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What are the values of x y and k when the line y equals 3x plus 1 is a tangent to the circle x squared plus y squared equals k?
If y = 3x + 1 is a tangent to x² + y² = k (k > 0 since it is a square), then where they meet has a repeated root; they meet at: x² + (3x + 1)² = k → x² + 9x² + 6x + 1 - k = 0 → 10x² + 6x + (1 - k) = 0 This is the point of contact when it has a repeated root which is when the discriminant is zero, ie when: 6² + 4 × 10 × (1 - k) = 0 → 36 + 40 - 40k = 0 → 40k = 4 → k = 1/10 I guess for x & y you mean the point where y = 3x + 1 is a tangent to x² + y² = k, ie the point of contact. The value of k can now be substituted into the equation of the point of contact: 10x² + 6x + (1 - k) = 0 → 10x² + 6x + (1 - 1/10) = 0 → 10x² + 6x + 9/10 = 0 → x² + 6x/10 + 9/100 = 0 → (x + 3/10)² → The point of contact is when x = -3/10 → y = 3× -3/10 + 1 = 9/10 + 1 = 1/10 → point of contact is (-3/10, 1/10) with k = 1/10
What is the value of k when the curve x squared plus y squared equals k touches the line y equals 3x plus 1 at just one point?
If: x^2 +y^2 = k then y^2 = k-x^2 If: y = 3x +1 then y^2 = (3x +1)^2 => y^2 = 9x^2 +6x +1 So: 9x^2 +6x +1 = k -x^2 Transposing terms: 10x^2 +6x +(1 -k) = 0 Using the discriminant b^2 -4ab = 0: 36 -4*10*(1 -k)= 0 => -k = -1/10 Therefore: k = 1/10
What is the value of k when the line y equals 3x plus 1 is a tangent to the curve of y2 plus x2 equals k?
If: y = 3x +1 then y^2 = 9x^2 +6x +1 If: y^2 +x^2 = k then y^2 = k -x^2 So: 9x^2 +6x +1 = k -x^2 Transposing terms: 10x^2 +6x +(1 -k) = 0 Using the discriminant: 6^2 -4*10*(1 -k) = 0 Solving the discriminant: k = 1/10
What is the greatest digit number that is divisible by 4?
There is no limit to the number of digits.If, for example, a X is a k-digit number which is divisible by 4 then 10*X is divisible by 4 and 10*X will be a (k+1)-digit number.
What value of k makes the line x equals 7 the perpendicular bisector of the segment with endpoints A 10 2 and B k 2?
As there is no change in y, the perpendicular bisector is given by x = (10 + k)/2 This is given as x = 7; thus: → (10 + k)/2 = 7 → 10 + k = 14 → k = 4
In an equilibruim with a Keq of 1 X 10 8 the?
products are favored
What are the values of x y and k when the line y equals 3x plus 1 is a tangent to the circle x squared plus y squared equals k?
If y = 3x + 1 is a tangent to x² + y² = k (k > 0 since it is a square), then where they meet has a repeated root; they meet at: x² + (3x + 1)² = k → x² + 9x² + 6x + 1 - k = 0 → 10x² + 6x + (1 - k) = 0 This is the point of contact when it has a repeated root which is when the discriminant is zero, ie when: 6² + 4 × 10 × (1 - k) = 0 → 36 + 40 - 40k = 0 → 40k = 4 → k = 1/10 I guess for x & y you mean the point where y = 3x + 1 is a tangent to x² + y² = k, ie the point of contact. The value of k can now be substituted into the equation of the point of contact: 10x² + 6x + (1 - k) = 0 → 10x² + 6x + (1 - 1/10) = 0 → 10x² + 6x + 9/10 = 0 → x² + 6x/10 + 9/100 = 0 → (x + 3/10)² → The point of contact is when x = -3/10 → y = 3× -3/10 + 1 = 9/10 + 1 = 1/10 → point of contact is (-3/10, 1/10) with k = 1/10
What is the hydronium ion concentration of a solution at 298 K whose hydroxide ion concentration is 1 x 10-8 A 1 x 10-6 B 1 x 10-7 C 1 x 10-8 x D 1 x 10-14?
The answer is A 1 x 10^(-6)
What is the value of k when the curve x squared plus y squared equals k touches the line y equals 3x plus 1 at just one point?
If: x^2 +y^2 = k then y^2 = k-x^2 If: y = 3x +1 then y^2 = (3x +1)^2 => y^2 = 9x^2 +6x +1 So: 9x^2 +6x +1 = k -x^2 Transposing terms: 10x^2 +6x +(1 -k) = 0 Using the discriminant b^2 -4ab = 0: 36 -4*10*(1 -k)= 0 => -k = -1/10 Therefore: k = 1/10
What is the numerical value of Kw at 298 k?
The value of Kw (ion product of water) at 298 K is approximately 1.00 x 10^-14.
What are the values of the variables when the line y equals 3x plus 1 is a tangent to the curve x2 plus y2 equals k?
Equations: y = 3x +1 and x^2 +y^2 = k If: y = 3x +1 then y^2 = 9x^2 +6x +1 If: x^2 +y^2 = k then y^2 = k -x^2 Transposing terms: 10x^2 +6x +(1 -k) = 0 Using the discriminant formula: k = 1/10 Using the quadratic equation formula: x = -3/10 By substitution: y = 1/10
What is the value of k when the line y equals 3x plus 1 is a tangent to the curve of y2 plus x2 equals k?
If: y = 3x +1 then y^2 = 9x^2 +6x +1 If: y^2 +x^2 = k then y^2 = k -x^2 So: 9x^2 +6x +1 = k -x^2 Transposing terms: 10x^2 +6x +(1 -k) = 0 Using the discriminant: 6^2 -4*10*(1 -k) = 0 Solving the discriminant: k = 1/10
How many atoms are in 0.0671 mol K?
There are 4.05 x 10^22 atoms in 0.0671 mol of potassium (K). This is calculated by multiplying the Avogadro's number (6.022 x 10^23) by the number of moles.
What is the greatest digit number that is divisible by 4?
There is no limit to the number of digits.If, for example, a X is a k-digit number which is divisible by 4 then 10*X is divisible by 4 and 10*X will be a (k+1)-digit number.
What is the value of k when the line of y equals 3x plus 1 is a tangent to x2 plus y2 equals k?
If: y = 3x +1 then y^2 = 9x^ +6x +1 If: x^2 +y^2 = k then 10^x^2 +6x +(1-k) = 0 Using the discriminant: -4 +40k = 0 Add 4 to both sides: 40k = 4 Divide both sides by 40: k = 1/10 Therefore the value of k is 1/10
What k -k equals 2?
k and -k right? -k x -1 =k k+k= 2 k= 1 unless you mean multiply then that would be -k x-1 =k k x k= 2 1.4142 rounded to the nearest ten thousandth
What is the integral of 10x?
∫ 10x dx Factor out the constant: 10 ∫ x dx Therefore, by the power rule, we obtain: 10x(1 + 1)/(1 + 1) + k = 10x²/2 + k = 5x² + k
