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Find the curvature of the curve r(t).r(t) = (9 + ln(sec t))i + (9 + t)k, -π/2 < t < π/2

A retiring dentist entered into a written agreement with an agent whereby the agent would receive a commission of 10% of the sale price if he procured a “ready, willing, and able buyer” for the purchase of the dentist’s dental practice and if the sale of the practice actually occurred. The agent found a buyer who agreed in writing to buy the practice from the dentist for $500,000, the dentist’s asking price. The buyer put up $30,000 as a down payment. The agreement between the dentist and the buyer contained a liquidated damages clause providing that, if the buyer defaulted by failing to tender the balance due of $470,000 within 60 days, damages would be 10% of the purchase price. The dentist included that clause because she was counting on using the proceeds of the sale for another business venture that would likely net her at least $50,000. The buyer became seriously ill and defaulted. When he recovered, he demanded that the dentist return his $30,000, but the dentist refused. The agent also demanded the $30,000 from the dentist and was refused. The agent and the buyer filed separate suits against the dentist, with the buyer pleading impossibility of performance. The two cases are consolidated into a single case. How should the court rule as to the disposition of the $30,000?

A landowner inherited a parcel of land, free of encumbrances, and promptly recorded his deed. The landowner took out a $100,000 mortgage on the land with a bank to pay for improvements to the property. The instrument was properly recorded. The landowner regularly made the scheduled payments on the mortgage. Subsequently, the landowner decided to further improve the property and took out another mortgage with a financing company for $50,000. The instrument was properly recorded. The landowner then sold the land to a buyer subject to both mortgages. The buyer procured another loan of $100,000 secured by a mortgage on the land from a lender. The lender knew about the bank’s mortgage, but the buyer did not inform her of the financing company’s mortgage. The lender lent the money to the buyer on the understanding that the buyer would use the money to pay off the bank’s mortgage, placing the lender in first priority. The buyer promptly paid off the bank but made no further payments to the financing company. The financing company initiated steps to foreclose on the land. The lender brings an appropriate action seeking to have her rights declared superior to those of the financing company.  The state in which the land is located has the following statute: “Any conveyance of an estate in land, other than a lease for less than one year, shall not be valid against any subsequent purchaser whose conveyance is first recorded.” If the court rules in the lender’s favor, what is the likely reason?

Solve the problem.How much work does it take to slide a box 44 meters along the ground by pulling it with a 125 N force at an angle of 45° from the horizontal?

A boy was playing softball in a neighborhood park when a ball was hit over the fence and into a neighbor’s yard. The boy knocked on the neighbor’s door and obtained permission from her to retrieve the ball from her yard. As he bent to retrieve the ball in some bushes, the boy brushed against an exposed electric wire that was partially hidden by the bushes and received a severe electric shock and burns. The neighbor had failed to maintain the bushes, allowing them to become overgrown, and was not aware of the exposed wire. If the boy sues the neighbor in a jurisdiction that applies the traditional rules for landowners and possessors of land, what is the likely result?

On April 1, a landscaper read an ad in a trade magazine from a nursery offering a new variety of hydrangea bushes for $40 per bush. The landscaper immediately filled out the order form included in the ad ordering 10 bushes and deposited it, properly stamped and addressed, into the mail. On April 2, the landscaper received in the mail a letter from the same nursery, sent out as part of its advertising campaign, stating in relevant part that it will sell the landscaper 10 hydrangea bushes at $40 per bush. A day later, on April 3, the nursery received the landscaper’s order. On April 4, the bushes were shipped. On what day did an enforceable contract arise?

A worker who missed his ride home because he was working late walked across the street to a tavern to get a drink. He chatted with a patron of the tavern and discovered that he lived only a short distance from the patron. The patron offered to give the worker a ride home. Although he knew the patron was probably too drunk to drive, the worker reluctantly agreed. On the way home, the patron, driving in a dangerous manner, was involved in a collision with another car, whose driver was also driving negligently, and the worker was injured. If the worker sues the patron to recover for his injuries and the above facts are established at trial, will the worker’s recovery be reduced?

A farmer purchased several acres of land for grazing his sheep. Because of the terrain, the land was not useful for much else and was relatively inexpensive. Shortly thereafter, an adjacent neighbor accidentally discovered gold on the property and began seeking the necessary permits to begin mining. As soon as word got out, real estate values in the area soared. Rather than sell his land for a profit, the farmer decided to try to open a mine on his property. To finance the mining project, the farmer borrowed $100,000 from the bank secured by a mortgage on his land. The bank promptly recorded the mortgage. A week later, the farmer went to a friend asking her to invest in the mining project. The friend loaned the farmer an additional $50,000 in exchange for a mortgage on the property. The friend knew of the bank’s mortgage, and the friend promptly recorded her mortgage. A few weeks after that, the farmer went back to the bank and, after notifying them of the friend’s mortgage, obtained another advance of $25,000 from the bank, increasing the amount of the bank’s mortgage from $100,000 to $125,000. The bank promptly recorded the change. After spending most of the funds on engineers, surveys, and construction equipment, it was determined that the gold strike was limited to a very small portion of the neighbor’s land. No gold was found on the farmer’s land or any of the neighboring parcels. Land values plummeted. The farmer stopped making the mortgage payments to the friend but continued to make payments to the bank. The friend brought a foreclosure action against the farmer and included the bank as a party. The proceeds at the foreclosure sale were just $60,000 after attorneys’ fees and court costs. How should the proceeds be divided?

A man owned a 50-acre lot. He had purchased 40 of those acres from his uncle and had acquired title to an adjacent 10-acre strip from an absent neighbor by adverse possession. The man entered into a land sale contract to convey the 50 acres to a friend. The contract included all necessary details as to the property, the parties, and the transaction, but was silent as to the nature of title that the man would convey to the friend. At the time of closing, the friend paid the purchase price and accepted the deed conveyed by the man for the 50-acre lot. Three months later, the neighbor came back to the area and brought an action in ejectment against the friend for the ten acres. The friend now sues the man. Which of the following statements most accurately describes the friend’s rights?

A father conveyed his land to his son by warranty deed. The deed stated that the son paid $125,000 for the land but, in fact, the son had not. However, the son and the father agreed orally that the son would not record the deed until he paid the father the $125,000. The son neither paid the father nor recorded the deed for three years, at which time the property values in the area began to climb rapidly. Wishing to turn a fast profit, the son recorded the deed from the father and one week later conveyed the land to a buyer for $200,000. The buyer promptly recorded the deed. When the father discovered what had transpired, he filed a lawsuit, and the court determined that the son owed the father $125,000. Unfortunately, the son and his $200,000 from the buyer are nowhere to be found. The father asked the court to levy on the land, which the buyer opposed. The jurisdiction in which the land is located has the following statute: “No interest in land shall be good against a subsequent purchaser for value, without notice, unless the interest is recorded.” Which of the following is the buyer’s best defense against the levy?