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How would you work out the possible values of k when the line y equals x -8 is tangent to the curve y equals 4x squared plus kx plus 1?
Wiki User
∙ 10y ago
Since the curves are tangent, they have the same slope at that point and the same x and y value at that point.
Set equations equal and set slopes equal and solve
Togetslope, you need to know calculus first derivative
slope of one equation is dy/dx = 8x +k
and the othereqaution slope is dy/dx = 1
so youhave
4x^2 + kx + 1 = x -8
8x + k = 1
4x^2 +kx -x + 9 = 0
8x + k -1 = 0
solve for k
k = -11 or +13
Another way but with the same answer:-
If: y = 4x2+kx+1 and y = x-8
Then: 4x2+kx+1 = x-8
So: 4x2+kx-x+9 = 0
For the line to be tangent with the curve the discriminant b2-4ac must = 0
So if: -4*4*9 = -144 then (k-1)2 must = 144
So it follows: (k-1)(k-1) = 144 => k2-2k-143 = 0
Solving the quadratic equation: k = -11 or k = 13
Wiki User
∙ 10y ago
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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 values of x and y when x minus y equals 0 and x squared plus y squared equals 18?
(x, y) = (-3, -3) or (3, 3)
What are the values of the variables when y equals x plus c is a tangent to the curve y equals 3 -x -5x squared?
-2
How do you prove in 3 different ways that the line of y equals x -4 is tangent to the curve of x squared plus y squared equals 8?
If: y = x-4 and y = x2+y2 = 8 then 2x2-8x+8 = 0 and the 3 ways of proof are: 1 Plot the given values on a graph and the line will touch the curve at one point 2 The discriminant of b2-4ac of 2x2-8x+8 must equal 0 3 Solving the equation gives x = 2 or x = 2 meaning the line is tangent to the curve
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 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 when the equation x squared plus 2kx plus 81 equals 0 has equal roots?
Using the discriminant the possible values of k are -9 or 9
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.
What are the values of x and y when x minus y equals 0 and x squared plus y squared equals 18?
(x, y) = (-3, -3) or (3, 3)
What are the values of the variables when y equals x plus c is a tangent to the curve y equals 3 -x -5x squared?
-2
What are the possible values of k when the line y equals kx -2 is a tangent to the curve y equals x squared -8x plus 7?
If the line y = kx - 2 is a tangent to the curve y = x² - 8x + 7, then where they meet: kx - 2 = x² - 8x + 7 → x² - (8+k)x + 9 = 0 will have a repeated root, ie the determinant is zero: (8+k)² - 4 ×1 × 9 = 0 → 64 + 16k + k² - 36 = 0 → k² + 16k + 28 = 0 → (k + 2)(k + 14) = 0 → k = -2 or -14.
How do you prove in 3 different ways that the line of y equals x -4 is tangent to the curve of x squared plus y squared equals 8?
If: y = x-4 and y = x2+y2 = 8 then 2x2-8x+8 = 0 and the 3 ways of proof are: 1 Plot the given values on a graph and the line will touch the curve at one point 2 The discriminant of b2-4ac of 2x2-8x+8 must equal 0 3 Solving the equation gives x = 2 or x = 2 meaning the line is tangent to the curve
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
Is there Two possible squared values of 100?
If you mean "are there two values which, when squared, equal 100" then the answer is yes. 102 = 100 -102 =100 If you mean "Can 1002 result in two different answers" then the answer is no. 1002 = 10,000
How many values of l are possible when n equals 5?
4,3,2,1,0
What is sin squared x equals cos squared minus 2 sin x?
Since the word 'equals' appears in your questions it might be what is called a trigonometric identity, in other words a statement about a relationship between various trigonometric values.
What are the possible values of c in the line y equals cx plus 1 which is a tangent to the curve y equals 3x squared -4x plus 4 showing work?
If y = cx + 1 is a tangent then it intersects the curve only once. Therefore cx + 1 = 3x^2 - 4x + 4 has only one root that is, 3x^2 - (c+4)x + 3 has a single root therefore the discriminant is 0: (c+4)^2 - 4*3*3 = 0 (c+4)^2 = 36 c + 4 = sqrt(36) = -6 or +6 Therefore c = -10 or c = 2.
