APLICACIONES DE ECUACIONES DIFERENCIALES en el extremo de un resorte espiral sujeto al techo, se coloca un peso que pesa 10 kg. El cuerpo queda en reposo en su posicion de equilibrio, en la que el resorte se ha alargado 5cm. A continuacion el peso se desplaza 3 cm por debajo de la posicion de equilibrio y se abandona en t=0 con una velocidad inicial de 1m/seg dirigida hacia arriba. Hallar el desplazamiento del cuerpo en funcion del tiempo con los siguientes casos:

A) despreciando la resistencia del medio y suponiendo que no existen fuerzas exteriores.
B)No existen fuerzas, exteriores, pero el coeficiente de amortiguamiento es a=80 Nt/m/seg.
C)No existen fuerzas, exteriores, pero el coeficiente de amortiguamiento es a=280 Nt/m/seg.
D)No existen fuerzas, exteriores, pero el coeficiente de amortiguamiento es a=350 Nt/m/seg.
E) el coeficiente de amortiguamiento es a=80 Nt/m/seg y existe una fuerza de excitacion exterior dada por F(t)=50cos(25t)Nt
F) el coeficiente de amortiguamiento es a=80 Nt/m/seg y al cabo de 3seg. se une una fuerza de excitacion exterior dada por F(t)=50cos(25t)Nt.

Jonathan pays $1.90 per pound for potatoes. he buys 8.3 pounds of potatoes. he determines that he will pay $15.77, before tax, for the potatoes. which best describes the reasonableness of jonathan’s solution? jonathan’s answer is reasonable because there are two decimal places in the factors and two in the product. jonathan’s answer is unreasonable because there are three decimal places in the factors and two in the product. jonathan’s answer is reasonable because is 16, and 16 is close to 15.77. jonathan’s answer is unreasonable because is 8, and 8 is not very close to 15.77.

You and three friends will be going out to eat at your favorite restaurant! each of you will order three items of your choice. you will also need to leave a tip. if you split the bill evenly among all four of you, how much will each person need to contribute? locate a menu for your favorite restaurant and pick three items for yourself and each friend. list the restaurant name, items, and prices in a table like the one below. in the column labeled subtotal, determine the cost of each person’s order. the customary tip is 20% of the total bill. in the column labeled tip, calculate the amount of tip each person should leave. in the column labeled total bill, determine the total of each person’s order, including the tip. restaurant name: names item 1 price item 2 price item 3 price subtotal tip total bill your name friend #1 friend #2 friend #3 part 2: questions answer the following questions, showing all work: what is the total cost of the entire bill (all four meals), including tip? write an expression using fractions to show how to determine the amount that each person will pay. then calculate each person's contributions showing all steps in long division. if each person paid an equal amount, who would save the most money? explain your reasoning using at least two complete sentences.

What dimensions can créate more than one triangle ?