Mathematics, 24.03.2021 01:00 cherri22

You are designing an aquarium for your new office. The dimensions of the aquarium are restricted as shown in the diagram below. Dimensions:
Height: (w+9)in.
Width: w in.
Length: (49-w)in.

Write a polynomial expression that represents the volume of the aquarium according to the specified dimensions. (I got w(w+9)(49-w))

You need the aquarium to hold 17,640 cubic inches of water. Find the possible dimensions of the aquarium.

Answers: 1

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Answer from: magicallyhello

Part 1)

V=w(w+9)(49-w)

Part 2)

We can have the aquarium have a width of 40 inches, a height of 49 inches, and a length of 9 inches.

Or we can have the aquarium have a width of 21 inches, a height of 30 inches, and a length of 28 inches.

Step-by-step explanation:

The dimensions of the aquarium is as follows:

$\text{Height}= (w+9)\text{ inches}\\\text{Width} = w\text{ inches} \text{ and } \\\text{Length} = (49-w)\text{ inches}$

Part 1)

We want to find a polynomial expression that represents the volume of the aquarium according to the specified dimensions.

Since the aquarium is a rectangular prism, the volume will simply be the product of all the dimensions. Hence:

V=w(w+9)(49-w)

Part 2)

We want to aquarium to hold 17, 640 cubic inches of water. In other words, the volume V should be 17640. Thus:

17640=w(w+9)(49-w)

First, we can distribute the right-hand side:

17640=(w^2+9w)(49-w)

Distribute:

(w^2+9w)(49)+(w^2+9w)(-w)=17640

Distribute:

(49w^2+441w)+(-w^3-9w^2)=17640

Simplify:

-w^3+40w^2+441w-17640=0

Now, we can factor. From the first two terms, factor out a -w² and from the second two terms, we can factor out 441:

-w^2(w-40)+441(w-40)=0

Grouping:

(441-w^2)(w-40)=0

Zero Product Property:

$441-w^2=0\text{ or } w-40=0$

Solve for each case:

$w=21\text{ or } w= 40$

So, we have two possible sets of dimensions.

We can have the aquarium have a width of 40 inches, a height of 49 inches, and a length of 9 inches.

Or we can have the aquarium have a width of 21 inches, a height of 30 inches, and a length of 28 inches.

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

Answer from: Quest

correct answer is c. just did it

step-by-step explanation:

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