Inequalities math homework problem

In summary, the rectangular solid is to be constructed with a special kind of wire along all edges. The length of the base is twice the width, the height is such that the total amount of wire used is 40 cm. The range of possible values for the width of the base is between 1.14 cm and 1.43 cm, with the volume of the figure between 2 cm3 and 4 cm3.
  • #1
xCanx
45
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A rectangular solid is to be constructed with a special kind of wire along all
the edges. The length of the base is to be twice the width of the base. The
height of the rectangular solid is such that the total amount of wire used (for
the whole figure) is 40 cm. Find the range of possible values for the width of
the base so that the volume of the figure will lie between 2 cm3 and 4 cm3.
Write your answer correct to two decimal places.

Can someone show me how to start off?
 
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  • #2
w=width, L=length, h=height;

w+L+h=40, L=2w

wLh>2 and wLh<4
 
  • #3


I can provide guidance on how to approach this math homework problem. First, let's define our variables. Let the width of the base be represented by "w" and the length of the base be represented by "2w" (since it is twice the width). The height can be represented by "h" and the total amount of wire used can be represented by "40 cm".

Next, we can use the formula for the volume of a rectangular solid: V = lwh. In this case, we can substitute the length and width as 2w and w respectively, giving us V = 2w^2h.

Since the total amount of wire used is 40 cm, we can set up an equation to represent this: 40 = 4w + 4w + 2h. This is because each edge of the base has a length of w and there are 4 edges in total, and the height has two edges with a length of h. Simplifying this equation, we get 40 = 8w + 2h.

Now, we can use the given range of possible values for the volume (2 cm^3 to 4 cm^3) to create two equations and solve for the width of the base.

For V = 2 cm^3, we can substitute this into our volume formula and set it equal to 2: 2 = 2w^2h. We can also substitute the equation for the total amount of wire used (40 = 8w + 2h) into this equation, giving us 2 = 2w^2(40 - 8w). Simplifying this, we get the quadratic equation 4w^2 - 80w + 2 = 0. Solving for w, we get two possible values: 4.83 cm and 0.21 cm. However, since the width cannot be negative, we can disregard the second solution.

For V = 4 cm^3, we can follow the same steps as above, substituting 4 into our volume formula and setting it equal to 4: 4 = 2w^2h. Substituting the equation for the total amount of wire used, we get 4 = 2w^2(40 - 8w). Simplifying, we get the quadratic equation 4w^2 - 80w + 4 =
 

What are inequalities in math?

Inequalities in math are mathematical expressions that compare the relative size or order of two quantities. They are represented by symbols such as <, >, ≤, and ≥.

How do I solve inequalities?

To solve inequalities, you must follow similar rules as solving equations, except when multiplying or dividing by a negative number, the direction of the inequality sign changes. The solution is represented by a range of values that satisfy the inequality.

What is the difference between an inequality and an equation?

An equation is a mathematical statement that shows the equality between two expressions, while an inequality shows the relationship between two expressions, where one is greater than, less than, or equal to the other.

Can inequalities have more than one solution?

Yes, inequalities can have infinitely many solutions, represented by a range of values that satisfy the inequality. However, some inequalities may have no solution if the range of values does not exist.

How are inequalities used in real life?

Inequalities are used in real life to represent relationships between quantities, such as income, age, weight, and temperature. They are also used in making decisions, such as budgeting, determining the best price for a product, or setting eligibility requirements.

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