradiction) that the real numbers are uncountable.
(1 point) Suppose u 2i +2j + 5k, v = -4i - k and w Compute the following values: -i-4j+ 2k. Jul v=| 4 1-7ul+8v 6v+w 2u W- w 1 w
2. Which of the following pairs of vectors are orthogonal? (a) v = 3i - 2j, w = --i +2j (b) v = -2i, w = 5j (c) v = -i + 2j, w = -1 (d) v = 2i – 3j, w = -2i + 3j (e) None of these
Compute the value of each summation. a) Σj=1,8 (j + 2j + 1) b) Σj=1,5 Σk=2,4 (jk - k)
I. Suppose population 1 has mean μί with variance σ2 and population 2 has mean μ2 with the same variance σ2. Let s and s denote the sample variances from two samples with size ni and n2 from the corresponding populations, respectively. Show that the pooled estimator 1i+(2-1)si pooled ni + n2 -2 is an unbiased estimator of σ2.
I. Suppose population 1 has mean μ1 with variance σ2 and population 2 has mean μ2 denote the sample variances from two samples with the same variance σ2 Let s and s with size n and n2 from the corresponding populations, respectively. Show that the pooled estimator pooled n1 2 - 2 is an unbiased estimator of σ2