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3. Parametric Curves (7 marks total) (a) (3 marks) Explain in your own words the similarities...
1. a. Consider the curve defined by the following parametric equations: r(t) = et-e-t, y(t) = et ...
1. a. Consider the curve defined by the following parametric equations: r(t) = et-e-t, y(t) = et + e-t where t can be any number. Determine where the particle describing the curve is when tIn(3) In(2). 0, ln(2) and In(3). Split up the work among your group Onex, vou l'ave found i lose live polnia, try to n"惱; wbai ille wlu le curve "u"ht lex k like. b. Verify that every point on the curve from the previous problem solves...
Let the curve C in the (x, y)-plane be given by the parametric equations x =...
Let the curve C in the (x, y)-plane be given by the parametric equations x = e + 2, y = e2-1, tER. (a) Show that the point (3,0) belongs to the curve C. To which value of the parameter t does the point (3,0) correspond? (b) Find an expression for dy (dy/dt) without eliminating the parameter t, i.e., using de = (da/dt) (c) Using your result from part (b), find the value of at the point (3,0). (d) From...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-1 orthogonally at (-1,0) and (1,0). Let H be the set of curves y2b with b ER. (a) Prove that the tangent line of each curve in H at a point (r, y) with y / 0 has slope (b) Let y -f(x) be a...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-1 orthogonally at (-1,0) and (1,0). Let H be the set of curves y2-2.2-b with b є R. (a) Prove that the tangent line of each curve in H at a point (x, y) with y 0 has slope - (b) Let y-f(x) be a...
4. Tired from the long week, with the amusement park and the wok and dinner plate designs, you retreat to be in peace and study parametric equations. A curious leaflike curve called the "foli...
4. Tired from the long week, with the amusement park and the wok and dinner plate designs, you retreat to be in peace and study parametric equations. A curious leaflike curve called the "folium of Descartes" catches your eye; it is defined by the parametric equations 3t 3t2 (a) (4 points) Show that if the point (a, b) lies on the curve, then so does (b, a); that is, the curve is symmetric with respect to the line y a....
1. (26 marks total) Math Review: Recall the IS-L.M model from your intermediate macro course In...
1. (26 marks total) Math Review: Recall the IS-L.M model from your intermediate macro course In particular, the goods-market equilibrium condition was Y-C(Y-T)+I (r) +G, and the money-market ecluilibrunn condition was m = L (r, Y). Here, the exogenous variables are G government spending), T (taxes), and m (real money supply). The endogenous variables are Y (output, or income) and r (real interest rate). C() is the consumption function, which is increasing in disposable income Y-T, bit less than one-for-one...
3. You're so thrilled by your geometric and designing capabilities (see problems 1 and 2) that you decide to design a thin dinner plate that on your blueprint covers the region between the r-...
3. You're so thrilled by your geometric and designing capabilities (see problems 1 and 2) that you decide to design a thin dinner plate that on your blueprint covers the region between the r-axis and the curve To impress the friends, you decide to make two versions of the plate and exhibit them by holding them up on a single finger. In order to do this, you need to calculate the center of mass of each. (a) (5 points) One...
3. You're so thrilled by your geometric and designing capabilities (see problems 1 and 2) that...
3. You're so thrilled by your geometric and designing capabilities (see problems 1 and 2) that you decide to design a thin dinner plate that on your blueprint covers the region between the r-axis and the curve To impress the friends, you decide to make two versions of the plate and exhibit them by holding them up on a single finger. In order to do this, you need to calculate the center of mass of each. (a) (5 points) One...
2 dv do sine Math 2120 Spring 2019 Final Exam Show Works fo NAME #1 Give a set of parametric equations that describes the following curves. The piecewise linear path from P(-2.3) to 0(2.-3) to R...
2
dv do sine Math 2120 Spring 2019 Final Exam Show Works fo NAME #1 Give a set of parametric equations that describes the following curves. The piecewise linear path from P(-2.3) to 0(2.-3) to R(3.5). using parameter values Osis2 #2. Find the points at which the following polar curves have a horizontal or a vertical tange #3. Find an Equation for describing the following object: A sphere with center (1, 2,0 pa point (3, 4, 5). dy Slopes of...
5. The minimum points of the average variable cost and average total cost curves occur where...
5. The minimum points of the average variable cost and average total cost curves occur where the a. marginal cost curve lies below the average variable cost and average total cost curves. b. slope of total cost is the smallest. c. average variable cost and average total cost curves intersect. d. marginal cost curve intersects those curves. 6. The Carters' oldest son attends Big State University. He and his parents pay all his foes and tuition. These payments count in...
1. a. Consider the curve defined by the following parametric equations: r(t) = et-e-t, y(t) = et + e-t where t can be any number. Determine where the particle describing the curve is when tIn(3) In(2). 0, ln(2) and In(3). Split up the work among your group Onex, vou l'ave found i lose live polnia, try to n"惱; wbai ille wlu le curve "u"ht lex k like. b. Verify that every point on the curve from the previous problem solves...
Let the curve C in the (x, y)-plane be given by the parametric equations x = e + 2, y = e2-1, tER. (a) Show that the point (3,0) belongs to the curve C. To which value of the parameter t does the point (3,0) correspond? (b) Find an expression for dy (dy/dt) without eliminating the parameter t, i.e., using de = (da/dt) (c) Using your result from part (b), find the value of at the point (3,0). (d) From...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-1 orthogonally at (-1,0) and (1,0). Let H be the set of curves y2b with b ER. (a) Prove that the tangent line of each curve in H at a point (r, y) with y / 0 has slope (b) Let y -f(x) be a...
2. We say that two curves intersect orthogonally if they intersect and their tangent lines are orthogonal at each point in the intersection. For example, the curve y = 0 intersects the curve x2 + y2-1 orthogonally at (-1,0) and (1,0). Let H be the set of curves y2-2.2-b with b є R. (a) Prove that the tangent line of each curve in H at a point (x, y) with y 0 has slope - (b) Let y-f(x) be a...
4. Tired from the long week, with the amusement park and the wok and dinner plate designs, you retreat to be in peace and study parametric equations. A curious leaflike curve called the "folium of Descartes" catches your eye; it is defined by the parametric equations 3t 3t2 (a) (4 points) Show that if the point (a, b) lies on the curve, then so does (b, a); that is, the curve is symmetric with respect to the line y a....
1. (26 marks total) Math Review: Recall the IS-L.M model from your intermediate macro course In particular, the goods-market equilibrium condition was Y-C(Y-T)+I (r) +G, and the money-market ecluilibrunn condition was m = L (r, Y). Here, the exogenous variables are G government spending), T (taxes), and m (real money supply). The endogenous variables are Y (output, or income) and r (real interest rate). C() is the consumption function, which is increasing in disposable income Y-T, bit less than one-for-one...
3. You're so thrilled by your geometric and designing capabilities (see problems 1 and 2) that you decide to design a thin dinner plate that on your blueprint covers the region between the r-axis and the curve To impress the friends, you decide to make two versions of the plate and exhibit them by holding them up on a single finger. In order to do this, you need to calculate the center of mass of each. (a) (5 points) One...
3. You're so thrilled by your geometric and designing capabilities (see problems 1 and 2) that you decide to design a thin dinner plate that on your blueprint covers the region between the r-axis and the curve To impress the friends, you decide to make two versions of the plate and exhibit them by holding them up on a single finger. In order to do this, you need to calculate the center of mass of each. (a) (5 points) One...
2
dv do sine Math 2120 Spring 2019 Final Exam Show Works fo NAME #1 Give a set of parametric equations that describes the following curves. The piecewise linear path from P(-2.3) to 0(2.-3) to R(3.5). using parameter values Osis2 #2. Find the points at which the following polar curves have a horizontal or a vertical tange #3. Find an Equation for describing the following object: A sphere with center (1, 2,0 pa point (3, 4, 5). dy Slopes of...
5. The minimum points of the average variable cost and average total cost curves occur where the a. marginal cost curve lies below the average variable cost and average total cost curves. b. slope of total cost is the smallest. c. average variable cost and average total cost curves intersect. d. marginal cost curve intersects those curves. 6. The Carters' oldest son attends Big State University. He and his parents pay all his foes and tuition. These payments count in...
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