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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
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 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
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
A direct relationship can be represented by?
You think probable to a chemical equation.
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
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 do you determine whether a relationship shown in a table is a proportional relationship?
A proportional relationship is of the form y = kx where k is a constant. This can be rearranged to give: y = kx → k = y/x If the relationship in a table between to variables is a proportional one, then divide the elements of one column by the corresponding elements of the other column; if the result of each division is the same value, then the data is in a proportional relationship. If the data in the table is measured data, then the data is likely to be rounded, so the divisions also need to be rounded (to the appropriate degree).
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
