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meriva
2 years ago
5

Integrate 1/x(x-1) dx

Mathematics
1 answer:
amm18122 years ago
7 0

Decompose the integrand into partial fractions:

1 / (<em>x</em> (<em>x</em> - 1)) = 1/(<em>x</em> - 1) - 1/<em>x</em>

Then

∫ 1 / (<em>x</em> (<em>x</em> - 1)) d<em>x</em> = ln|<em>x</em> - 1| - ln|<em>x</em>| + C = ln|1 - 1/<em>x</em>| + C

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The Henley's took out a loan for $195,000 to purchase a home. At a 4.3% interest rate
ella [17]

Interest paid after 30 years is $494,546.99.

Solution:

Principal (P) = $195,000

Interest rate (r) = 4.3%

Time (t) = 30 years

n = number of times interest calculated per year

n = 1

Compound interest formula:

$A=P\left(1+\frac{r}{n}\right)^{n t}

where A is the final amount

$A=195000\left(1+\frac{4.3\%}{1}\right)^{1\times 30}

$A=195000\left(1+\frac{4.3}{100}\right)^{30}

$A=195000\left(\frac{100+4.3}{100}\right)^{30}

$A=195000\left(\frac{104.3}{100}\right)^{30}

A = 689546.99

Interest = Amount  - Principal

             = 689546.99 - 195000

             = 494546.99

Interest paid after 30 years is $494,546.99.

6 0
3 years ago
1/6 +3/8 = in simplest form
MrRa [10]
1/6+3/8=13/24 (13/24 is the simplest form in this case)
4 0
3 years ago
A woman starts out walking due north for 2 miles, and then she turns due west and continues for another 2 miles. How far from he
Mrac [35]
For this case we can model the problem as a rectangle triangle.
 We have:
 Length of the sides of the triangle.
 We want to find:
 Length of the hypotenuse.
 Using the Pythagorean theorem we have:
 d ^ 2 = 2 ^ 2 + 2 ^ 2&#10;
 d =  \sqrt{2 ^ 2 + 2 ^ 2} &#10;&#10;d =  \sqrt{4 + 4} &#10;&#10;d =  \sqrt{8} &#10;&#10;d =  2\sqrt{2} &#10;
 Answer:
 
She is:
 
d = 2\sqrt{2}
 miles far from her starting point
4 0
3 years ago
When you are trying to find the endpoint when given the midpoint and one point, what would the new formula be? Manipulate the fo
MariettaO [177]

Answer:

(x_2,y_2) = (2x_m - x_1 ,2y_m - y_1 )

Step-by-step explanation:

Given

\left(\frac{x_1+\:x_2}{2},\:\:\frac{y_{1\:}+y_2}{2}\right)\:=\:\left(x_m,\:y_m\right)

Required

Determine x2, y2

Start by splitting the expression

x_m = \left(\frac{x_1+\:x_2}{2}) and y_m = (\frac{y_{1\:}+y_2}{2})

Solving for x2 in x_m = \left(\frac{x_1+\:x_2}{2})

Multiply through by 2

2 * x_m = \frac{x_1 + x_2}{2} * 2

2x_m = x_1 + x_2

Make x2 the subject;

x_2 = 2x_m - x_1

Similarly:

y_m = (\frac{y_{1\:}+y_2}{2})

Multiply through by 2

2 * y_m = \frac{y_1 + y_2}{2} * 2

2y_m = y_1 + y_2

Make y2 the subject;

y_2 = 2y_m - y_1

Hence:

(x_2,y_2) = (2x_m - x_1 ,2y_m - y_1 )

7 0
3 years ago
7-7(5+x)-9x in simplified​
Luden [163]

Answer:

-28 - 16x

Step-by-step explanation:

7-7(5+x)-9x

Distribute

7 - 35 -7x -9x

Combine like terms

-28 - 16x

5 0
2 years ago
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