3. The slope of tangent line at any point (x, y) on the curve is 3x²-2x+7. What is the equation ofthe curve (the general solution)?x2a. y =-+7x +Cb. у %3D х3 — х2 + 7x + Сc. 2y = x3 – x² + 7x + Cd. y = 3x3 – 2x² + 7x + Cа. у %3D3

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Answered: 3. The slope of tangent line at any…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. The slope of the tangent to a curve at any point (x, y) on the curve is O x+y=-1 O x² + y² = 5 O x² + y² = 25 O x² - y² = -7 Find the equation of the curve if the point (3, -4) is on the curve.
Find the approx. distance of the point (6, -3) from the line 2x – y +4 = 0 a. 6.5 units O b. 10.5 units O c. 12.5 units O d. 8.5 units
Please answer first three questions
Suppose you are climbing a hill whose shape is given by the equation z = 1300- 0.005x² - 0.01y², where x, y, and z are measured in meters, and you are standing at a point with coordinates (60, 40, 1266). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend? Ⓒascend O descend At what rate? 1.6 X descend (b) If you walk northwest, will you start to ascend or descend? O ascend vertical meters per horizontal meter At what rate? (Round your answer to two decimal places.) .57 vertical meters per horizontal meter X (c) In which direction is the slope largest? What is the rate of ascent in that direction? vertical meters per horizontal meter At what angle above the horizontal does the path in that direction begin? (Round your answer to two decimal places.) 60.81
3. In the given equation below, a is the value that will make the equation exact. Find a. 2хy^3 3y - (3x + ax^2y^2 = 0. 2ay) y' = A. -4 -1 -2 в. С. D. -3
8. What is the slope of the fine that passes through the points (4, 5) and (7, 3y? The solution of the quadratic equation 2x2 -x-14 = 0 is 9. -1t VIII A. 1t VI13 C. 2 4. -1t VI13 D. В. 4 2 Due Monday @ 8:53 am

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3. The slope of tangent line at any point (x, y) on the curve is 3x²-2x+7. What is the equation of the curve (the general solution)? a. y = b. у %3 х3 — х2 + 7x + C x2 + 7x + C c. 2y = x³ – x² + 7x + C d. y %3D Зx3 — 2х2 + 7х + С у 3D 2 -