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3 years ago

Integrate 1/x(x-1) dx

Mathematics

1 answer:

amm18123 years ago

7 0

Decompose the integrand into partial fractions:

1 / (x (x - 1)) = 1/(x - 1) - 1/x

Then

∫ 1 / (x (x - 1)) dx = ln|x - 1| - ln|x| + C = ln|1 - 1/x| + C

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6(x+9)+7x+14= Distributive Property=simplifying am Expression By multiplying a number a sum or difference.

barxatty [35]

Answer:

13x+38

Step-by-step explanation:

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3 years ago

Enter your answer and shot all the steps that you use to solve this problem in the space provided. This diameter of a tire is 2.

alexdok [17]

A- The circumference of the tire is about 7.85 feet

B- The tire will rotate about 672 times to travel 1 mile

Step-by-step explanation:

The formula of the circumference of a circle is C = π d, where d is the diameter of the circle
If a circle rotates for n turns and make a distance S, then n = $\frac{S}{C}$

∵ The diameter of a tire is 2.5 ft

∴ d = 2.5 ft

∵ C = π d, where C is the circumference of tire

∴ C = π(2.5) = 7.85398 ft

∴ C ≅ 7.85 feet

A- The circumference of the tire is about 7.85 feet

∵ The tire have to travel 1 mile

∵ 1 mile = 5280 feet

∴ S = 5280 feet

- To find the number of rotation of the tire divide S by C

∵ n = $\frac{S}{C}$

∴ n = $\frac{5280}{7.85}$ ≅ 672 revolution

B- The tire will rotate about 672 times to travel 1 mile

Learn more;

You can learn more about rotation in brainly.com/question/2860697

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3 years ago

The concentration C (in mg/dl), of an antibiotic in a patient’s bloodstream per hour, t, is given by:

lilavasa [31]

We want the concentration of the antibiotic to be at a minimum of 5 mg/dL, so we want to find the time interval, where $t>0$ , for which $C(t)\ge5$ .

We have

$\dfrac{55t}{t^2+25}\ge5\iff55t\ge5t^2+625\iff t^2-11t+25\le0$

Completing the square, we get

$t^2-11t+\dfrac{121}4-\dfrac{121}4+25\le0\iff\left(t-\dfrac{11}2\right)^2\le\dfrac{21}4$

$\implies\left|t-\dfrac{11}2\right|\le\dfrac{\sqrt{21}}2$

$\implies-\dfrac{\sqrt{21}}2\le t-\dfrac{11}2\le\dfrac{\sqrt{21}}2$

$\implies\dfrac{11-\sqrt{21}}2\le t\le\dfrac{11+\sqrt{21}}2$

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3 years ago

Dominque lives One in 1 and

Ludmilka [50]

The answer to your question is 3/4

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3 years ago

Question in the photo

melisa1 [442]

Answer:

Step-by-step explanation:

To make this not a function, the same input would need to go to two different outputs

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3 years ago

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