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iVinArrow [24]
2 years ago
14

Find x please. Thank you!!! :)))

Mathematics
2 answers:
Grace [21]2 years ago
8 0

Answer:

x = 27

Step-by-step explanation:

Because lines AC and DE are parallel, angles ABD and CDE are equal.  Therefore angle BDE is 72.  Angle ADF is a straight angle, so 2x + 72 + 2x = 180, or 4x = 108, 2x = 54 and x = 27.

abruzzese [7]2 years ago
5 0

Answer:

<h3>             x = 27°</h3>

Step-by-step explanation:

2x + 2x + 72° = 180°

4x = 108°

 x = 27°

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Can anyone help me integrate :
worty [1.4K]
Rewrite the second factor in the numerator as

2x^2+6x+1=2(x+2)^2-2(x+2)-3

Then in the entire integrand, set x+2=\sqrt3\sec t, so that \mathrm dx=\sqrt3\sec t\tan t\,\mathrm dt. The integral is then equivalent to

\displaystyle\int\frac{(\sqrt3\sec t-2)(6\sec^2t-2\sqrt3\sec t-3)}{\sqrt{(\sqrt3\sec t)^2-3}}(\sqrt3\sec t)\,\mathrm dt
=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{\sqrt{\sec^2t-1}}\,\mathrm dt
=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{\sqrt{\tan^2t}}\,\mathrm dt
=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{|\tan t|}\,\mathrm dt

Note that by letting x+2=\sqrt3\sec t, we are enforcing an invertible substitution which would make it so that t=\mathrm{arcsec}\dfrac{x+2}{\sqrt3} requires 0\le t or \dfrac\pi2. However, \tan t is positive over this first interval and negative over the second, so we can't ignore the absolute value.

So let's just assume the integral is being taken over a domain on which \tan t>0 so that |\tan t|=\tan t. This allows us to write

=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{\tan t}\,\mathrm dt
=\displaystyle\int(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\csc t\,\mathrm dt

We can show pretty easily that

\displaystyle\int\csc t\,\mathrm dt=-\ln|\csc t+\cot t|+C
\displaystyle\int\sec t\csc t\,\mathrm dt=-\ln|\csc2t+\cot2t|+C
\displaystyle\int\sec^2t\csc t\,\mathrm dt=\sec t-\ln|\csc t+\cot t|+C
\displaystyle\int\sec^3t\csc t\,\mathrm dt=\frac12\sec^2t+\ln|\tan t|+C

which means the integral above becomes

=3\sqrt3\sec^2t+6\sqrt3\ln|\tan t|-18\sec t+18\ln|\csc t+\cot t|-\sqrt3\ln|\csc2t+\cot2t|-6\ln|\csc t+\cot t|+C
=3\sqrt3\sec^2t-18\sec t+6\sqrt3\ln|\tan t|+12\ln|\csc t+\cot t|-\sqrt3\ln|\csc2t+\cot2t|+C

Back-substituting to get this in terms of x is a bit of a nightmare, but you'll find that, since t=\mathrm{arcsec}\dfrac{x+2}{\sqrt3}, we get

\sec t=\dfrac{x+2}{\sqrt3}
\sec^2t=\dfrac{(x+2)^2}3
\tan t=\sqrt{\dfrac{x^2+4x+1}3}
\cot t=\sqrt{\dfrac3{x^2+4x+1}}
\csc t=\dfrac{x+2}{\sqrt{x^2+4x+1}}
\csc2t=\dfrac{(x+2)^2}{2\sqrt3\sqrt{x^2+4x+1}}

etc.
3 0
3 years ago
Write the fraction as a product of a whole number 4/8, 8/12, 3/4
Mademuasel [1]
You simplefie them and get 1/2 for 4/8
2/3 for 8/12
3/4 cannot be somplified
8 0
3 years ago
Read 2 more answers
Determine whether the two expressions are equivalent.
Julli [10]

Answer:

They are equivalent because they equal the same, but the numbers are just flipped around. True

Step-by-step explanation:


8 0
3 years ago
√85 between which two intergers ​
lilavasa [31]

Answer:

I think that it is 9 and 10 because when you simply the number 85 it would be 9.21 which is round by 9

7 0
3 years ago
What is the slope of the line passing through the points (6,7) and (1,5)
Vladimir79 [104]

Answer:

2/5

Step-by-step explanation:

The formula for slope is

m = (y2-y1)/(x2-x1)

 = (5-7)/(1-6)

 =-2/-5

=2/5

3 0
3 years ago
Read 2 more answers
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