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STatiana [176]
3 years ago
6

Factor completely: 1331x^3 - 729y^3

Mathematics
1 answer:
Studentka2010 [4]3 years ago
5 0

Answer:

(11x - 9y) (121x² + 99xy + 81)

Step-by-step explanation:

Difference of cubes

∛1331x³ = 11x = a

∛729y³ = 9y = b

(a³ + b³) = (a + b) (a² - ab + b²)

(a³ - b³) = (a - b) (a² + ab + b)

(1331x³ - 729y³) = (11x - 9y) (121x² + 99xy + 81)

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Solve the equation. dy dx = ay + b cy + d , where a, b, c, and d are constants. (assume a ≠ 0 and ay + b ≠ 0.)
Reil [10]

 

It solves it in x. the solution for y includes heavy use of the product log function.

dy/dx                                = ay + b/cy +d

(cy +d/ ay + b) dy            = dx

∫ (cy +d/ ay + b) dy          = x (t) + C

 

Into solving the integral, integration by parts followed by u substitution and another integration by parts.

 

∫ (cy +d/ ay + b) dy

u            = cy + d dv          = dy/ay + b

du          = c dy v               = ln I ay + b l / a

 

Then, use u substitution for the new integral

 

u            = ay + b

du          = a dy

∫ ln l ay + b I dy                = ∫ ln IuI /a du    = 1/a ∫ ln luI du

 

Integrating the natural log includes thus far another integration by parts

r             = ln IuI ds            = du

dr          = du / u (s)           = du

∫ ln IuI / du                         = u ln IuI - ∫ du   = u ln IuI - ∫ a dy                                                                                   = (ay + b) ln Iay +bl – ay

 

The original integral of expression

∫ (cy +d/ ay + b) dy             = cy + d/a ln lay+bl – c/a² [(ay+b) ln lay+bl – ay]

Then simplify

∫ (cy +d/ ay + b) dy             = cy + d/a ln lay+bl – c/a²[(ay+b) ln lay+bl – ay]

                                           = a (cy + d)/a² ln lay+bl – c (ay+b)/ a²ln lay+bl +                                                               c/a² ay

                                           = cay + ad – cay – cb/ a² ln lay+bl + cay/a²

                                           = ad – cb/a²ln lay+bl + cy/a

 The final answer will be

x(t) + C                               = ad – cb/a² ln lay+bl + cy/a

x(t)                                     = ad – cb/a² ln lay+bl + cy/a + k

 

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3 0
3 years ago
What is the slope of this grid?
elixir [45]
The slope would be rise over run so it should be 2 over -1
7 0
3 years ago
What is the slope of the line that contains the points (-1, 8) and (5,-4)?
Jlenok [28]

Answer:

-2

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask ;)

8 0
3 years ago
The volume V of a cone varies jointly as the area of the base B and the height
seraphim [82]

Answer:

h = 9 cm.

Step-by-step explanation:

V = kBh   where k is the constant of variation.

From the given info:

32 = k*16*6 = 96k

So k = 32/96 = 1/3.

So we have the equation of variation:

V = 1/3Bh

When V = 60 B = 20, so:

60 = 1/3 20h

20h = 60 * 3 = 180

h = 180 /20 = 9.

3 0
2 years ago
Help pls. I will give brainliest to whom ever gets the answer correct.
Ivanshal [37]

Answer:

your answer will be 18 in

Step-by-step explanation:

I hope this helps u ^_^

have a great day

3 0
3 years ago
Read 2 more answers
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