0
What are the possible values of k when the line y equals kx -2 is a tangent to the curve y equals x2 -8x plus 7?
If: y = x^2 -8x +7 and y = kx -2
Then: X^2 -8x +7 = kx -2
Transposing terms: x^2 +(-8x -kx) +9 = 0
Using the discriminant: (-8 -k)^2 -4(1*9) = 0
Expanding brackets: 64 +16k +k^2 -36 = 0
Collecting like terms: k^2 +16k +28 = 0
Factorizing the above: (k +2)(k +14) = 0 meaning k = -2 or -14
Therefore the possible values of k are: -2 or -14
What else can I help you with?
What is the definition of a tangent line?
A tangent is a line that just touches a curve at a single point and its gradient equals the rate of change of the curve at that point.
What are the possible values of k in the line y equals kx -2 which is tangent to the curve y equals x squared -8x plus 7?
The possible values for k are -2 and -14 because in order for the line to be tangent to the curve the discriminant must be equal to 0 as follows:- -2x-2 = x2-8x+7 => 6-x2-9 = 0 -14x-2 = x2-8x+7 => -6-x2-9 = 0 Discriminant: 62-4*-1*-9 = 0
What are the possible values of k in the line y equals kx -2 which is tangent to the curve of y equals x squared -8x plus 7?
To find the possible values of ( k ) for which the line ( y = kx - 2 ) is tangent to the curve ( y = x^2 - 8x + 7 ), we need to set the two equations equal and solve for ( x ): ( kx - 2 = x^2 - 8x + 7 ). Rearranging gives us the quadratic equation ( x^2 - (k + 8)x + 9 = 0 ). For the line to be tangent to the curve, this quadratic must have exactly one solution, which occurs when the discriminant is zero: ((k + 8)^2 - 4 \cdot 1 \cdot 9 = 0). Solving this gives ( k + 8 = \pm 6 ), leading to possible values ( k = -2 ) and ( k = -14 ).
What is the value of y when y equals 2x plus 1.25 is a tangent to the curve y squared equals 10x?
If the line y = 2x+1.25 is a tangent to the curve y^2 = 10x then it works out that when x = 5/8 then y = 5/2
What are the possible values of k when y equals kx -2 which is tangent to the curve of y equals x squared -8x plus 7 showing work?
The gradient to the curve y = x2 - 8x + 7 is dy/dx = 2x - 8The gradient of the tangent to the curve is, therefore, 2x - 8.The gradient of the given line is kTherefore k = 2x - 8. That is, k can have ANY value whatsoever.Another Answer:-If: y = kx-2 and y = x2-8x+7Then: x2-8x+7 = kx-2 => x2-8x-kx+9 = 0Use the discriminant of: b2-4ac = 0So: (-8-k)2-4*1*9 = 0Which is: (-8-k)(-8-k)-36 = 0 => k2+16k+28 = 0Using the quadratic equation formula: k = -2 or k = -14 which are the possible values of k for the straight line to be tangent with the curve
What is the definition of a tangent line?
A tangent is a line that just touches a curve at a single point and its gradient equals the rate of change of the curve at that point.
Why we draw tangent in newton raphson method?
A line tangent to a curve, at a point, is the closest linear approximation to how the curve is "behaving" near that point. The tangent line is used to estimate values of the curve, near that point.
What are the possible values of k in the line y equals kx -2 which is tangent to the curve y equals x squared -8x plus 7?
The possible values for k are -2 and -14 because in order for the line to be tangent to the curve the discriminant must be equal to 0 as follows:- -2x-2 = x2-8x+7 => 6-x2-9 = 0 -14x-2 = x2-8x+7 => -6-x2-9 = 0 Discriminant: 62-4*-1*-9 = 0
What are the possible values of k in the line y equals kx -2 which is tangent to the curve of y equals x squared -8x plus 7?
To find the possible values of ( k ) for which the line ( y = kx - 2 ) is tangent to the curve ( y = x^2 - 8x + 7 ), we need to set the two equations equal and solve for ( x ): ( kx - 2 = x^2 - 8x + 7 ). Rearranging gives us the quadratic equation ( x^2 - (k + 8)x + 9 = 0 ). For the line to be tangent to the curve, this quadratic must have exactly one solution, which occurs when the discriminant is zero: ((k + 8)^2 - 4 \cdot 1 \cdot 9 = 0). Solving this gives ( k + 8 = \pm 6 ), leading to possible values ( k = -2 ) and ( k = -14 ).
What is the value of y when y equals 2x plus 1.25 is a tangent to the curve y squared equals 10x?
If the line y = 2x+1.25 is a tangent to the curve y^2 = 10x then it works out that when x = 5/8 then y = 5/2
What are the possible values of k when y equals kx -2 which is tangent to the curve of y equals x squared -8x plus 7 showing work?
The gradient to the curve y = x2 - 8x + 7 is dy/dx = 2x - 8The gradient of the tangent to the curve is, therefore, 2x - 8.The gradient of the given line is kTherefore k = 2x - 8. That is, k can have ANY value whatsoever.Another Answer:-If: y = kx-2 and y = x2-8x+7Then: x2-8x+7 = kx-2 => x2-8x-kx+9 = 0Use the discriminant of: b2-4ac = 0So: (-8-k)2-4*1*9 = 0Which is: (-8-k)(-8-k)-36 = 0 => k2+16k+28 = 0Using the quadratic equation formula: k = -2 or k = -14 which are the possible values of k for the straight line to be tangent with the curve
What is the gradient of the tangent to the curve at x equals 2 if Y equals x2?
Gradient to the curve at any point is the derivative of y = x2 So the gradient is d/dx of x2 = 2x. When x = 2, 2x = 4 so the gradient of the tangent at x = 2 is 4.
What are the values of k when the line of y equals kx -2 is a tangent to the curve of y equals x squared -8x plus 7?
If: y = kx -2 and y = x^2 -8x+7 Then the values of k work out as -2 and -14 Note that the line makes contact with the curve in a positive direction or a negative direction depending on what value is used for k.
At what point is the line of y equals x -4 tangent to the curve of x squared plus y squared equals 8?
(2, -2)
How do you find the slope of an Indifference curve?
You find the tangent to the curve at the point of interest and then find the slope of the tangent.
What is the value of k in the line of y equals kx plus 1 and is tangent to the curve of y squared equals 8x?
If: y = kx+1 is a tangent to the curve y^2 = 8x Then k must equal 2 for the discriminant to equal zero when the given equations are merged together to equal zero.
What is the value of k when y equals 3x plus 1 is a line tangent to the curve of x squared plus y squared equals k hence finding the point of contact of the line to the curve?
It is (-0.3, 0.1)
