What is an example of a solution of zero ?

chegg evaluate the following integral using trigonometric substitution. dx/square root(x^2-81), x > 9

vesna_86 [32]

Integration will be ln | ( x /9 ) + ( $\sqrt{(x/9)^{2} - 1 }$ ) | + c .

Given ∫ 1 dx / ( $x^{2}$ - 81 )

Put ,

x = 9 secθ

dx = 9 secθ tanθ dθ

and

$\sqrt{x^{2} - 9^{2} }$ = 9 tanθ

Substituting values in ∫ 1 dx / ( $x^{2}$ - 81 ) ,

∫ (9 secθ tanθ ) dθ / ( 9 tanθ )

∫ secθ dθ = ln | secθ + tanθ | + c

= ln | ( x /9 ) + ( $\sqrt{x^{2} - 9^{2} }$ / 9 ) | + c

= ln | ( x /9 ) + ( $\sqrt{(x/9)^{2} - 1 }$ ) | + c

Hence , the integration will be ln | ( x /9 ) + ( $\sqrt{(x/9)^{2} - 1 }$ ) | + c .

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6 0

1 year ago

The table below shows the numbers of tickets sold at a movie theater on Friday.

prisoha [69]

Answer:

Number of Adult's tickets sold on Saturday = 3,356

Number of Children's tickets sold on Saturday = 2, 928

Total number of tickets sold over these two days is 8,938.

Step-by-step explanation:

Here, the number of tickets sold on FRIDAY:

Adult Ticket sold = 1,678

Children's Tickets sold = 976

So, the total number of tickets sold on Friday

= Sum of ( Adult + Children's ) tickets = 1,678 + 976 = 2,654 .... (1)

The number of tickets sold on SATURDAY:

Adult Ticket sold = 2 times the number of adult tickets sold on Friday

= 1,678 x 2 = 3,356

Children's Tickets sold = 3 x the number of children's tickets sold on Friday.

= 976 x 3 = 2, 928

So, the total number of tickets sold on Saturday

= Sum of ( Adult + Children's ) tickets = 3,356 + 2,928 = 6, 284 .... (2)

Now, the total number of tickets booked in these two days :

Sum of tickets booked on (Friday + Saturday)

= 2,654 + 6, 284 = 8,938

Hence, total number of tickets sold over these two days is 8,938.

6 0

3 years ago

It is common to leave a 10% tip when the service was just mediocre. At one such occasion, a patron left a 10% tip on a $23.45 bi

shusha [124]

Answer: $2.3

Step-by-step explanation: well you need to find 10% of 23.45, so multiply .1 by 23.45.

3 0

2 years ago

Read 2 more answers

What is the y-coordinate for the solution of the system of equations below? 7y+5x=19 3y+5x=7

RoseWind [281]

I would go about solving this by elimination because the x variables are already the same so all you would have to do is change one equation to the opposite signs and add them, so it would look like:

7y + 5x = 19
+ -3y - 5x = -7
-------------------
4y=12
y=3

7 0

3 years ago

Read 2 more answers

A bag of candy containing 320 pieces is to be divided up into 18 smaller bags for distribution with fourteen left over. How many

nikitadnepr [17]

Answer:

17

Step-by-step explanation:

A bag of candy contains 320 pieces

It is to be divided into 18 smaller bags with fourteen left over

Therefore the pieces that will go in each bag after the distributorn can be calculated as follows

= 320/18

= 17 remainder 14

Hence 17 pieces of candy will be in each bags

5 0

3 years ago