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Find the range of values of k which the equation 3x2-3kx plus k2 is always positive?
3x2 - 3kx + k2 > 0, k = ? (a = 3, b = -3k, c = k2)The parabola opens upward (a > 0), so we have a minimum point at thevertex = (- b/2a, c - b2/4a) = (- -3k/6, k2 - (-3k)2/12) = (k/2, k2/4).Since the y-coordinate of the vertex is always a positive value, except when k = 0, then the x-coordinate could have a positive or negative value.So that, the parabola would lie above the x-axis for all values of k, except when k is zero.Thus, the equation 3x2 - 3kx + k2 > 0, for k ≠ 0.OrComplete the square:3x2 - 3kx + k2 (divide by 3 all the terms)= x2 - kx + k2/3= [x2 - kx + (k/2)2]+ k2/3 - (k/2)2= (x - k/2)2 + k2/3 - k2/4= (x - k/2)2 + k2/12So the equation (x - k/2)2 + k2/12 represents the translation of x2, k/2 units right when k > 0, or k/2 units left when k < 0, and k2/12 units up.Thus, for k ≠ 0 the given equation is always positive.
What is the perfect square of 16k plus 40k plus 25?
3,136 k2 + 2,800 k + 625
What are the factors for k plus 18k plus 81?
k + 18k + 81 = 19k + 81 which cannot be factorised. HOWEVER If the question was about k2 + 18k + 81, but was foiled by the inability of this browser, then the answer is k2 + 18k + 81 = (k + 9)2
Find the center and radius of the circle given by the equation x2 plus y2-10x plus 8y plus 5 equals 0?
The standard equation of a circle with center C(h,k) and radius r is as follows:(x - h)2 + (y - k)2 = r2(x2 -2hx +h2) + (y2 - 2ky + k2)We have...x2 + y2 - 10x + 8y + 5 =0x2 - 10x + y2 + 8y + 5 =0add h2 and k2 to both sides(x2 - 10x + h2) + (y2 + 8y + k2) = -5 + h2 + k2Using the above framework we can see that 10 = 2h, h = 5Using the above framework we can see that 8 = 2k, k = 4So the formula is(x2 - 10x + 25) + (y2 + 8y + 16) = -5 + 25 + 16(x - 5)2 + (y - 4)2 = 36the center of the circle is C(5,4) and radius 6
How does changing the dimensions of a figure affect perimeter area and volume?
When linear dimensions are multiplied by 'K', - perimeter is also multiplied by 'K' - area is multiplied by K2 - volume is multiplied by K3
What is the trinomial equation of k2 plus 3k equals 108?
k2 + 3k =108k2 + 3k - 108 = 0(k - 9) (k + 12)k = -9 , k = 12ANSWER:k = -9 , k = 12I hope this helps!
How do you factor -2bk2 plus 6bk - 2b?
-2bk2 + 6bk - 2b = -2b(k2 - 3k + 1)
Find the range of values of k which the equation 3x2-3kx plus k2 is always positive?
3x2 - 3kx + k2 > 0, k = ? (a = 3, b = -3k, c = k2)The parabola opens upward (a > 0), so we have a minimum point at thevertex = (- b/2a, c - b2/4a) = (- -3k/6, k2 - (-3k)2/12) = (k/2, k2/4).Since the y-coordinate of the vertex is always a positive value, except when k = 0, then the x-coordinate could have a positive or negative value.So that, the parabola would lie above the x-axis for all values of k, except when k is zero.Thus, the equation 3x2 - 3kx + k2 > 0, for k ≠ 0.OrComplete the square:3x2 - 3kx + k2 (divide by 3 all the terms)= x2 - kx + k2/3= [x2 - kx + (k/2)2]+ k2/3 - (k/2)2= (x - k/2)2 + k2/3 - k2/4= (x - k/2)2 + k2/12So the equation (x - k/2)2 + k2/12 represents the translation of x2, k/2 units right when k > 0, or k/2 units left when k < 0, and k2/12 units up.Thus, for k ≠ 0 the given equation is always positive.
What is k squared plus k squared?
k2 + k2 = 2k2
What is K2 plus 2K plus 4K?
If by K2 you are not referring to the mountain, the distributive property of multiplication tells us K * 2 = 2 * K.Therefore: K2 + 2K + 4K = 2K + 2K + 4K = 8K
What is the perfect square of 16k plus 40k plus 25?
3,136 k2 + 2,800 k + 625
What are the range of values of k when y equals 2x plus k and x squared plus y squared equals 4 but do not intersect?
Equation 1: y = 2x+k => y2 = 4x2+4kx+k2 when both sides are squared Equation 2: x2+y2 = 4 => y2 = 4-x2 when rearranged So by definition: 4x2+4kx+k2 = 4-x2 => 5x2+4kx+k2-4 = 0 If the values are tangent to the curve then the discriminant b2-4ac = 0 b2-4ac = 0 => 16k2-4*5*(k2-4) = 0 16k2-20k2+80 = 0 => 4k2-5k2+20 = 0 -k2+20 = 0 => -k2 = -20 Therefore the values of k are: plus or minus the square root of 20 Check: (4*k2)-(5*k2)+20 = 0
What are the factors for k plus 18k plus 81?
k + 18k + 81 = 19k + 81 which cannot be factorised. HOWEVER If the question was about k2 + 18k + 81, but was foiled by the inability of this browser, then the answer is k2 + 18k + 81 = (k + 9)2
How do you find the LCM of k to the 2nd power k to the 2nd power-1 and k to the 2nd power minus 2k plus 1?
Factor them. k2 = k x k k2 - 1 = (k - 1)(k + 1) k2 - 2k + 1 = (k - 1)(k - 1) Combine the factors, eliminating duplicates. k2(k + 1)(k - 1)(k - 1) = k5 - k4 - k3 + k2, the LCM
What country is mt K2 in?
K2 is in Pakistan.
What is in k2?
K2 is located on the Asian continent.
Do K2 Extreme sell their products online?
K2skis sell K2 Extreme products plus ski and Evo. Evo has a four star rating and looks the most trusted out of them. Also have a look at epic ski for more information.
