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Various options:
y is directly proportional to k, with x as the constant of proportionality;
y is directly proportional to x, with k as the constant of proportionality;
x is inversely proportional to k, with y as the constant of proportionality;
x is directly proportional to y, with 1/k as the constant of proportionality;
k is directly proportional to y, with 1/x as the constant of proportionality; and
k is inversely proportional to x, with y as the constant of proportionality.
What else can I help you with?
What are the values of k when kx plus y equals 4 is a tangent to the curve of y equals x squared plus 8 on the Cartesian plane showing work?
If: kx+y = 4 and y = x^2 +8 Then: x^2 +8 = 4-kx or x^2 +8 -4+kx = 0 => x^2+4+kx = 0 The discriminant of the above quadratic equation must equal 0 So: k^2 -4*(4*1) = 0 => k^2-16 = 0 Therefore: k^2 = 16 and so the values of k are -4 and +4
Find a equation of variation where y varies directly as x and y equals 0.8 when x equals 0.4?
direct variation: y = kx y = kx k = y/x = 0.8/0.4 = 2
What are the possible values of k when y equals x -8 is a tangent to the curve y equals 4x squared plus kx plus 1 showing work?
If: y = 4x^2 +kx +1 and y = x -8 Then: 4x^2 +kx +1 = x -8 Or: 4x^2 +(kx-x) +9 = 0 Using the discriminant: (k-1)^2 -4*4*9 = 0 => (k-1)^2 = 144 Square root both sides: k -1 = 12 or -12 Add 1 to both sides: k = 13 or k = -11
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 showing work?
If you mean: y = kx-2 and y = x^2-8x+7 Then: x^2-8x+7 = kx-2 => x^2-(8x-kx)+7+2 = 0 => x^2-8x+kx+9 = 0 For the tangent to touch the curve the discriminant of b^-4ab must = 0 So: (8+k)^2-4*(9*1) = 0 => (8+k)^2 -36 = 0 => (8+k)^2 = 36 Square root both sides and then subtract 8 from both sides: k = - or + 6 -8 Therefore possible values of k are: k = -2 or k = -14
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 is the value of k when the line y equals kx plus 1.25 is a tangent to the curve y squared equals 10x?
Equations: y = kx +1.25 and y^2 = 10x If: y = kx +1.25 then y^2 = (kx +1.25)^2 =>(kx)^2 +2.5kx +1.5625 So: (kx)^2 +2.5kx +1.5625 = 10x Transposing terms: (kx)^2 +2.5kx +1.5625 -10x = 0 Using the discriminant formula: (2.5k -10)^2 -4(1.5625*k^2) Multiplying out the brackets: 6.25k^2 -50k +100 -6.25^2 = 0 Collecting like terms: -50k +100 = 0 Solving the above equation: k = 2 Therefore the value of k is: 2
In the direct variation 2y equals 3x what is the k value?
The question is not clear. But if you want this in the form y=kx, then k must be 1.5
What are the values of k when kx plus y equals 4 is a tangent to the curve of y equals x squared plus 8 on the Cartesian plane showing work?
If: kx+y = 4 and y = x^2 +8 Then: x^2 +8 = 4-kx or x^2 +8 -4+kx = 0 => x^2+4+kx = 0 The discriminant of the above quadratic equation must equal 0 So: k^2 -4*(4*1) = 0 => k^2-16 = 0 Therefore: k^2 = 16 and so the values of k are -4 and +4
Find a equation of variation where y varies directly as x and y equals 0.8 when x equals 0.4?
direct variation: y = kx y = kx k = y/x = 0.8/0.4 = 2
A direct relationship can be represented by?
You think probable to a chemical equation.
What are the possible values of k when y equals x -8 is a tangent to the curve y equals 4x squared plus kx plus 1 showing work?
If: y = 4x^2 +kx +1 and y = x -8 Then: 4x^2 +kx +1 = x -8 Or: 4x^2 +(kx-x) +9 = 0 Using the discriminant: (k-1)^2 -4*4*9 = 0 => (k-1)^2 = 144 Square root both sides: k -1 = 12 or -12 Add 1 to both sides: k = 13 or k = -11
Is the equation y equals 16x plus 4 a proportional relationship?
No. A proportional relationship between "y" and "x" must be of the form:y = kx where "k" can be any constant. Thus, y = 16x would work perfectly. However, the additional "+4" makes it impossible to convert it to this form.
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.
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.
How can the graph of y equals kx be interpreted for different contexts?
It is a straight line through the origin and, if k > 0 reflects a direct relationship between x and y. This means that each unit increase in x is associated with y increasing by k. If k < 0 it reflects a direct but negative relationship and this means that each unit increase in x is associated with y decreasing by k. If k = 0 then the result is the x-axis. This means that changes in x are not associated with changes in y. None of the above imply causation.
How would you work out the possible values of k in the line y equals kx plus 1 which is tangent to the curve of y equals 3x squared -4x plus 4?
If: y = kx+1 and y = 3x2-4x+4 Then: 3x2-4x+4 = kx+1 So: 3x2-4x-kx+3 = 0 For the line to be tangent to the curve the discriminant of b2-4ac must = 0 So when: -4*3*3 = -36 then (-4-k)2 must = 36 So it follows: (-4-k)(-4-k) = 36 => k2+8k-20 = 0 Solving the quadratic equation: k = 2 or k = -10
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 showing work?
If you mean: y = kx-2 and y = x^2-8x+7 Then: x^2-8x+7 = kx-2 => x^2-(8x-kx)+7+2 = 0 => x^2-8x+kx+9 = 0 For the tangent to touch the curve the discriminant of b^-4ab must = 0 So: (8+k)^2-4*(9*1) = 0 => (8+k)^2 -36 = 0 => (8+k)^2 = 36 Square root both sides and then subtract 8 from both sides: k = - or + 6 -8 Therefore possible values of k are: k = -2 or k = -14
