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3 years ago

∫ (3x²-2)/x³ dx help

1 answer:

4 0

We will use integration by substitution, as well as the integrals
∫
1
x
d
x
=
ln
|
x
|
+
C
and
∫
1
d
x
=
x
+
C
∫
x
3
x
2
+
1
d
x
=
∫
x
2
x
2
+
1
x
d
x
=
1
2
∫
(
x
2
+
1
)
−
1
x
2
+
1
2
x
d
x
Let
u
=
x
2
+
1
⇒
d
u
=
2
x
d
x
. Then
1
2
∫
(
x
2
+
1
)
−
1
x
2
+
1
2
x
d
x
=
1
2
∫
u
−
1
u
d
u
=
1
2
∫
(
1
−
1
u
)
d
u
=
1
2
(
u
−
ln
|
u
|
)
+
C
=
x
2
+
1
2
−
ln
(
x
2
+
1
)
2
+
C
=
x
2
2
−
ln
(
x
2
+
1
)
2
+
1
2
+
C
=
x
2
−
ln
(
x
2
+
1
)
2
+
C
Final answer

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select all the sets that are the three side lengths of right triangles A.8,7,15 B.4, 10, √84 C. √8, 11, √129 D. √1, 2, √3

Semenov [28]

Answer:

Step-by-step explanation:

For any set of three side length of a triangle to be a right angled triangle, the sum of the square of the two of the sides must be equal to the square of the longest side according to pythagoras theorem.

The longest side is always the hypotenuse

For option D, 2 will be the longest side. Since 2 is the hypotenuse, the sum of the square of other two values must be equivalent to the square of 2,

$= (\sqrt{1})^{2} + (\sqrt{3})^{2} \\ = 1=3\\= 4\\= 2^{2} (hypotenuse)$

This shows that √1, 2, √3 are three sides of a right triangles.

Similarly for option C, the hypotenuse is √129 being the largest.

To show the sides are that of a right triangles;

$= (\sqrt{8}) ^{2} + 11^{2} \\= 8 + 121\\= 129\\= (\sqrt{129})^{2} \\$

Since the resulting value is the square of the hyp, then √8, 11, √129 are three sides of a right triangles.

For option B; 10 is the hypotenuse being the longest sides, To show the sides are that of a right triangles;

$=4^{2}+(\sqrt{84})^{2} \\ = 16+84\\= 100\\= 10^{2}$

Since the resulting value is the square of the hyp, then 4, 10, √84 are three sides of a right triangles.

Only option A is wrong since 15² is not equal to the sum of 8² and 7².

4 0

3 years ago

Help on problem 7!<br> i think i have to do a2/a1 to be correct or something. please help!

blondinia [14]

Answer:

It’s a2/a1 so 81/243 so the common ratio is 1/3

Step-by-step explanation:

7 0

3 years ago

A man and a woman share a prize

VladimirAG [237]

Step-by-step explanation:

What type of line the picture represent

3 0

3 years ago

Jolie can read around 14 sentences per minute of her current novel. She wants to finish her reading before the movie comes out n

vladimir1956 [14]

This is what you would do
120 x 17= 2040
Or you could do 12 x 17 then, add a zero to the end of it.
Then you would divid from what you got when you did 120 x 17 by 60
That should give you the answer.
Hope this helps if im not mistaken it should be 34

2040 <span>60 </span>= 34

34 = 340 to the nearest tenth

34 = 34 to the nearest hundredth

34 = 34 to the nearest thousandth

= 0 to the nearest tenth

= 0 to the nearest hundredth

= 0 to the nearest thousandth

4 0

3 years ago

Jackie earns $172 per week at her part time job. She is saving this money to buy a used car that cost $2000. At this rate, how m

vodomira [7]

Answer:

12 weeks

Step-by-step explanation:

It will take Jackie 12 weeks to buy her car because she earns 172 per week.

If you divide 2000 buy 172 you end up with 11.6

if you multiply 11 and 172 you get 1,892 which is just a little under 2000

if you add another week = 172$ you will arrive at 2064 which is enough to buy

her car.

Hope this helps.

3 0

3 years ago