Let us suppose {eq}a_{1}x+b_{1}y+c = 0 {/eq} and {eq}a_{2}x+b_{2}y+d = 0 {/eq} are the two linear equations having infinite number of solutions then $$\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2...
Determine the values of h and k so that the system of equations below has an infinite number of solutions. x+2y-3z=5 2x+y-2z=2 x-y+hz=k Determine if the following system has no solution, an infinite number of solutions or a unique solution...
We construct examples of strictly convex functionsfon(−∞,∞)satisfyingf″(−∞) < n2< f′(∞)such that the Dirichlet problemu″ + f(u) = h(x)in [0,π],u(0) = u(π) = 0, has an infinite number of solutions, for any choice ofh(x). Examples with five solutions were ...
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The Structures of Ring and Field 1.2.2.2 Remark In the following, we will be mainly concerned with finite fields (i.e. fields with a finite number of elements). Therefore, most of the examples will be for finite fields. Nevertheless, we will also give some examples concerning infinite field...
and wave equations extended to generalized functions, a singular variable length pendulum wrapping on a parallelepiped, the oscillation of a pendulum damped by different media, a nonlinear stress–strain model of steel, singular Lagrangians as used in optics, and some examples from quantum mechanics...
Examples Example Question:Does the infinite geometric sequence 2, 4, 8,… have a sum? Solution: Step 1:Find “r”, the common ratio. Each number is multiplied by 2 in this sequence (8 / 4 = 2), so r = 2. There’s no need to go any further: 2 is not between -1 and 1, ...
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Luckily, for that situation, we can use the rep function, which takes two arguments: the first is an integer number of repetitions, and the second is the expression to repeat. We can refactor the above definition to this: word := rep[2, syllable] | rep[3, syllable] | rep[4, ...
Answer to: Find whether the equation has one solution, no solution, or an infinite number of solutions. 1/4(2x-1)=1/2x+3/8 By signing up, you'll...