Various Math #16 - Q&A

Question 1 A person bending forward to lift a load "with his back" rather than with his knees" can be injured by large forces exerted on themuscles and vertebrae. A person is bending over to lift a200-N object. The spine and upper body are represented as auniform horizontal rod of weight 350 N, pivoted at the base of thespine. The erector spinalis muscle, attached at a pointtwo-thirds of the way up the spine, maintains the position of theback. The angle between the spine and this muscle is 12degrees. Find the tension in the back muscle and thecompressional force in the spine. Answer T Ry 2L/3 Tsin12 A Rx CG 12 Tcos12 B L/2 350N 200N You have not given the free body diagram which is very necessary to understand Anyway, I amgiving the diagram. We assume the length of the spine is L Taking the torques about A L = 350. +200-L Tsin 12. 2 2-3 L=0 solve for T b) Taking the forces about the x direction. FR-Tcos 12 = 0 Substituting for T solve for R Question 2 Which two processes are involved in mitotic cell division? Answer There are two main steps that a cell goes through as it divides. The duplicated information contained in the nucleus is divided into two daughter nuclei as the first step of mitosis. Then, cytokinesis takes place, splitting the cell body and cytoplasm into two new cells. A single cell splits into two completely identical daughter cells during the cell division process known as mitosis. This cell division's primary goals are cell growth and death-cell replacement. Prophase, metaphase, anaphase, and telophase are the final two stages of the process. The DNA material in the cell doubles and then condenses to create chromosomes. These chromosomes coalesce close to the center of the cell. The mitotic spindle pulls the sister chromatids apart to their opposing poles. Genetic material from the nucleus is split between two daughter cells in this instance. Karyokinesis is the term for this. Cytokinesis, in which two cells are created by cytoplasmic division, occurs next. Answer that the two processes are karyokinesis and cytokinesis. Question 3 x-1 x+1 On many calculators, graphs of rational functions produce lines at vertical asymptotes. For example, graphing y = on the window [-4.9, 4.9] by [-4.9, 4.9] produces such a line at x=-1 on the TI-84 Plus and TI-89. But with the window [-4.7, 4.7] by [-4.7, 4.7] on a TI-84 Plus, or [-7.9, 7.9] by [-7.9, 7.9] on a TI-89, the spurious line does not appear. Experiment with this function on your calculator, trying different windows, and try to figure out an explanation for this phenomenon. Answer Experiment with your calculator. Since we are using online graphing tools, like Desmos, Geogebra etc., they do not show the asymptote line by defualt, but you can graph it separataly on the same screen. Question 4 Let H be the set of all vectors of the form S 3s 2s Find a vector v in R³ such that H=Span {v}. Why does this show that H is a subspace of R3 ? Answer The set H=Span{v}, where v = [1] 3 2 Thus H is a subspace of R³ by Theorem 1. Question 5 Find out if the sequence converges or diverges. If it converges, discover the limit. an = 1- (0.2)" Answer Step 1 Take the limit as the equation goes to infinite. lim an = lim 1700 Step 2 3 n4 n→∞ n³ - 2η We start by dividing each term in the sequence by the greatest term in the denominator. In this case, that's n³ Step 3 2η Now take the limit of the new version of the sequence. lim n n-001-0 =n=8