Concept explainers
Exercises 116-118 will help you prepare for the material covered in the next section. In each exercise, use exact values of trigonometric functions to show that the statement is true. Notice that each statement expresses the product of sines and/or cosines as a sum or a difference.
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- 3 and = 5 3 ---8--8--8 Let = 3 U2 = 1 Select all of the vectors that are in the span of {u₁, u2, u3}. (Check every statement that is correct.) 3 ☐ A. The vector 3 is in the span. -1 3 ☐ B. The vector -5 75°1 is in the span. ГОЛ ☐ C. The vector 0 is in the span. 3 -4 is in the span. OD. The vector 0 3 ☐ E. All vectors in R³ are in the span. 3 F. The vector 9 -4 5 3 is in the span. 0 ☐ G. We cannot tell which vectors are i the span.arrow_forward(20 p) 1. Find a particular solution satisfying the given initial conditions for the third-order homogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y(3)+2y"-y-2y = 0; y(0) = 1, y'(0) = 2, y"(0) = 0; y₁ = e*, y2 = e¯x, y3 = e−2x (20 p) 2. Find a particular solution satisfying the given initial conditions for the second-order nonhomogeneous linear equation given below. (See Section 5.2 in your textbook if you need a review of the subject.) y"-2y-3y = 6; y(0) = 3, y'(0) = 11 yc = c₁ex + c2e³x; yp = −2 (60 p) 3. Find the general, and if possible, particular solutions of the linear systems of differential equations given below using the eigenvalue-eigenvector method. (See Section 7.3 in your textbook if you need a review of the subject.) = a) x 4x1 + x2, x2 = 6x1-x2 b) x=6x17x2, x2 = x1-2x2 c) x = 9x1+5x2, x2 = −6x1-2x2; x1(0) = 1, x2(0)=0arrow_forwardFind the perimeter and areaarrow_forward
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- 3. Let M = (a) - (b) 2 −1 1 -1 2 7 4 -22 Find a basis for Col(M). Find a basis for Null(M).arrow_forwardSchoology X 1. IXL-Write a system of X Project Check #5 | Schx Thomas Edison essay, x Untitled presentation ixl.com/math/algebra-1/write-a-system-of-equations-given-a-graph d.net bookmarks Play Gimkit! - Enter... Imported Imported (1) Thomas Edison Inv... ◄›) What system of equations does the graph show? -8 -6 -4 -2 y 8 LO 6 4 2 -2 -4 -6 -8. 2 4 6 8 Write the equations in slope-intercept form. Simplify any fractions. y = y = = 00 S olo 20arrow_forwardEXERCICE 2: 6.5 points Le plan complexe est rapporté à un repère orthonormé (O, u, v ).Soit [0,[. 1/a. Résoudre dans l'équation (E₁): z2-2z+2 = 0. Ecrire les solutions sous forme exponentielle. I b. En déduire les solutions de l'équation (E2): z6-2 z³ + 2 = 0. 1-2 2/ Résoudre dans C l'équation (E): z² - 2z+1+e2i0 = 0. Ecrire les solutions sous forme exponentielle. 3/ On considère les points A, B et C d'affixes respectives: ZA = 1 + ie 10, zB = 1-ie 10 et zc = 2. a. Déterminer l'ensemble EA décrit par le point A lorsque e varie sur [0, 1. b. Calculer l'affixe du milieu K du segment [AB]. C. Déduire l'ensemble EB décrit par le point B lorsque varie sur [0,¹ [. d. Montrer que OACB est un parallelogramme. e. Donner une mesure de l'angle orienté (OA, OB) puis déterminer pour que OACB soit un carré.arrow_forward
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