A rectangular cardboard sheet has a length that is 1.5 times greater than the width. Is it possible to make a topless box with a
volume of 6080 cm3 out of this cardboard sheet if squares with a side of 8 cm are cut from the corners? Find the dimensions of the cardboard sheet.
2 answers:
Answer:
Yes, it is possible to make a topless box with a volume of 6080 cm3 out of this cardboard sheet.
The dimensions of the cardboard sheet are 54 cm x 36 cm
Step-by-step explanation:
Let
x ----> the length of the cardboard sheet
y ----> the width of the cardboard sheet
we know that
----> equation A
The volume of the topless box is
where
substitute
----> equation B
substitute equation A in equation B
Solve for y
Solve the quadratic equation by graphing
The solution is y=36 cm
see the attached figure
Find the value of x
---->
therefore
Yes, it is possible to make a topless box with a volume of 6080 cm3 out of this cardboard sheet.
The dimensions of the cardboard sheet are 54 cm x 36 cm
Answer:
<h2>54 cm length and 36 cm width.</h2>Step-by-step explanation:
Let's call the width of the cardboard sheet,
is the length of it (the problem states that the length is 1.5 times the width).
Also, which is the removed part of the box.
Remember that the volume of a rectangular prism is the product between each dimension. In this case, we have
Where we already included the removed part of the box.
Replacing values, we have
Using a calculator, we have
Where only the positive number make sense to the problem, because there's no negative lengths.
So, the length is
Therefore, the dimensions are 54 cm length and 36 cm width.
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Answer:
Elements are of the form
(i)
(ii)
(iii)
(iv)
(v) (a,b) where a>b=
(vi) [a,b] where a>b=
Step-by-step explanation:
Given intervals are,
(i) [a,a] (ii) [a,a) (iii) (a,a] (iv) (a,a) (v) (a,b) where a>b (vi) [a,b] where a>b.
To show all its elements,
(i) [a,a]
Imply the set including aa from left as well as right side.
Its elements are of the form.
Since there is a singleton element a of real numbers, this set is empty.
Because there is no increment so if then the set [a,a] represents singleton sets, and singleton sets are empty so is [a,a].
(ii) [a,a)
This means given interval containing a by left and exclude a by right.
Its elements are of the form.
Since there is a singleton element a of real numbers withis the set, this set is empty.
Because there is no increment so if then the set [a,a) represents singleton sets, and singleton sets are empty so is [a.a).
(iii) (a,a]
It means the interval not taking a by left and include a by right.
Its elements are of the form.
Since there is a singleton element a of real numbers, this set is empty.
Because there is no increment so if then the set (a,a] represents singleton sets, and singleton sets are empty so is (a,a].
(iv) (a,a)
Means given set excluding a by left as well as right.
Since there is a singleton element a of real numbers, this set is empty.
Its elements are of the form.
Because there is no increment so if then the set (a,a) represents singleton sets, and singleton sets are empty, so is (a,a).
(v) (a,b) where a>b.
Which indicate the interval containing a, b such that increment of x is always greater than increment of y which not take x and y by any side of the interval.
That is the graph is bounded by value of a and it contains elements like it we fixed a=5 then,
e.t.c
So this set is connected and we know singletons are connected in . Hence given set is empty.
(vi) [a,b] where .
Which indicate the interval containing a, b such that increment of x is always greater than increment of y which include both x and y.
That is the graph is bounded by value of a and it contains elements like it we fixed a=5 then,
e.t.c
So this set is connected and we know singletons are connected in . Hence given set is empty.