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How do you find the values of k when the straight line y equals kx -2 is a tangent to the curve y equals x squared -8x plus 7?
By implication : x2-8x+7 = kx-2
Form a quadratic equation: x2-8x-kx+9 = 0
For a line to be a tangent to the curve it must have two equal roots and the discriminant b2-4ac of the quadratic equation must equal 0.
So: (-8-k)2-4*1*9 = 0
(-8-k)2-36 = 0
(-8-k)2 = 36
Square root both sides:
-8-k = -/+6
-k = 2 or 14
k = -2 or -14
When k = -2 is substituted into the quadratic equation x will have two equal roots of 3
When k = -14 is substituted into the quadratic equation x will have two equal roots of -3
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The formula is A-squared + B-squared = C-squared where A and B are the sides and C is the hypotenuse. Given the values of A and B as 3 inches and 2 inches we can use the formula: 3-squared (9) + 2-squared (4) = 13. The length of the hypotenuse is the square root of 13 (3.6055512).
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If the points are (b, 2) and (6, c) then to satisfy the straight line equations it works out that b = -2 and c = 4 which means that the points are (-2, 2) and (6, 4)
Where are the points of intersection on the curve and line of x squared plus y squared plus 4x plus 6y minus 40 equals 0 and x equals 10 plus y?
x2+y2+4x+6y-40 = 0 and x = 10+y Substitute the second equation into the first equation: (10+y)2+y2+4(10+y)+6y-40 = 0 2y2+30y+100 = 0 Divide all terms by 2: y2+15y+50 = 0 (y+10)(y+5) = 0 => y = -10 or y = -5 Substitute the above values into the second equation to find the points of intersection: Points of intersection are: (0, -10) and (5, -5)
Where are the points of intersection of the straight line 3x -y equals 5 with the curve 2x squared plus y squared equals 129?
(52/11, 101/11) and (-2, -11) Rearrange 3x-y = 5 into y = 3x-5 and substitute this into the curve equation and then use the quadratic equation formula to find the values of x which leads to finding the values of y by substituting the values of x into y = 3x-5.
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 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 the variables when y equals x plus c is a tangent to the curve y equals 3 -x -5x squared?
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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 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 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
Where do the curves of y equals 4x squared -2x -1 and y equals -2x squared plus 3x plus 5 intersect?
They intersect at points (-2/3, 19/9) and (3/2, 5) Solved by combining the two equations together to equal nought and then using the quadratic equation formula to find the values of x and substituting these values into the equations to find the values of y.
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 do the asymptotes represent when you graph the tangent function?
When you graph a tangent function, the asymptotes represent x values 90 and 270.
What are the values of y equals x plus 5?
It is a straight line equation in the form of: y = x+5
