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3 years ago

My attempts at solving this integral keep failing... I'd really appreciate some help :)

1 answer:

5 0

$\bf \displaystyle \int \cfrac{csc^2(x)}{1+cot(x)}\cdot dx\\\\
-----------------------------\\\\
u=1+cot(x)\implies \cfrac{du}{dx}=-csc^2(x)\implies \cfrac{du}{-csc^2(x)}=dx\\\\
-----------------------------\\\\
\displaystyle \int\cfrac{csc^2(x)}{u}\cdot \cfrac{du}{-csc^2(x)}\implies -\int \cfrac{1}{u}\cdot du
\\\\\\
-ln|u|+C\implies -ln|1+cot(x)|+C$

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An apartment complex rents an average of 2.3 new units per week. If the number of apartment rented each week Poisson distributed

masya89 [10]

Answer:

$P(X\leq 1) = 0.331$

Step-by-step explanation:

Given

Poisson Distribution;

Average rent in a week = 2.3

Required

Determine the probability of renting no more than 1 apartment

A Poisson distribution is given as;

$P(X = x) = \frac{y^xe^{-y}}{x!}$

Where y represents λ (average)

y = 2.3

<em>Probability of renting no more than 1 apartment = Probability of renting no apartment + Probability of renting 1 apartment</em>

<em />

Using probability notations;

$P(X\leq 1) = P(X=0) + P(X =1)$

Solving for P(X = 0) [substitute 0 for x and 2.3 for y]

$P(X = 0) = \frac{2.3^0 * e^{-2.3}}{0!}$

$P(X = 0) = \frac{1 * e^{-2.3}}{1}$

$P(X = 0) = e^{-2.3}$

$P(X = 0) = 0.10025884372$

Solving for P(X = 1) [substitute 1 for x and 2.3 for y]

$P(X = 1) = \frac{2.3^1 * e^{-2.3}}{1!}$

$P(X = 1) = \frac{2.3 * e^{-2.3}}{1}$

$P(X = 1) =2.3 * e^{-2.3}$

$P(X = 1) = 2.3 * 0.10025884372$

$P(X = 1) = 0.23059534055$

$P(X\leq 1) = P(X=0) + P(X =1)$

$P(X\leq 1) = 0.10025884372 + 0.23059534055$

$P(X\leq 1) = 0.33085418427$

$P(X\leq 1) = 0.331$

Hence, the required probability is 0.331

6 0

3 years ago

Solving the linear equations variable on one side

Brums [2.3K]

The pick up fee is $2.50.

After each mile, $1.95 is added.

That is, after the first mile, we have;

$\begin{gathered} \text{Fe}e=\text{ 2.50 + 1.95(1)} \\ \text{After the second mile, we have;} \\ Fee=\text{ 2.50+1.95(2)} \end{gathered}$

Isaac total charge = $27.46;

Generally, let the number of miles driven by the taxi be x, then we have;

$1.95x+2.50=27.46$

Solving for the number of miles Isaac travelled, we have;

$\begin{gathered} 1.95x=27.46-2.50 \\ 1.95x=24.96 \\ x=\frac{24.96}{1.95} \\ x=12.8\text{miles} \end{gathered}$

CORRECT OPTION:

$1.95x+2.50=27.46;\text{ Isaac traveled 12.8 miles.}$

4 0

1 year ago

The perimeters of square region S and rectangular region R are equal. If the sides of R are in the ratio 2 : 3, what is the rati

Ksivusya [100]

<h2>Answer:</h2>

The ratio of the area of region R to the area of region S is:

$\dfrac{24}{25}$

<h2>Step-by-step explanation:</h2>

The sides of R are in the ratio : 2:3

Let the length of R be: 2x

and the width of R be: 3x

i.e. The perimeter of R is given by:

$Perimeter\ of\ R=2(2x+3x)$

( Since, the perimeter of a rectangle with length L and breadth or width B is given by:

$Perimeter=2(L+B)$ )

Hence, we get:

$Perimeter\ of\ R=2(5x)$

i.e.

$Perimeter\ of\ R=10x$

Also, let " s " denote the side of the square region.

We know that the perimeter of a square with side " s " is given by:

$\text{Perimeter\ of\ square}=4s$

Now, it is given that:

The perimeters of square region S and rectangular region R are equal.

i.e.

$4s=10x\\\\i.e.\\\\s=\dfrac{10x}{4}\\\\s=\dfrac{5x}{2}$

Now, we know that the area of a square is given by:

$\text{Area\ of\ square}=s^2$

and

$\text{Area\ of\ Rectangle}=L\times B$

Hence, we get:

$\text{Area\ of\ square}=(\dfrac{5x}{2})^2=\dfrac{25x^2}{4}$

and

$\text{Area\ of\ Rectangle}=2x\times 3x$

i.e.

$\text{Area\ of\ Rectangle}=6x^2$

Hence,

Ratio of the area of region R to the area of region S is:

$=\dfrac{6x^2}{\dfrac{25x^2}{4}}\\\\=\dfrac{6x^2\times 4}{25x^2}\\\\=\dfrac{24}{25}$

6 0

3 years ago

Read 2 more answers

ILL MARK BRAINIEST IF YOU DO THIS CORRECTLY!!!

ehidna [41]

Answer:

76 percent done.

Step-by-step explanation:

Reasoning for this if its 76/100 you know that it will be 76. Or im Just got confused.

7 0

2 years ago

Find the value of x. Round to the nearest degree.

Fantom [35]

Answer:

x = 51

Step-by-step explanation:

Here, we want to find the value of x

To do this, we are going to use the appropriate trigonometric identity

We have the side facing the right angle ( hypotenuse) and the side facing the angle given (opposite)

The trigonometric identity that links both is the sine and it is the ratio of the opposite to the hypotenuse

Thus, we have it that;

sine x = 7/9

x = arisine (7/9)

x = 51

4 0

2 years ago