A sphere is defined as the set of points that is at an equal distance (its radius, {eq}r {/eq}) from a fixed point (its center, {eq}(a,b,c) {/eq}). The general equation of a sphere can be written as: {eq}{\left( {x - a} \right)^2} + {\left( {y - b} \right...
A sphere is expanding at the rate of {eq}8 \; \mathrm{cm^3/sec} {/eq}, the formula for volume of a sphere is {eq}v = \frac{4}{3} \pi r^3 {/eq}, what is {eq}\frac{\mathrm{d}r}{\mathrm{d}t} {/eq} when {...
A sphere is a three-dimensional, round object, such as a marble or soccer ball. The volume represents the space enclosed by the object. The formula for the volume of a sphere is 4/3 times pi times the radius cubed. Cubing a number means multiplying it by itself three times, in this ...
equation of statehard spherevolume dependenceMost equations of state for hard spheres proposed in literature fail to satisfy the close-packed limit and predict a finite value for compressibility factor at the close-packing state. In this work we propose a new volume dependence for equations of ...
10 What is the maximum speed of the runner for 0 £m £ 3 ? (A) 6.5 (B) 6.6 (C) 7.0 (D) 7.5 dy 2 16. Which of the following could be a slope field for the differential equation x =+y ? dx (A) (B) (C) (D) ⌠ 8x − 10 17. ⎮ dx ⌡ (2x − 1)(x...
We have developed an analytic expression for the volume of intersection of any cylinder with any sphere in the usual three-dimensional space. To our knowledge, it is the first time that an exact expression, valid in all cases, is presented for this volume. Here we derive this expression, sh...
To do so, a generalization of the Carnahan–Starling method for obtaining the equation of state of the hard‐sphere fluid is used. The equation of state obtained in this way reproduces accurately the simulation data for both the stable and metastable fluid regions. Agreement remains good up to...
Sphere:The sphere is the three-dimensional object. The trace of the sphere in the two-dimension coordinate system is a circle. The volume of the sphere can be found using the triple integration. The standard equation of the sphere can be of the form (x−a)2+(y−b)2+(z...
Given data The equation for the solid that lies within the sphere is x2+y2+z2=4. The given equation for the solid below the...Become a member and unlock all Study Answers Start today. Try it now Create an account Ask ...
Does the point (0,1,0) lie on the sphere? Point on a Curve: Suppose the equation of a curve and a point not necessarily on the curve are given. To check whether the point lies on the curve, we may substitute the coordinates of ...