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3 years ago

Find the integral of 1/sqrt(x^2-9)

1 answer:

6 0

Let x = 3secβ, then dx = 3secβtanβ

∫dx/√(x²-9) = ∫[(3secβtanβ)/(3tanβ)]dβ
                 = ∫secβdβ
                 = ln |tanβ - secβ| + c
                 = ln |√(x² - 9)/3 - x/3| + C
                 = ln |√(x² - 9)/x| + C

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2x+6= 45 Solve for x 49 pts

Gemiola [76]

2x+6=45

2x=39

x=19.5

i hope that's helpfull......... is it?

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3 years ago

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A patient in the emergency room is monitored for heart rate, oxygenation level, etc. The nurse notices that the heart beat ave

creativ13 [48]

The nurse is using Deductive reasoning.

Deductive reasoning is a valid form of proof. Here, a person makes conclusions based on previously known facts. It is process of reasoning from one or more statements to reach a logically certain conclusion. If all the parameters are true and the terms are clear then the conclusion reached is necessarily true.

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4 years ago

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BaLLatris [955]

First, find what percentage of students had 3 or more by adding up your known percents:

45% + 23 % + 21% + x% = 100%
x = 11%

Since you're given that 96 students had 2 or more, you add up the percentages of 2 and 3 or more:

11 + 21 = 32%

Now set up a proportion that relates it to the whole:

$\frac{96 students}{32 percent} = \frac{x students}{100 percent}$

This will allow you to find the total number of students at the school.

Cross multiplying and solving for x results in 300 total students.

Question 1:
45% had one or more absences. 45% of 300 students is 135 students.

Question 2:
As we found before, 11% of students had three or more. 11% of 300 is 33 students.

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4 years ago

What is the volume of the box

iris [78.8K]

Answer:

V = l * w * h

Step-by-step explanation:

V = 14 * 5 * 7

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3 years ago

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Find the sum of the first 20 terms of the arithmetic sequence 4, -4, -12, -20

Vsevolod [243]

Answer:

The sum of the first 20 terms is -1440.

Step-by-step explanation:

We want to find the sum of the first 20 terms of the arithmetic sequence:

4, -4, -12, -20...

The sum of an arithmetic sequence is given by:

$\displaystyle S=\frac{k}{2}(a+x_k)$

Where k is the number of terms, a is the initial term, and x_k is the last term.

Since we want to find the sum of the first 20 terms, k = 20.

Our initial term a is 4.

Our last term is also the 20th term as we want the sum of the first 20 terms.

To find the 20th term, we can write an explicit formula for our sequence. The explicit formula for an arithmetic sequence is given by:

$x_n=a+d(n-1)$

Where a is the initial term, d is the common difference, and n is the nth term.

Our initial term is 4. From the sequence, we can see that our common difference is -8 since each subsequent term is eight less than the previous term. Therefore:

$x_n=4-8(n-1)$

Then the last or 20th term is:

$x_{20}=4-8(20-1)=4-8(19)=-148$

Therefore, the sum of the first 20 terms are:

$\displaystyle\begin{aligned} S_{20}&=\frac{(20)}{2}\left((4)+(-148))\\&=10(-144) \\&= -1440\end{aligned}$

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