42.51 is the right answer
The answer is D could you give me brainlist
Answer:
20 m
Step-by-step explanation:
Given:
- Length in mud = ¹/₂ its length
- Length in water = ¹/₃ its length
- Length above water = 3 ¹/₃ m
Let x be the length of the lamp post.
Convert 3 ¹/₃ to an improper fraction:
![\sf \implies 3 \frac{1}{3}=\dfrac{3 \times 3+1}{3}=\dfrac{10}{3}](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%203%20%5Cfrac%7B1%7D%7B3%7D%3D%5Cdfrac%7B3%20%5Ctimes%203%2B1%7D%7B3%7D%3D%5Cdfrac%7B10%7D%7B3%7D)
The total length of the lamp post (x) is the sum of the three given lengths:
![\implies \sf mud+water+above\: water=x](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20mud%2Bwater%2Babove%5C%3A%20water%3Dx)
![\sf \implies \dfrac{x}{2}+\dfrac{x}{3}+\dfrac{10}{3}=x](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Cdfrac%7Bx%7D%7B2%7D%2B%5Cdfrac%7Bx%7D%7B3%7D%2B%5Cdfrac%7B10%7D%7B3%7D%3Dx)
Multiply both sides by 6:
![\sf \implies \dfrac{6x}{2}+\dfrac{6x}{3}+\dfrac{6 \cdot 10}{3}=6x](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%5Cdfrac%7B6x%7D%7B2%7D%2B%5Cdfrac%7B6x%7D%7B3%7D%2B%5Cdfrac%7B6%20%5Ccdot%2010%7D%7B3%7D%3D6x)
![\sf \implies 3x+2x+20=6x](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%203x%2B2x%2B20%3D6x)
![\sf \implies 5x+20=6x](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%205x%2B20%3D6x)
Isolate x:
![\sf \implies 20=6x-5x](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%2020%3D6x-5x)
![\implies \sf x=20](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20x%3D20)
Therefore, the whole length of the post is 20 m.
Step-by-step explanation:
<u>Step 1: Answer problem 1</u>
<em>Pull out 4</em>
![4(9x^2 - 4)](https://tex.z-dn.net/?f=4%289x%5E2%20-%204%29)
<em>Factor</em>
![4(3x + 2)(3x - 2)](https://tex.z-dn.net/?f=4%283x%20%2B%202%29%283x%20-%202%29)
<u>Step 2: Answer problem 2</u>
<em>Fact</em>or
![(11 + 2x)(11 - 2x)](https://tex.z-dn.net/?f=%2811%20%2B%202x%29%2811%20-%202x%29)
<u>Step 3: Answer problem 3</u>
<em>Pull out 9</em>
![9(x^2 - 9)](https://tex.z-dn.net/?f=9%28x%5E2%20-%209%29)
![9(x + 3)(x - 3)](https://tex.z-dn.net/?f=9%28x%20%2B%203%29%28x%20-%203%29)
<h3>
Answer: 576 </h3>
============================================================
Check out the diagram below.
I've split the figure into 3 separate blocks. We calculate the volume of each block, then add up those volumes to get the final answer.
- Block A = largest block on the left
- Block B = middle block
- Block C = smallest block on the right
So,
- volume of block A = length*width*height = 6*6*8 = 288 ft^3
- volume of block B = length*width*height = 6*6*5 = 180 ft^3
- volume of block C = length*width*height = 6*6*3 = 108 ft^3
Therefore, the total volume we're working with is:
A+B+C = 288+180+108 = 576 cubic feet
The "cubic feet" or "ft^3" portion is already taken care of by your teacher, so you just need to type in the number itself.