For example, lines are represented as the intersection of two planes, circles as the intersection of a sphere and a plane (or of two spheres). Of course, a given curve can be realized by intersection in infinit
A system of equations is said to be inconsistent if the two equations do not agree, meaning that there is no set of values that can simultaneously satisfy each equation. For example, the most basic inconsistent system of equations could be: x=4 & x=5, which can never both be true at ...
two unknowns to vary. Imagine you have three circles. You are expecting them all to intersect at a common point. That would only happen for special radii and centers. Two circles can intersect at two common points but how likely is it that a third circle would pass through either of ...
Step by step video, text & image solution for Obtain the equation of the circle orthogonal to both the circles x^2+y^2+3x-5y+6=0 and 4x^@+4y^2-28x+29=0 and whose centre lies on the line 3x+4y+1=0 by Maths experts to help you in doubts & scoring excellent marks in Class ...
The discrete Klein–Gordon equation on a two-dimensional square lattice satisfies an ℓ1↦ℓ∞ dispersive bound with polynomial decay rate |t|−3/4. We determine the shape of the light cone for any choice of the mass parameter and relative propagation speeds along the two coordinate axes...
Equations (8.7) and (8.8) are two forms of the Clausius–Clapeyron equation. Under the conditions for which these equations are valid, a graph of In p against 1/T should be a straight line with slope (−ΔvapHm)/R or (−ΔsubHm)/R. Figure 8.3 shows such graphs for CO2, using...
When I look back on all that I’ve managed to accomplish over the past 5 years, I always give thanks for Molly and The Joy Equation.Working through the course invigorated a piece of me that I had forgotten existed. It helped me rediscover my passion for writing, community, and creativity...
Examining enzyme kinetics is critical for understanding cellular systems and for using enzymes in industry. The Michaelis-Menten equation has been widely used for over a century to estimate the enzyme kinetic parameters from reaction progress curves of s
Equation of a circle An equation of a circle is an algebraic way to define all points that lie on the circumference of the circle. That is, if the point satisfies the equation of the circle, it lies on the circle's circumference. There are different forms of the equation of a circle:...
We begin by finding locally D-optimal designs for estimating the two parameters in the Arrhenius equation commonly used in chemical experiments [37]. This model describes the relationship between the mean temperature and reaction rate of a process. Its basic form is given by (10)Er=Aexp(−B...