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4 days ago

Tim knows the volume and base area of a wooden chest that is in the shape of a rectangular prism. If the volume is 5/24 cubic un

it and the base area is 1/5 square unit, what is the height of the chest? 124 unit 1124 units 112 unit 1112 units

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A rectangular prism must have a base with an area of no more than 27 square meters. The width of the base must be 9 meters less

Leona [12618]

Answer:

The upper limit for the height of the prism is $12\ m$

Step-by-step explanation:

Let

x------> represent the height of the prism

It is known that

the area of the base of the prism must not exceed

$A=L*W$

$A\leq 27\ m^{2}$

thus

$L*W\leq 27$ -------> inequality A

$W=x-9$ ------> equation B

$L=W+6$ -----> equation C

Insert equation B into equation C

$L=(x-9)+6$

$L=x-3$ ------> equation D

Substituting equations B and D into inequality A

$(x-3)*(x-9)\leq 27$ -------> using a graphing tool to solve the inequality

The resultant solution for x lies in the interval----------> $[0,12]$

consult the attached figure

but bear in mind that

The width of the base must be $9$ meters shorter than the height of the prism

thus

the solution for x is confined to the interval ------> $(9,12]$

The maximum height of the prism equals $12\ m$

8 1

3 months ago

Read 2 more answers

Mike earned x dollars the first week of his new job. He earned 5% more the second week than the first week. Which expression rep

zzz [12365]

The expression indicates that the total earnings of Mike over the two weeks amount to 2.05x dollars

Solution:

It is given that Mike earned x dollars during the first week at his new job,

While in the second week, he earned 5% more than the earnings of the first week.

To determine: Total earnings over the two weeks

From the information provided,

Earnings in the first week = "x" dollars

Earnings in the second week = 5% more than first week earnings

Thus,

Earnings in the second week = x + 5% of x

$\rightarrow x + 5 \% \times x\\\\\rightarrow x + \frac{5}{100} \times x\\\\\rightarrow x + 0.05x = 1.05x$

Therefore, earnings in the second week equal to 1.05x dollars

The total earnings over the two weeks:

Total earnings = Earnings from first week + Earnings from second week

$Total\ Amount = x + 1.05x = 2.05x$

Thus, the expression for the total earnings of Mike for both weeks is 2.05x dollars

5 0

3 months ago