Se desea cortar una tela en pedazos rectangulares cuya área sea igual a 72 cm2 a. Elaborar la tabla que muestra los posibles val
ores para el largo y el ancho de los rectángulos. b. Determinar la relación entre el largo, l, y el ancho, a, de los rectángulos. c. Determinar la expresión matemática que relaciona el largo y el ancho. d. Realizar la gráfica que representa los valores del largo y el ancho
me ayudan por favor!!
me ayudan por favor!!
1 answer:
Answer:
the mathematical expression that relates the length and width:
y = 72/x
See explanation and attachments below for other answers to the question.
Question:
You want to cut a fabric into rectangular pieces whose area is equal to 72 cm2
a. Prepare the table that shows the possible values for the length and width of the rectangles.
b. Determine the relationship between the length, l, and the width, a, of the rectangles.
c. Determine the mathematical expression that relates the length and width.
d. Make the graph that represents the values of the length and width.
Explanation:
a) Area of the rectangle = 72cm²
Area of a rectangle = length × breadth = l×b
Let's find the factors of 72:
1,2,3,4,6,8,9,12,18,24,36,72
Since length is longer than width, the length would have the longest side in each possible dimension.
Possible dimensions of the rectangles (width ×length):
1×72; 2×36; 3×24; 4×18; 6×12; 8×9
See the attachment for the table that shows the possible values for the length and width of the rectangle.
Let y = length and x= width
b) The relationship between the length, l, and the width, w, of the rectangles:
Area = l × w
72 = lw
l = 72/w
The relationship between the length, l, and the width, w, of the rectangles: l = 72/w
c) Area = x × y
Since y = length and x= width
72 = xy
y = 72/x
the mathematical expression that relates the length and width:
y = 72/x
d) see attachment for the graph
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Answer:
Explanation:
In order to solve this problem, we can do an analysis of the energies involved in the system. Basically the addition of the initial potential energy of the spring and the kinetic energy of the mass should be the same as the addition of the final potential energy of the spring and the kinetic energy of the block. So we get the following equation:
In this case, since the block is moving from rest, the initial kinetic energy is zero. When the block loses contact with the spring, the final potential energy of the spring will be zero, so the equation simplifies to:
The initial potential energy of the spring is given by the equation:
the Kinetic energy of the block is then given by the equation:
so we can now set them both equal to each other, so we get:
This new equation can be simplified if we multiplied both sides of the equation by a 2, so we get:
so now we can solve this for the final velocity, so we get:
