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Blababa [14]
2 years ago
5

Factorise: 27x^3 - 1/216 -9/2x^2 +1/4x

Mathematics
1 answer:
g100num [7]2 years ago
7 0

Answer:

Hello,

Step-by-step explanation:

27x^3-\dfrac{9}{2}x^2+\dfrac{1}{4}x-\dfrac{1}{216}   \\\\=(3x)^3-3*(3x)^2*\dfrac{1}{6} +3*(3x)*(\dfrac{1}{6} )^2-(\dfrac{1}{6} )^3\\\\=\boxed{(3x-\dfrac{1}{6} )^3}

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What is the volume of a rectangle prism with a length of 8 1/2 centimeters width of 9 1/3 centimeters and a height of 12 2/5 cen
Gala2k [10]

Answer:

983.733

Step-by-step explanation:

8.5 * 9 1/3 = 79 1/3

79 1/3 * 12 2/5 = 983.733

8 0
3 years ago
Read 2 more answers
Ryan bought a new computer for $2,100. The value of the computer decreases by 50% each year. When will the
noname [10]

Answer:

After 2.80 years the price drops to 300 $

Step-by-step explanation:

Ryan bought a new computer for $2,100.

Price of computer = 2100 $

The value of the computer decreases by 50% each year.

Let p(n) be the price of computer after n years.

\texttt{Price of computer after 1 year =}2100-\frac{50}{100}\times 2100=0.50^1\times 2100\$\\\\\texttt{Price of computer after 2 years =}0.50^2\times 2100\$\\\\\texttt{Price of computer after 3 years =}0.50^3\times 2100\$\\\\\texttt{Price of computer after n years =}0.50^n\times 2100\$

Now we need to find n when price is 300 $.

              0.50ⁿ x 2100 = 300

                 0.50ⁿ = 0.143

                 n log (0.5) = log 0.143

                  n x -0.301 = -0.845

                  n = 2.80

After 2.80 years the price drops to 300 $

8 0
3 years ago
-4xy if x is 4 and y is -5
Mars2501 [29]

Answer:

-5

Step-by-step explanation:

-4xy

-4+4-5

-5

Hope this helped! :)

P.S. You might wanna practice PEDMAS for it is in this equation. ;)

7 0
3 years ago
Which number is larger 0.707 or 0.71?
mash [69]
0.71 is a larger number
5 0
3 years ago
Read 2 more answers
A 65 ft. long swimming pool is to be constructed. The pool will be 4 ft. deep at one end and 11 ft. deep at the other. To the ne
pishuonlain [190]

Answer:

Measure of the acute angle = 84°

Step-by-step explanation:

In the figure attached,

ABDE is a swimming pool having length 'AB' = 65 feet

Depth of one end of the pool is BE = 4 feet

And depth of the other end AD = 11 feet

Acute angle between the bottom of the pool (DE) and wall of the deep end (AD) is ∠ADE.

Now from ΔCDE,

tanx = \frac{EC}{DC}

tanx = \frac{7}{65}

x = \text{tan}^{-1}(\frac{7}{65})

x = 6.15°

Now measure of acute angle the bottom of the pool makes with wall at he deep end,

m∠ADE = (90 - 6.15)°

             = 83.85°

             ≈ 84°

3 0
3 years ago
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