MATH 8_Q1 WEEK 2

ELECTRONICS FACTORY

A factory produces two types of electronic components, A and B. The cost of producing x units of Component A is given by:

$$C_A(x)=(〖6x〗^2+9x)/3x$$ pesos.

The cost of producing x units of Component B is given by:
$$C_B(x)=(〖4x〗^2-2x)/2x$$ pesos.

What is the simplified form of the given rational algebraic expression in Component A?

ELECTRONICS FACTORY

A factory produces two types of electronic components, A and B. The cost of producing x units of Component A is given by:

$$C_A(x)=(〖6x〗^2+9x)/3x$$ pesos.

The cost of producing x units of Component B is given by:
$$C_B(x)=(〖4x〗^2-2x)/2x$$ pesos.

When x =10 is substituted into both simplified expressions, what is the calculated cost per unit for each component?

ELECTRONICS FACTORY

A factory produces two types of electronic components, A and B. The cost of producing x units of Component A is given by:

$$C_A(x)=(〖6x〗^2+9x)/3x$$ pesos.

The cost of producing x units of Component B is given by:
$$C_B(x)=(〖4x〗^2-2x)/2x$$ pesos.

What is the slope of both components?

ELECTRONICS FACTORY

A factory produces two types of electronic components, A and B. The cost of producing x units of Component A is given by:

$$C_A(x)=(〖6x〗^2+9x)/3x$$ pesos.

The cost of producing x units of Component B is given by:
$$C_B(x)=(〖4x〗^2-2x)/2x$$ pesos.

Analyze how the cost per unit for Component A changes as x increases, which of the following scenarios is not possible?

CIRCULAR TRACK AND FIELD

Athletics is a sport that includes a number of events involving running, jumping, throwing or walking. The sport is often referred to as track and field.

In the track and field competition played during the PPSCI Intramural Meet 2024, two runners start at the same time on a circular track. Runner A runs at a speed of $$(3x+5)/5$$ meters per second, and Runner B runs at   $$(4x+2)/7$$  meters per second.

The relative speed is the difference in the speed of the two runners.

What is the mathematical expression that represents the relative speed between Runner A and Runner B?

CIRCULAR TRACK AND FIELD

Athletics is a sport that includes a number of events involving running, jumping, throwing or walking. The sport is often referred to as track and field.

In the track and field competition played during the PPSCI Intramural Meet 2024, two runners start at the same time on a circular track. Runner A runs at a speed of $$(3x+5)/5$$ meters per second, and Runner B runs at $$(4x+2)/7$$  meters per second.

The relative speed is the difference in the speed of the two runners.

What is the relative speed (RS) between Runner A and Runner B?

CIRCULAR TRACK AND FIELD

Athletics is a sport that includes a number of events involving running, jumping, throwing or walking. The sport is often referred to as track and field.

In the track and field competition played during the PPSCI Intramural Meet 2024, two runners start at the same time on a circular track. Runner A runs at a speed of $$(3x+5)/5$$ meters per second, and Runner B runs at $$(4x+2)/7$$  meters per second.

The relative speed is the difference in the speed of the two runners.

Given the value of the relative speed between the two runners, who is faster between them if x = 10?

FILLING A WATER TANK

A water tank is being filled and emptied simultaneously. The rate at which water flows into the tank is given by:

$$R_{in}=(2x+3)/4$$ ​ liters per minute,

while the rate at which water flows out of the tank is:

​          $$R_{in}=(x+3)/6$$ liters per minute.

What is the mathematical expression that represents the net rate of change in the water level of the tank?

FILLING A WATER TANK

A water tank is being filled and emptied simultaneously. The rate at which water flows into the tank is given by:

$$R_{in}=(2x+3)/4$$ ​ liters per minute,

while the rate at which water flows out of the tank is:

​          $$R_{in}=(x+3)/6$$ liters per minute.

Given the inflow and outflow of the tank, what is the numerical value of the $$R_{net}$$ ?

FILLING A WATER TANK

A water tank is being filled and emptied simultaneously. The rate at which water flows into the tank is given by:

$$R_{in}=(2x+3)/4$$ ​ liters per minute,

while the rate at which water flows out of the tank is:

​          $$R_{in}=(x+3)/6$$ liters per minute.

When x = 3 is substituted to value of the $$R_{net}$$ , what is the net rate of change?