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(5k3 - 3k + 7) - (-2k3 + k2 - 9) = 7k3 - k2 - 3k + 16
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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.
Where was K2 located?
K2 is located on the China-Pakistan border in the Karakoram Range of the Himalayas. It is the second-highest mountain in the world after Mount Everest.
What is in k2?
K2 is located on the Asian continent.
