Nisha collects comic books, and she convinced her friend Hakim to start collecting as well. Every week, they go to the store tog
ether, and they each buy a new comic book. This table shows how many books they each have:
1 answer:
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Solution set for a statement is a set of values which satisfy the given statement. The solution set for given condition is: (16, positive infinity)
<h3>How to find the solution set for a given problem?</h3>Solution set is the set of values of unknown variable for which the given mathematical statement holds true.
<h3>How to form mathematical expression from the given description?</h3>You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
For the given case, the mathematical statement given is
(where that unknown number was assumed to be 'x', and we used "less than" phrase as subtraction and 'greater than' as >)
Converting mixed fractions to normal fractions, we get the statement as:
Thus, for all values of bigger than 16, the given statement is true.
Thus, The solution set for given condition is: (16, positive infinity)
Learn more about solution set here:
Answer:
The dimensions are 13.92inches by 36.92inches by 5.04inches
Volume is 2590.18 inches³
Step-by-step explanation:
see attachment for the figure
supposing 'h' is side length of the square and also the height of the box
then, According to the question
Length of the box 'L'= 47 - 2h
Width of the box 'w'= 24 - 2h
Volume of the box 'V'= hLw
Substituting the values of 'L' and 'w' in above equation
V= h(47 - 2h)(24 - 2h)
V=(47h - 2h²)(24 - 2h) => 1128h - 94h²-48h²+4h³
V= 4h³ -142h²+1128h -->eq(1)
Taking derivative on both sides.
V' = 12h² - 284h + 1128
Setting the equation to zero, we will have
0=12h² - 284h + 1128
0= 3h² - 71h + 282
Using Quadratic formula to find h
h= (-b+-√b²-4ac) / 2a
= 71+-√71² - (4 x 3 x 282) / (2 x 3)=> 71+-√5041- 3384 / 6
h =(71+- 40.706)/ 6
EITHER h= 18.6
OR h=5.04
By substituting the value of 'h' in eq(1)
(1)=>V(18.6)= 4(18.6)³ -142(18.6)²+1128(18.6) => -2406.096
(1)=>V(5.04)= 4(5.04)³ -142(5.04)²+1128(5.04) => 2590.18
By ignoring the negative value, we will have h=5.04
Therefore,
L= 47 - 2h => 47 -2(5.04) =>36.92
w= 24 - 2h=> 24- 2(5.04)=> 13.92
The dimensions are 13.92inches x 36.92inches x 5.04inches
Volume is 2590.18 inches³
