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4vir4ik [10]
3 years ago
14

Find the general indefinite integral. (Use C for the constant of integration. Remember to use absolute values where appropriate.

) integral 9 + Squareroot x + x/x dx x + Squareroot x + 9 log (x) +
Mathematics
1 answer:
Maru [420]3 years ago
4 0

Answer:

9\text{ln}|x|+2\sqrt{x}+x+C

Step-by-step explanation:

We have been an integral \int \frac{9+\sqrt{x}+x}{x}dx. We are asked to find the general solution for the given indefinite integral.

We can rewrite our given integral as:

\int \frac{9}{x}+\frac{\sqrt{x}}{x}+\frac{x}{x}dx

\int \frac{9}{x}+\frac{1}{\sqrt{x}}+1dx

Now, we will apply the sum rule of integrals as:

\int \frac{9}{x}dx+\int \frac{1}{\sqrt{x}}dx+\int 1dx

9\int \frac{1}{x}dx+\int x^{-\frac{1}{2}}dx+\int 1dx

Using common integral \int \frac{1}{x}dx=\text{ln}|x|, we will get:

9\text{ln}|x|+\int x^{-\frac{1}{2}}dx+\int 1dx

Now, we will use power rule of integrals as:

9\text{ln}|x|+\frac{x^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}+\int 1dx

9\text{ln}|x|+\frac{x^{\frac{1}{2}}}{\frac{1}{2}}+\int 1dx

9\text{ln}|x|+2x^{\frac{1}{2}}+\int 1dx

9\text{ln}|x|+2\sqrt{x}+\int 1dx

We know that integral of a constant is equal to constant times x, so integral of 1 would be x.

9\text{ln}|x|+2\sqrt{x}+x+C

Therefore, our required integral would be 9\text{ln}|x|+2\sqrt{x}+x+C.

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A bacteria culture contains 1500 bacteria initially and doubles every hour. (a) Find a function N that models the number of bact
Tpy6a [65]

Answer: a) N(t)=1500(2)^t

b) 25165824000

Step-by-step explanation:

The exponential equation for growth is given by :-

y= ab^t , where a= initial value , b =multiplicative growth factor and t = time.

Given : A bacteria culture contains 1500 bacteria initially and doubles every hour.

i.e. a = 1500 and b= 2

Then, the function N that models the number of bacteria after t hours will be :

N(t)=1500(2)^t

To find , the number of bacteria after 24 hours , we put t= 24 in above equation , we get

N(24)=1500(2)^{24}\\\\=1500(16777216)=25165824000

Hence, the number of bacteria after 24 hours is 25165824000.

7 0
3 years ago
compará y ordena de mayor a menor las siguientes cantidades 23.4 ,15/20 ,32.245,.056,4/10,50/100,8/9,.009,9/1000 y 54.45​
nignag [31]

Answer:

El orden de mayor a menor es:

54.45 ; 32.245 ; 23.4 ; 8/9 ; 15/20 ; 50/100 ; 4/10 ; 0.056 ; 9/1000

Step-by-step explanation:

El mayor número será el que tenga el mayor entero, o  si tienen el mismo entero será aquel que tenga el primer decimal mayor de izquierda a derecha,  o si tienen el mismo se observa el siguiente decimal y así sucesivamente.

Para ordenar y comparar las cantidades es conveniente en primer lugar pasar todos los números a decimales. Para convertir una fracción en un decimal, debes dividir el numerador entre el denominador.

Entonces, en este caso el valor decimal de cada cantidad (o una aproximación) es:

23.4

15/20= 0.75

32.245

0.056

4/10= 0.4

50/100= 0.5

8/9= 0.8888

0.009

9/1000= 0.009

54.45​

Entonces <u><em>el orden de mayor a menor es: </em></u>

<u><em> 54.45 ; 32.245 ; 23.4 ; 8/9 = 0.8888 ; 15/20 = 0.75 ; 50/100 = 0.5 ; 4/10 = 0.4 ; 0.056 ; 9/1000 = 0.009</em></u>

7 0
2 years ago
The triangle below is isosceles. Find the length of side xx in simplest radical form with a rational denominator.
coldgirl [10]

Answer:

Solution given:

Since the given triangle is isosceles and right angled triangle

perpendicular [p]=base[b]=x

hypotenuse [h]=6

we have

by using Pythagoras law

p²+b²=h²

x²+x²=6²

2x²=36

x²=36/2

x²=18

x=\sqrt{18}

<u>x</u>=\bold{3\sqrt{2}}

6 0
3 years ago
PLEASE ANSWER THE QUESTION ON THE SCREENSHOT ASAP!
mars1129 [50]
9 possibly could be the answer makes sense to me lol
4 0
3 years ago
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The cost of 50 pounds of beans is $?<br> Pls help!!
maksim [4K]

Answer:

69,78!!

Step-by-step explanation:

Espero te sirva  

4 0
3 years ago
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