Show that if R is a ring with identity element and x is an element in R, then

Rx = {rx: r in R} is the principal left ideal generated by x. Similarly,

xR = {xr: r in R} is the principal right ideal generated by x.

Determine how much heat is evolved : LiI has a lattice E of -7.3x10^2 kJ/mol and a heat of hydration of -793kJ/mol. Heat of solution is -60kJ/mol. Determine how much heat is evolved |

Result of receiving the group-term life benefit : Assuming that Gray is 52 years old, determine the monthly premium that Gray must include in income as a result of receiving the group-term life benefit? |

What should be the amount of rent expense incurred : Maris Co. purchased a machine on January 1, 2013, for $1,200,000 for the express purpose of leasing it. The machine is expected to have a five-year life, no salvage value, and be depreciated on a straight-line monthly basis. |

Multiplicative inverses and identities : If a ring R has a multiplicative identity, then the multiplicative identity is unique. |

Left and right ideals : Show that if R is a ring with identity element and x is an element in R, then Rx = {rx: r in R} is the principal left ideal generated by x. Similarly, |

What is the direct labor cost : In August direct labor was 60% of conversion cost. If the manufacturing overhead for the month was $54,000 and the direct materials cost was $34,000, the direct labor cost was: |

Draw a project diagram network for project : the finished subassembly 2 must be inspected. A list of activities, their predecessors, and their durations. Draw a project diagram (network) for this project? What is the total project time? |

Information about rings-ideals : Let S be a subset of a set X. Let R be the ring of real-valued functions on X, and let I be the set of real-valued functions on X whose restriction to S is zero. |

Explain for the board member why the district audit report : A new board member for the Fire Protection District (a special purpose government) was reviewing the audit report for the district and noted that, although the district received an unqualified opinion, the audit report was longer the one received .. |

## Determining cylindrical coordinatesWhat are the cylindrical coordinates of the point whose rectangular coordinates are x = - 4 , y= 2, and z = 4? |

## The graph of cosecant functionSketching the graph of Cosecant function and identifying its asymptotes |

## Real-life application of rational functionsDescribe the cost C(x), in millions of dollars to inoculate x % of the Canadian population against a particularly virulent strain of flu |

## Compute lu decomposition and gaussian eliminationUse Gaussian elimination with partial pivoting to find matrices L and U such that U is upper triangular, L is lower triangular with | l_ij| = j and LU = A', where A' can be obtained from A by interchanging rows. |

## Condition of system of equationsWhich of the following can be solved by using a system of equations? Laura and Mark went to the movies and spent $29 on movie tickets and snacks. Mark paid $10 more than Laura. How much did each spend? |

## Linear function of a springThe distance d between a fixed spring and the floor is a linear function of the weight w attached to the bottom of the spring. The bottom of the spring is 18 inches from the floor when the weight is 3 pounds and 10 inches from the floor when the w.. |

## Graphs for three equations and find common pointUsing first two equations determine 3 possible points that the 2 conic sections that you get from equations meet. Add a third equation figure to out the one point that all three conic sections meet. |

## Evaluate the height of the cliff from the word problemSketch the graph of the given function and evaluate the height of the cliff from the word problem. |

## Arrival and service rates for check out lanesIn planning for a major redesign, Beth collected data at her store on several consecutive Saturday mornings. She noticed that customers arrived at the checkout at a rate of approximately 100 per hour. Fully 20 percent of the customers had 10 items.. |

## A fast food outlet has an average of carsA fast food outlet has an average of 8 cars at the drivethrough during "lunch rush" 11am-1pm. On average, 2 cars per min. arrive at the resaurant parking lot, and consider the drivethrough |

## Solve heat equation problemHeat Equation Problem, Find the solution u(x,t) of the heat equation: with initial data u(x,0) = x |

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