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3 years ago

Integrate 1/((x^5)sqrt(9x^2-1)) ...?

1 answer:

5 0

Let 9x^2-1 = y^2
=> 18xdx = 2ydy 
=> ydy = 9xdx 

lower limit = sqrt(9*2/9 - 1) = sqrt(1) = 1 
upper limit = sqrt(9*4/9 - 1) = sqrt(3) 

Int. [sqrt(2)/3,2/3] 1/(x^5(sqrt(9x^2-1)) dx 

= Int. [sqrt(2)/3,2/3] xdx/(x^6(sqrt(9x^2-1)) 
= 81* Int. [1,sqrt(3)] ydy/((y^2+1)^3y) 
=81* Int. [1,sqrt(3)] dy/(y^2+1)^3 

y=tanz 
dy = sec^2z dz 

=81*Int [pi/4,pi/3] cos^4(z) dz 
=81/4*int [pi/4,pi/3] (1+cos(2z))^2 dz 
=81/4* Int. [pi/4,pi/3] (1+2cos(2z)+cos^2(2z)) dz 

=81/4*(pi/3-pi/4) + 81/4*(sin(2pi/3)-sin(pi/2)) + 81/8 * (pi/3-pi/4) 
+ 81/32 *(sin(-pi/3)-sin(pi)) 
=81(pi/48+pi/96+1/4*(sqrt(3)/2 - 1) - 1/32 * sqrt(3)/2) 
=81/32*(pi+3sqrt(3)-8)

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Will GIVE BRAINLIEst

snow_lady [41]

Answer:

answer will be an=3n+11

Step-by-step explanation:

because when we substitute them...it make sense.

the rule is an=3n+11

lets substitute:

(i).14=3(1)+11

(ii)17=3(2)+11

(iii)20=3(3)+11

(iv)23=3(4)+11

it does make sense....

I hope it will help u....

8 0

2 years ago

The function ƒ(x) = 2x is vertically translated 5 units down and then reflected across the y-axis. What's the new function of g(

TEA [102]

Answer:

g(x) = -2x - 5

2x becomes -2x as a reflection across the y-axis

add on -5 to shift the function 5 units down

7 0

3 years ago

What is the value of x?

Nikolay [14]

Answer: 7 centimeters

Explanation:

Let triangle ABC and triangle CDE form a bow tie such that
- triangle ABC is smaller than triangle CDE
- Segment AC and segment CD are the north sides
- Segment BC and segment CE are the bottom sides
- AC = 6, CD = 42, CE = 36, BC = x

Since angle ACB and angle ECD are formed by intersecting segment AE and segment BD at point C, they are vertical angles. (See the attached picture) So, angle ACB and angle ECD are congruent.

Moreover when we form our bowtie, point A is in the north side and point E is in the bottom sides and this implies that angle BAC and angle CED are alternate interior angles as shown in the attached figure.

Since it is given in the problem that alternating interior angle are congruent, angle BAC and angle CED are congruent.

Now, we have the following pairs of angles in triangle ABC and triangle CDE that are congruent:

- angle BAC and angle CED
- angle ACB and angle ECD

By AA Similarity theorem, when we have two pairs of congruent angles for two triangles, then the two triangles are similar. So, triangle ABC and triangle CDE are similar.

In similar triangles, the sides that are opposite to the congruent angles are proportional to each other. So,

$\frac{BC}{CD} = \frac{AC}{CE} 


$ (1)

Since $AC = 6, CD = 42, CE = 36, BC = x$ , we can substitute these values to equation (1). So, equation (1) becomes

$\frac{x}{42} = \frac{6}{36}$
$\frac{x}{42} = \frac{1}{6}$ (2)

SInce we are solving for x, we can multiply both sides of equation (2) by the denominator at the left side which is 42 so that

x = 42(1/6)
x = 7 centimeters

8 0

3 years ago

I need to find the area .

nikklg [1K]

Answer:

104 ft^2

Step-by-step explanation:

area of rectangle = 8 × 10 = 80

area of triangle = 1/2 × 6 × 8 = 24

∴total area = 104 ft^2

5 0

3 years ago

Jackson loves to take day trips during weekends. Last weekend, he drove 80 miles to Crabclaw Beach. He used 4 gallons of gas to

ra1l [238]

Answer:

5 gallons of gas

Step-by-step explanation:

From the above question:

If:

80 miles = 4 gallons of gas

100 miles = x gallons of gas

Cross Multiply

80 × x = 100 × 4

x = 100 × 4/80

x = 5 gallons of gas

Therefore, Jackson would use 5 gallons of gas to get to Mount Highmore.

4 0

3 years ago

Integrate 1/((x^5)*sqrt(9*x^2-1)) ...?

Integrate 1/((x^5)sqrt(9x^2-1)) ...?