Select two distinct values of X, designated X1 and X2, from the table, read the corresponding values Y1 and Y2 from the table, and calculate the slope from the formula:
slope = (Y2 - Y1)/(X2 - X1)
The equation (xy = c), where (c) is a constant, represents a hyperbola in the xy-plane. To find the slope, we can implicitly differentiate the equation with respect to (x). This gives us (y + x \frac{dy}{dx} = 0), leading to the slope (\frac{dy}{dx} = -\frac{y}{x}). The slope varies depending on the values of (x) and (y), indicating that it is not constant across the hyperbola.
Form a right angle triangle under the slope and divide the base of the triangle into the height of the triangle.
The expression (xy - 1) does not define a slope on its own. To determine the slope, you need to rearrange the equation into the slope-intercept form (y = mx + b). If you set (xy - 1 = 0) and solve for (y), you get (y = \frac{1}{x}), which represents a hyperbola and does not have a constant slope. Instead, the slope varies depending on the value of (x).
To find the value of (xy^2) given (x = 4) and (y = 2), substitute the values into the expression. This gives (xy^2 = 4 \times (2^2) = 4 \times 4 = 16). Therefore, the value of (xy^2) is 16.
To find the xy-trace, set z = 0 in the equation -5x - 2y - 3z = 10. Simplifying, we get -5x - 2y = 10. This is the equation of the xy-trace for the given plane.
Form a right angle triangle under the slope and divide the base of the triangle into the height of the triangle.
The expression (xy - 1) does not define a slope on its own. To determine the slope, you need to rearrange the equation into the slope-intercept form (y = mx + b). If you set (xy - 1 = 0) and solve for (y), you get (y = \frac{1}{x}), which represents a hyperbola and does not have a constant slope. Instead, the slope varies depending on the value of (x).
True.
If the curve is on the xy-plane, finding an expression for dy/dx will give you the slope of a curve at a point.
Points for example: (4, 8) and (2, 4) Slope: (8-4)/(4-2) = 2 The slope formula is m = (y2 - y1) / (x2 - x1) where the 2 points are (x1,y1) and (x2,y2)
To find the value of (xy^2) given (x = 4) and (y = 2), substitute the values into the expression. This gives (xy^2 = 4 \times (2^2) = 4 \times 4 = 16). Therefore, the value of (xy^2) is 16.
You're familiar with the xy-plane. A line with negative slope is one that goes down toward the right. A curve has a negative slope at a point if the tangent line to the curve at that point has a negative slope.
To find the xy-trace, set z = 0 in the equation -5x - 2y - 3z = 10. Simplifying, we get -5x - 2y = 10. This is the equation of the xy-trace for the given plane.
x = 4 is a straight line that is vertical when plotted on the xy graph, where y is the vertical axis and x is the horizontal axis. A vertical line has an infinite slope; the slope is infinity
1 whenever there is a coefficient of one then it is not written but "understood"
y' is a derivative so y'=xy^3 represents the slope of y. We find that the limit of y' as x approaches zero is zero. Therefore we can say that the instantaneous slope of y as x approaches zero is zero.
The greatest possible slope is 1.