A Problem Solving Approach to Mathematics for Elementary School Teachers, Books a la Carte Edition plus NEW MyLab Math with Pearson eText - Access Card Package (12th Edition)
12th Edition
ISBN: 9780133865479
Author: Rick Billstein, Shlomo Libeskind, Johnny Lott
Publisher: PEARSON
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Chapter 10.2, Problem 11MC
To determine
To provide:
The rationale for the type of graph that you would use to show the percentage of working time that professors spend on teaching, service, and research.
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What is the vertex, axis of symmerty, all of the solutions, all of the end behaviors, the increasing interval, the decreasing interval, describe all of the transformations that have occurred EXAMPLE Vertical shrink/compression (wider). or Vertical translation down, the domain and range of this graph EXAMPLE Domain: x ≤ -1 Range: y ≥ -4.
use a graphing utility to sketch the graph of the function and then use the graph to help identify or approximate the domain and range of the function. f(x)= x*sqrt(9-(x^2))
use a graphing utility to sketch the graph of the function and then use the graph to help identify or approximate the domain and range of the function. f(x)=xsqrt(9-(x^2))
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- 4. Select all of the solutions for x²+x - 12 = 0? A. -12 B. -4 C. -3 D. 3 E 4 F 12 4 of 10arrow_forward2. Select all of the polynomials with the degree of 7. A. h(x) = (4x + 2)³(x − 7)(3x + 1)4 B h(x) = (x + 7)³(2x + 1)^(6x − 5)² ☐ Ch(x)=(3x² + 9)(x + 4)(8x + 2)ª h(x) = (x + 6)²(9x + 2) (x − 3) h(x)=(-x-7)² (x + 8)²(7x + 4)³ Scroll down to see more 2 of 10arrow_forward1. If all of the zeros for a polynomial are included in the graph, which polynomial could the graph represent? 100 -6 -2 0 2 100 200arrow_forward
- 3. Select the polynomial that matches the description given: Zero at 4 with multiplicity 3 Zero at −1 with multiplicity 2 Zero at -10 with multiplicity 1 Zero at 5 with multiplicity 5 ○ A. P(x) = (x − 4)³(x + 1)²(x + 10)(x — 5)³ B - P(x) = (x + 4)³(x − 1)²(x − 10)(x + 5)³ ○ ° P(x) = (1 − 3)'(x + 2)(x + 1)"'" (x — 5)³ 51 P(r) = (x-4)³(x − 1)(x + 10)(x − 5 3 of 10arrow_forwardMatch the equation, graph, and description of transformation. Horizontal translation 1 unit right; vertical translation 1 unit up; vertical shrink of 1/2; reflection across the x axis Horizontal translation 1 unit left; vertical translation 1 unit down; vertical stretch of 2 Horizontal translation 2 units right; reflection across the x-axis Vertical translation 1 unit up; vertical stretch of 2; reflection across the x-axis Reflection across the x - axis; vertical translation 2 units down Horizontal translation 2 units left Horizontal translation 2 units right Vertical translation 1 unit down; vertical shrink of 1/2; reflection across the x-axis Vertical translation 2 units down Horizontal translation 1 unit left; vertical translation 2 units up; vertical stretch of 2; reflection across the x - axis f(x) = - =-½ ½ (x − 1)²+1 f(x) = x²-2 f(x) = -2(x+1)²+2 f(x)=2(x+1)²-1 f(x)=-(x-2)² f(x)=(x-2)² f(x) = f(x) = -2x²+1 f(x) = -x²-2 f(x) = (x+2)²arrow_forwardWhat is the vertex, increasing interval, decreasing interval, domain, range, root/solution/zero, and the end behavior?arrow_forward
- Calculate a (bxc) where a = i, b = j, and c = k.arrow_forwardi+2j+3k = (1,2,3) and b = -i-k. Calculate the cross product a x b where a Next calculate the area of the parallelogram spanned by a and b.arrow_forwardThe measured receptance data around two resonant picks of a structure are tabulated in the followings. Find the natural frequencies, damping ratios, and mode shapes of the structure. (30 points) (@)×10 m/N α₁₂ (@)×10 m/N w/2z (Hz) 99 0.1176 0.17531 0.1114 -0.1751i 101 -0.0302 0.2456i -0.0365 -0.2453i 103 -0.1216 0.1327i -0.1279-0.1324i 220 0.0353 0.0260i -0.0419+0.0259i 224 0.0210 0.0757i |-0.0273 +0.0756i 228 -0.0443 0.0474i 0.0382 +0.0474iarrow_forward
- Q3: Define the linear functional J: H(2) R by 1(v) = a(v. v) - L(v) Let u be the unique weak solution to a(u,v) = L(v) in H() and suppose that a(...) is a symmetric bilinear form on H(2) prove that 1- u is minimizer. 2- u is unique. 3- The minimizer J(u,) can be rewritten under algebraic form u Au-ub. J(u)=u'Au- Where A. b are repictively the stiffence matrix and the load vectorarrow_forward== 1. A separable differential equation can be written in the form hy) = g(a) where h(y) is a function of y only, and g(x) is a function of r only. All of the equations below are separable. Rewrite each of these in the form h(y) = g(x), then find a general solution by integrating both sides. Determine whether the solutions you found are explicit (functions) or implicit (curves but not functions) (a) 1' = — 1/3 (b) y' = = --- Y (c) y = x(1+ y²)arrow_forwardJa дх dx dx Q3: Define the linear functional J: H()-R by تاریخ (v) = ½a(v, v) - (v) == Let u be the unique weak solution to a(u,v) = L(v) in H₁(2) and suppose that a(...) is a symmetric bilinear form on H() prove that a Buy v) = 1- u is minimizer. 2- u is unique. 3- The minimizer J(u,) can be rewritten under J(u)=u' Au-ub, algebraic form Where A, b are repictively the stiffence matrix and the load vector Q4: A) Answer only 1-show that thelation to -Auf in N, u = 0 on a satisfies the stability Vulf and show that V(u-u,)||² = ||vu||2 - ||vu||2 lu-ulls Chu||2 2- Prove that Where =1 ||ul|= a(u, u) = Vu. Vu dx + fu. uds B) Consider the bilinear form a(u, v) = (Au, Av) + (Vu, Vv) + (Vu, v) + (u, v) Show that a(u, v) continues and V- elliptic on H(2) (3) (0.0), (3.0)arrow_forward
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