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jonny [76]
3 years ago
12

Use the sum of cubes identity to write this polynomial expression in factored form: 8x3 + 27.

Mathematics
2 answers:
lorasvet [3.4K]3 years ago
8 0
The answer is 1989 because that’s how much I know
zvonat [6]3 years ago
3 0

Answer:

{8x}^{3}  + 27 \\   =  {8x}^{3}  +  {3}^{3}  \\ let : 8x \: be \: a \\  : 3 \: be \: b \\  =  >  {a}^{3}  +  {b}^{3}  :  \\  {(a + b)}^{3}  = (a + b)( {a}^{2}  + 2ab +  {b}^{2} ) \\  {(a + b)}^{3}  = ( {a}^{3}  + 3{a}^{2} b + 3a {b}^{2}  +  {b}^{3} ) \\ ( {a}^{3}  +  {b}^{3} ) =  {(a + b)}^{3}  - 3ab(a + b) \\  \therefore( {8x}^{3}  + 27) =  {(8x + 3)}^{3}  - 72(8x + 3)

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Find a power series representation of e^x sin(x)
liberstina [14]
The Taylor series is defined by:
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Let a = 0.
Then its just a matter of finding derivatives and determining how many terms is needed for the series.

Derivatives can be found using product rule:
f^n (x) = e^x g^{n-1} (x) + e^x g^n (x)  \\ g^0 (x) = sin x

Do this successively to n = 6.
f^1 (x) = e^x (sinx +cos x) \\ f^2 (x) = e^x (2cos x)  \\ f^3 (x) = e^x(2cos x - 2sin x)  \\ f^4 (x) = e^x (-4 sin x)  \\ f^5 (x) = e^x(-4sinx -4cos x) \\ f^6(x) = e^x(-8cos x)

Plug in x=0 and sub into taylor series:
e^x  sin x = x+x^2 +\frac{x^3}{3} -\frac{x^5}{30}-\frac{x^6}{90}...

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6 0
3 years ago
Find the sum of (x+5), (-4x-2), and (2x-1)
RideAnS [48]
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3 0
3 years ago
12.125 rounded to the nearest tenth.
nika2105 [10]
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8 0
3 years ago
Tan39= x/68<br> Plz help. Will give brainliet
lesya [120]

Answer:

\huge\boxed{x \approx 55}

Step-by-step explanation:

We need to note that this is an equation, in which we can solve for x.

tan(39) = \frac{x}{68}

We can use a calculator to find the tangent of 39 - we type 39 into the calculator then press the "TAN" button to find it's tangent. We find that to be around 0.81.

We now have the formula simplified down to 0.81 = \frac{x}{68}. To solve for x, we want to isolate it on one side, so we can multiply both sides by 68 to get rid of the fraction.

We know have 0.81 \cdot 68 = x

0.81 \cdot 68 = 55.08 \approx 55, so x is approximately 55.

Hope this helped!

6 0
3 years ago
Read 2 more answers
12-y=2x-5 in slope-intercept form
Gemiola [76]

Answer: y = -2x + 7  

Step-by-step explanation:

Slope intercept form is the same as solving for y in the equation .

So solve for y and it will be in slope intercept form.

12 - y = 2x + 5   Subtract 12 from both sides

-12             -12

-y = 2x  -7      Now divide both sides by -1

y = -2x + 7

8 0
3 years ago
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