Suppose you're climbing a hill whose shape is given by the equation z = 1000 – 0.003x² – 0.005y?, where the positive x-axis represents east, the positive y-axis represents north, and z represents the upward direction. If you are standing at a point with coordinates (60,45), in what direction is the slope of the hill largest?

Q: Find the point on the line y = 2x + 3 that is closest to the origin.

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The equation of the line with slope 4 and y-intercept (0, 5) can be written in the form y = mx + b |…

A: Given, The slope of the line is 4 y-intercept of the line is 0, -5 We have to write the equation…

Q: Suppose there is a straight line from z1 0 to z2 = 2+ 4i . You know that the equation of a straight…

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Q: Find an equation for the contour of f(x, y) = 2x°y+ 8x + 15 that goes through the point (5, 2).

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Q: b. Find the slope of the curve at the given point. y* = 2x; (648,6)

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Q: Find the slope of any line that is perpendicular to the line whose equation is x + 3y = 12.

A: x+3y=12 On simplification, we get 3y=-x+12⇒y=-13x+4 Now comparing with y=mx+c, we get m=-13,  c=4…

Q: Find the general equation Ax + By = C for the line with slope m y-intercept - 2. and

A: Given:General equation Ax+By=Cslope m=-23y-intercept  -2Equation:y=mx+b

Q: Find an equation for the set of points equidistant from the x-axis and the y-axis.

A: Let the point be (x,y,z) which is equidistant from the x-axis and the y-axis. Concept used:

Q: find the slope of the curve at the point indicated y = 5x - 3x2, x = 1

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Q: Find an equation for the line which passes through the origin and is perpendicular to  2x + 3y = -2

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Q: Find the equation of the line that is parallel to y = 3x -2 and contains the point (2,11). y = [ ?…

A: Two parallel lines have the same slope.

Q: What is the equation of the curve whose slope at the point (x, y) is 3x² if the curve is also…

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Q: Find the point on the line y = 2x + 8 that is closest to the origin.

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Q: Find the point on the line  y = 4x + 3  that is closest to the origin

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Q: Find an equation of the curve that passes through the point and has the given slope. 4y (32, 6), y'…

A: Here is the solution of the given problem.

Q: At what point along the curve x^3-9x-y=0 will the slope be 18?

A: Given,                      x3-9x-y=0                   y = x3-9x   Given slope, m=dy/dx=18

Q: What is the equation of the line that cuts the y-axis at g and is parallel to y= 5x + 2 ? O y=-8x+2…

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Q: Find the point on the line y = 3x + 4 that is closest to the origin.

A: Given, the line equation

Q: Find all points on the y-axis that are 6 units from the point (4, - 3).

A: Consider the point A(4, - 3) which is 6 units from the point B(0,y).

Q: find the equation of the line parallel to 8x+13y=16 and passing through the point (0,16).

A: Given equation of a line 8x+13y=16 and a point 0,16 through which a parallel line passes. To find…

Q: Containing the points (-3,4) and (2,5)

A: The points are (-3, 4) and (2,5). The equation of line in slope-intercept form is given as…

Q: Find the standard form for the equation of the line which passes through the point (2,0) and which…

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Q: Find the equation in general form of a line perpendicular to 2x + 3y – 9 = 0 that passes through the…

A: The equation of a line is given by 2x+3y-9 = 0                     ........1 The point is x0, y0 =…

Q: Find the general equation of the straight line that intercepts the x-axis at 2 and the y-axis at -6.

A: on solving this we get

Q: Horizontal; containing the point (-3,2)

A: We have to find the equation

Q: find the slope of the curve at the point indicated y = x3 - 2x + 7, x = -2

A: Slope of the curve is determined by taking the derivative of the given function:   The given…

Q: Find the equation of the line that passes through the point (-3, 5) and is parallel to the line X+…

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Q: Find the slope of the curve y = x2 + 4x - 10 At the point (2, 3)

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Q: Find the point on the line y = 5x + 3 that is closest to the origin.

A: *to find:- shortest distance point coordiantes from origin.

Q: Give the slope and y-intercept of the line whose equation is Ax + By = C . Assume that B ≠ 0.

A: Give the slope and y-intercept of the line whose equation is Ax + By = C . Assume that B ≠ 0.

Q: What point on the line y=2x-5 is closest to the origin?

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Q: 3. If y = 3x – 2x², what is the slope of the curve at the point (2, -2)? а. 3 b. - 4 С. - 5 d. -1

A: Given y=3x-2x22,-2

Q: Find the slope of the curve defined by the equation x²y – 8 = 0 at the point (2, 2)?

A: The required slope of the given curve can be found as below

Q: Find an equation for the contour of f(x, y) = 2x2y + 6x + 10 that goes through the point (2, -2).

A: We have to find an equation that is the contour of  f(x,y)=2x2y+6x+10      that goes through the…

Q: What is an equation of the line that passes through the po parallel to the line x + 6y = 12?

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Q: Solve for the distance and midpoint from the given equation. a. {(x,y)|y=2x-5, x=-3 and 4} b.…

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Q: Find the point on the line y=3x-10 that is closest to the origin.

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Q: Find the point on the line y = 5x + 4 that is closest to the origin. (х, у) %3

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Q: The equation for FG is y = 2x + 1. Which equation represents a line that is perpendicular to FG and…

A: Equation of line FG =2x+1 so the slope of FG is m=2

Q: Find the equation of the line passing through the (1,3) and having the slope m=4

A: Solution: The objective is to find the equation of the line passing through the (1,3) and having the…

Q: Find the equation of a line that intersects the curve y = x² + 14x + 52 at x = -10 and is parallel…

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Q: Determine the slope of 3(x2+y2)2=100xy at the point (3,1)

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Q: Find the point on the line y= 7x + 2 that is closest to the origin.

A: Given,           The line y=7x+2 that is closest to the origin.

Q: Give the equation of the line perpendicular to Y=-4x+2 that has an x-intercept of -1

A: First find slope of perpendicular line then use equation of line

Q: What point on the line y=3x+6 is closest to the​ origin?

A: The point on the line closest to the origin is the foot of perpendicular drawn from origin to the…

Q: Find the point on the y-axis that is equidistant from the points A(-4,-2) and B(3,1).

A: Given points (-4,-2) & (3,1)Point on y-axis means x-coordinate is zero i.e.,point is (0,y)

Q: Find the curve whose slope at any point (x,y) is 6x^2−2x−5 if the curve is required to pass through…

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Q: Find the equation of the line that is perpendicular to y = 6x – 2 and %3D

A: To find the equation of line perpendicular to given line.

Q: Find the point on the line  y = 5x + 2  that is closest to the origin.

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Q: Find the slope of x²y=8 at the point (2,2).

A: Given: x2y=8 To find: Slope of x2y=8 at (2,2)