5 K 2 K
Author: m | 2025-04-24
The expanded form of the polynomial − 5 k 2 (k 2 − 4 k) in standard form is 20 k 3 − 5 k 4. To expand the expression − 5 k 2 (k 2 − 4 k), we'll use the distributive property (also known as the FOIL method for binomials) to multiply each term inside the parentheses by − 5 k 2: − 5 k 2 (k 2 − 4 k) = − 5 k 2 ∗ k 2 (− 5 2 r 1. k 3 r 1. k 4 r 2. k 5 r 2. k 6 r 3. k 7 r 3. k 8 r 4. k 9 r 5. k 10 r 5. k 11 r
Solve for k 5 k-2 11
. . , K [ 31 ] (reduced result).1: A ← ( K [ 31 ] & 0 b 1 ) ≪ 6 2: B ← ( K [ 31 ] & 0 b 10 ) ≪ 5 3: C ← ( K [ 31 ] & 0 b 1111111 ) 4: K [ 16 ] ← K [ 16 ] ⨁ ( ( A ⨁ B ⨁ C ) ≪ 1 ) 5: K [ 8 ] ← K [ 8 ] ⨁ K [ 24 ] ⨁ ( ( K [ 23 ] ≪ 7 ) ∣ ( K [ 24 ] ≫ 1 ) ) ⨁ ( ( K [ 23 ] ≪ 6 ) ∣ ( ( K [ 24 ] ≫ 2 ) ) ⨁ ( ( K [ 23 ] ≪ 1 ) ∣ ( K [ 24 ] ≫ 7 ) ) 6: K [ 0 ] ← K [ 0 ] ⨁ K [ 16 ] ⨁ ( K [ 16 ] ≫ 2 ) ⨁ ( K [ 16 ] ≫ 7 ) 7:forl = 1 to 7 do8: K [ i + 8 ] ← K [ i + 8 ] ⨁ K [ i + 24 ] ⨁ ( ( K [ i + 23 ] ≪ 7 ) ∣ ( K [ i + 24 ] ≫ 1 ) ) ⨁ ( ( K [ i + 23 ] ≪ 6 ) ∣ ( K [ i + 24 ] ≫ 2 ) ) ⨁ ( ( K [ i + 23 ] ≪ 1 ) ∣ ( K [ i + 24 ] ≫ 7 ) ) 9: K [ i ] ← K [ i ] ⨁ K [ i + 16 ] ⨁ ( ( K [ i + 15 ] ≪ 7 ) ∣ ( K [ i + 16 ] ≫ 1 ) ) ⨁ ( ( K [ i + 15 ] ≪ 6 ) ∣ ( K [ i + 16 ] ≫ 2 ) ) ⨁ ( ( K [
Simplify (k^2-5k2)(k-5) - Mathway
Open.Elliptic Paraboloid & Hyperbolic ParaboloidHyperbolic And Elliptic Paraboloid 3D GraphAnd here’s the cool part! We can even combine our quadric surfaces to yield such surfaces as elliptic paraboloids or hyperbolic paraboloids.Traces Of Quadric SurfacesSo, how do we determine the resulting surface?We look for traces.ExampleFor instance, let’s name the shapes by identifying the traces:\begin{equation}x-5 y^{2}+2 z^{2}=0\end{equation}First, we notice that one of the variables is not squared. This instantly tells us that we are dealing with a paraboloid. Now, all we have to do is determine what kind of paraboloid (i.e., elliptic, or hyperbolic)How?Finding traces means we let each variable become a constant (number), and identify it’s resulting curve.If \(x=k\) where \(k\) is any constant, then \(k-5 y^{2}+2 z^{2}=0\) which is a hyperbola.If \(y=k\) where \(k\) is any constant, then \(x-5 k^{2}+2 z^{2}=0\) which is a parabola.If \(z=k\) where \(k\) is any constant, then \(x-5 y^{2}+2 k^{2}=0\) which is a parabola.This means that \(x-5 y^{2}+2 z^{2}=0\) in the Cartesian coordinate system is a hyperbolic paraboloid that will open along the x-axis because it is the non-squared term.ExampleLet’s tackle this problem.Name the shapes by identifying the traces\begin{equation}x^{2}-5 y^{2}+2 z^{2}=8\end{equation}First, we notice that all of the variables are squared, but one of the variables is negative. This instantly tells us that we are dealing with a hyperboloid of one-sheet. Let’s confirm our suspicions by finding the traces.If \(x=k\) where \(k\) is any constant, then \(k^{2}-5 y^{2}+2 z^{2}=8\) which is a hyperbola.If \(y=k\) where \(k\) is any constant, then \(x^{2}-5 k^{2}+2 z^{2}=8\) which is aSolve for k (5k)/ (k2)2/k=5
The winner. For example, tens full of 3s (10-10-10-3-3) beats fours full of Aces (4-4-4-A-A). Someone will always have the better Full House hand and kickers are not used.FlushIf two players have flushes, the highest card determines which is the winning poker hand. If the highest cards are equal then the second highest card is used to determine the winner, and so one. In other words, use the kickers to determine the winner. For example: 2-4-5-8-9 all in spades beats 2-3-5-6-7 all in clubs because you compare the highest card (9 vs 7). All suits are equal.Best Flush Example:10-3-8-K-A (suited) beats 9-4-J-Q-K (suited) – Highest card is A vs K.Q-10-9-5-2 (suited) beats Q-10-3-6-5 (suited) – since the two top cards are the same in both hands, the third card determiens the winner. In this example, 9 beats 6.StraightWhen comparing two straights, the one with the highest ranking top card is better. An Ace can ONLY count high or low in a straight. For example, A-2-3-4-5 does not beat 10-J-Q-K-A. Also, Q-K-A-2-3 does not count as a straight because the ace doesn’t count as either the low card or the high card. A tie can occur when two players make the exact same straight based on the card ranks, and card suit is irrelevent. Unless of course it results in a straight flush explained earlier.Best Straight Example2-3-4-5-6 beats A-2-3-4-510-J-Q-K-A beats 9-10-J-Q-K4-5-6-7-8 ties 4-5-6-7-8Three of a kindThe highest three of a kind when comparing two hands is ranked better. For example the hand 8-8-8-3-2 beats 5-5-5-A-Q. Unless wild cards are used, a tie cannot occur. Someone will always have the better Three of a Kind hand.Two pairIf both players have two pairs, the hand with the highest pair has the winning poker hand and the smaller pair is irrelevant. For example, Q-Q-5-5-3 beats 10-10-7-7-A because the queens beat the tens. If the higher pairs are the same then the smaller pair is used to determine the higher ranking hand. Q-Q-10-10-4 would beat Q-Q-9-9-K. If both pairs are the same then kicker cards are compared.Best Two Pair ExampleA-A-3-3-5 beats K-K-J-J-9K-K-3-3-5 beats K-K-2-2-AK-K-3-3-5 beats K-K-3-3-2PairThe higher pair determines the best hand. If two players have the same pair then the highest card is used. If this card is the same, then the second highest card is compared and finally the third if it comes down to it.Best Pair Hand8-8-3-2-5 wins over 5-5-A-K-J10-10-A-2-5 wins over. The expanded form of the polynomial − 5 k 2 (k 2 − 4 k) in standard form is 20 k 3 − 5 k 4. To expand the expression − 5 k 2 (k 2 − 4 k), we'll use the distributive property (also known as the FOIL method for binomials) to multiply each term inside the parentheses by − 5 k 2: − 5 k 2 (k 2 − 4 k) = − 5 k 2 ∗ k 2 (− 5Factor k^2-k-2
K − 1 ) + a 2 · φ CO ( k − 1 ) + a 3 · φ CO 2 ( k − 1 ) + a 4 · φ CH 4 ( k − 1 ) + a 5 · T max ( k − 1 ) , (8) u 2 ≡ V O 2 ( k ) = a 0 + a 1 · V air ( k − 1 ) V O 2 ( k − 1 ) + a 2 · φ CO ( k − 1 ) + a 3 · φ CO 2 ( k − 1 ) + a 4 · φ CH 4 ( k − 1 ) + a 5 · T max ( k − 1 ) . (9) The third model type aims to achieve the necessary temperature for syngas production. The models regarding the ratio of gasification agents and the maximum temperature T m a x in the channel are in the linear and quadratic form. The structure of the model is as the following [25]: u 1 ≡ V air ( k ) = a 0 + a 1 · V air ( k − 1 ) V O 2 ( k − 1 ) + a 2 · T max ( k − 1 ) + a 3 T max 2 ( k − 1 ) , (10) u 2 ≡ V O 2 ( k ) = a 0 + a 1 ·Solve for k k^ k^2=0
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Nothing 0 1 1 1 Return 0.959471 0.960118 0.960810 Double Double Bonus Poker Return TablesDouble Double Bonus 9/6 Hand Pays Multiplier 3-Play Multiplier 5-Play Multiplier 10-Play Royal flush 800 2 2 4 Straight flush 50 2 2 4 Four aces + 2-4 400 2 2 4 Four 2-4 + A-4 160 2 2 4 Four aces + 5-K 160 2 2 4 Four 2-4 + 5-K 80 2 2 4 Four 5-K 50 2 3 3 Full house 9 12 12 12 Flush 6 10 10 10 Straight 4 8 8 8 Three of a kind 3 4 4 4 Two pair 1 3 3 3 Jacks 1 2 2 2 Nothing 0 1 1 1 Return 0.997261 0.997928 0.998663 Double Double Bonus 9/5 Hand Pays Multiplier 3-Play Multiplier 5-Play Multiplier 10-Play Royal flush 800 2 2 4 Straight flush 50 2 2 4 Four aces + 2-4 400 2 2 4 Four 2-4 + A-4 160 2 2 4 Four aces + 5-K 160 2 2 4 Four 2-4 + 5-K 80 2 2 4 Four 5-K 50 2 3 3 Full house 9 12 12 12 Flush 5 10 10 10 Straight 4 8 8 8 Three of a kind 3 4 4 4 Two pair 1 3 3 3 Jacks 1 2 2 2 Nothing 0 1 1 1 Return 0.983633 0.984253 0.984940 Double Double Bonus 8/5 Hand Pays Multiplier 3-Play Multiplier 5-Play Multiplier 10-Play Royal flush 800 2 2 4 Straight flush 50 2 2 4 Four aces + 2-4 400 2 2 4 Four 2-4 + A-4 160 2 2 4 Four aces + 5-K 160 2 2 4 Four 2-4 + 5-K 80 2 2 4 Four 5-K 50 2 3 3 Full house 8 12 12 12 Flush 5 10 10 10 Straight 4 8 8 8 Three of a kind 3 4 4 4 Two pair 1 3 3 3 Jacks 1 2 2 2 Nothing 0 1 1 1 Return 0.972266 0.972859 0.973521 Double Double Bonus 7/5 Hand Pays Multiplier 3-Play Multiplier 5-Play Multiplier 10-Play Royal flush 800 2 2 4. The expanded form of the polynomial − 5 k 2 (k 2 − 4 k) in standard form is 20 k 3 − 5 k 4. To expand the expression − 5 k 2 (k 2 − 4 k), we'll use the distributive property (also known as the FOIL method for binomials) to multiply each term inside the parentheses by − 5 k 2: − 5 k 2 (k 2 − 4 k) = − 5 k 2 ∗ k 2 (− 5Comments
. . , K [ 31 ] (reduced result).1: A ← ( K [ 31 ] & 0 b 1 ) ≪ 6 2: B ← ( K [ 31 ] & 0 b 10 ) ≪ 5 3: C ← ( K [ 31 ] & 0 b 1111111 ) 4: K [ 16 ] ← K [ 16 ] ⨁ ( ( A ⨁ B ⨁ C ) ≪ 1 ) 5: K [ 8 ] ← K [ 8 ] ⨁ K [ 24 ] ⨁ ( ( K [ 23 ] ≪ 7 ) ∣ ( K [ 24 ] ≫ 1 ) ) ⨁ ( ( K [ 23 ] ≪ 6 ) ∣ ( ( K [ 24 ] ≫ 2 ) ) ⨁ ( ( K [ 23 ] ≪ 1 ) ∣ ( K [ 24 ] ≫ 7 ) ) 6: K [ 0 ] ← K [ 0 ] ⨁ K [ 16 ] ⨁ ( K [ 16 ] ≫ 2 ) ⨁ ( K [ 16 ] ≫ 7 ) 7:forl = 1 to 7 do8: K [ i + 8 ] ← K [ i + 8 ] ⨁ K [ i + 24 ] ⨁ ( ( K [ i + 23 ] ≪ 7 ) ∣ ( K [ i + 24 ] ≫ 1 ) ) ⨁ ( ( K [ i + 23 ] ≪ 6 ) ∣ ( K [ i + 24 ] ≫ 2 ) ) ⨁ ( ( K [ i + 23 ] ≪ 1 ) ∣ ( K [ i + 24 ] ≫ 7 ) ) 9: K [ i ] ← K [ i ] ⨁ K [ i + 16 ] ⨁ ( ( K [ i + 15 ] ≪ 7 ) ∣ ( K [ i + 16 ] ≫ 1 ) ) ⨁ ( ( K [ i + 15 ] ≪ 6 ) ∣ ( K [ i + 16 ] ≫ 2 ) ) ⨁ ( ( K [
2025-03-25Open.Elliptic Paraboloid & Hyperbolic ParaboloidHyperbolic And Elliptic Paraboloid 3D GraphAnd here’s the cool part! We can even combine our quadric surfaces to yield such surfaces as elliptic paraboloids or hyperbolic paraboloids.Traces Of Quadric SurfacesSo, how do we determine the resulting surface?We look for traces.ExampleFor instance, let’s name the shapes by identifying the traces:\begin{equation}x-5 y^{2}+2 z^{2}=0\end{equation}First, we notice that one of the variables is not squared. This instantly tells us that we are dealing with a paraboloid. Now, all we have to do is determine what kind of paraboloid (i.e., elliptic, or hyperbolic)How?Finding traces means we let each variable become a constant (number), and identify it’s resulting curve.If \(x=k\) where \(k\) is any constant, then \(k-5 y^{2}+2 z^{2}=0\) which is a hyperbola.If \(y=k\) where \(k\) is any constant, then \(x-5 k^{2}+2 z^{2}=0\) which is a parabola.If \(z=k\) where \(k\) is any constant, then \(x-5 y^{2}+2 k^{2}=0\) which is a parabola.This means that \(x-5 y^{2}+2 z^{2}=0\) in the Cartesian coordinate system is a hyperbolic paraboloid that will open along the x-axis because it is the non-squared term.ExampleLet’s tackle this problem.Name the shapes by identifying the traces\begin{equation}x^{2}-5 y^{2}+2 z^{2}=8\end{equation}First, we notice that all of the variables are squared, but one of the variables is negative. This instantly tells us that we are dealing with a hyperboloid of one-sheet. Let’s confirm our suspicions by finding the traces.If \(x=k\) where \(k\) is any constant, then \(k^{2}-5 y^{2}+2 z^{2}=8\) which is a hyperbola.If \(y=k\) where \(k\) is any constant, then \(x^{2}-5 k^{2}+2 z^{2}=8\) which is a
2025-04-20K − 1 ) + a 2 · φ CO ( k − 1 ) + a 3 · φ CO 2 ( k − 1 ) + a 4 · φ CH 4 ( k − 1 ) + a 5 · T max ( k − 1 ) , (8) u 2 ≡ V O 2 ( k ) = a 0 + a 1 · V air ( k − 1 ) V O 2 ( k − 1 ) + a 2 · φ CO ( k − 1 ) + a 3 · φ CO 2 ( k − 1 ) + a 4 · φ CH 4 ( k − 1 ) + a 5 · T max ( k − 1 ) . (9) The third model type aims to achieve the necessary temperature for syngas production. The models regarding the ratio of gasification agents and the maximum temperature T m a x in the channel are in the linear and quadratic form. The structure of the model is as the following [25]: u 1 ≡ V air ( k ) = a 0 + a 1 · V air ( k − 1 ) V O 2 ( k − 1 ) + a 2 · T max ( k − 1 ) + a 3 T max 2 ( k − 1 ) , (10) u 2 ≡ V O 2 ( k ) = a 0 + a 1 ·
2025-03-30