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2 years ago

What is the following product? root(3, 4) * sqrt(3)

Mathematics

1 answer:

gladu [14]2 years ago

3 0

Answer:

It’s option C

Step-by-step explanation: just took the quiz on edge

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\int (x+1)\sqrt(2x-1)dx

Nezavi [6.7K]

Answer:

$\int (x+ 1) \sqrt{2x-1} dx = \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15}(2x-1)^{\frac{5}{2}} + C$

Step-by-step explanation:

$\int (x+1)\sqrt {(2x-1)} dx\\Integrate \ using \ integration \ by\ parts \\\\u = x + 1, v'= \sqrt{2x - 1}\\\\v'= \sqrt{2x - 1}\\\\integrate \ both \ sides \\\\\int v'= \int \sqrt{2x- 1}dx\\\\v = \int ( 2x - 1)^{\frac{1}{2} } \ dx\\\\v = \frac{(2x - 1)^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}} \times \frac{1}{2}\\\\v= \frac{(2x - 1)^{\frac{3}{2}}}{\frac{3}{2}} \times \frac{1}{2}\\\\v = \frac{2 \times (2x - 1)^{\frac{3}{2}}}{3} \times \frac{1}{2}\\\\v = \frac{(2x - 1)^{\frac{3}{2}}}{3}$

$\int (x+1)\sqrt(2x-1)dx\\\\ = uv - \int v du$

$= (x +1 ) \cdot \frac{(2x - 1)^{\frac{3}{2}}}{3} - \int \frac{(2x - 1)^{\frac{3}{2}}}{3} dx \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ u = x + 1 => du = dx \ ]$

$= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \int (2x - 1)^{\frac{3}{2}}} dx\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{3}{2} + 1}}{\frac{3}{2} + 1}) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{5}{2}}}{\frac{5}{2} }) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15} \times (2x-1)^{\frac{5}{2}} + C\\\\$

6 0

3 years ago

Fill in the blank: To obtain the graph of y=2x+0.2, you can start with the graph of y=2x and translate it ___________.

Ad libitum [116K]

Answer:

Step-by-step explanation:

+0.2 will increase every y-value by 0.2, hence shifting the graph 0.2 units upwards

4 0

3 years ago

Read 2 more answers

A bag contains 28 counters all of different colours. Colin chooses one counter and gives it to

yawa3891 [41]

Answer:

756 ways

Step-by-step explanation:

Given

$Counters = 28$

$Selection = 2$

Required

Determine the number of ways

The first counter can be selected in 28 ways

The second can be selected in (28 - 1) ways

The number of selection is:

$Selection = 28 * (28 -1)$

$Selection = 28 * 27$

$Selection = 756$

<em>Hence, number of possible selection is 756</em>

6 0

2 years ago

how much simple interest will charged by the bank for a loan of RS.75000 for 3 months if rate is 4 1/4% per annum?

Anarel [89]

The simple interest is calculated using the formula,

$Simple \: Interest = \frac{P×T×R}{100} \:$
$P=RS. \: \: 75000 \:$
$T=3 \: months$
But remember that the in years (per annum).

Converting 3 months to years, we have,

$T = \frac{3}{12} = \frac{1}{4} \: years$

$R= 4 \frac{1}{4} = \frac{17}{4}$

Now let us plug in all these values into the simple interest formula,

$Simple \: Interest =RS. \: \frac{75000× \frac{1}{4} × \frac{17}{4} }{100} \:$

$Simple \: Interest = \:RS. \: \: 796.875$

5 0

3 years ago

Tina has 10 packages of yarn to knit a scarf. She uses ⅓ package of yarn for each inch of length she adds to the scarf. If Tina

Travka [436]

Answer: 30

Step-by-step explanation:

From the question, we are informed that Tina has 10 packages of yarn to knit a scarf and that he uses ⅓ package of yarn for each inch of length she adds to the scarf.

Since she used all the yarn, the length of the cloth would be:

= 10 ÷ 1/3

= 10 × 3

= 30 inch

7 0

2 years ago