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Y_Kistochka [10]

3 years ago

10

Albert mixes 10 grams of 15% sugar syrup and 25 grams of 10% sugar syrup. C What is the concentration of sugar in the mixture?

1 answer:

ser-zykov [4K]3 years ago

4 0

Answer:

4

Step-by-step explanation:

Given :

10 grams of 15% sugar syrup;

25 grams of 10% sugar syrup

Therefore,

(10grams * (15/100)) + (25 grams * (10/100))

(10 * 0.15) + (25 * 0.1)

1.5 + 2.5

= 4 grams

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Integral of x"2+4/x"2+4x+3

dolphi86 [110]

I'm guessing you mean

$\displaystyle \int\frac{x^2+4}{x^2+4x+3}\,\mathrm dx$

First, compute the quotient:

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Split up the remainder term into partial fractions. Notice that

<em>x</em> ² + 4<em>x</em> + 3 = (<em>x</em> + 3) (<em>x</em> + 1)

Then

$\displaystyle \frac{4x-1}{x^2+4x+3} = \frac a{x+3} + \frac b{x+1} \\\\ \implies 4x - 1 = a(x+1) + b(x+3) = (a+b)x + a+3b \\\\ \implies a+b=4 \text{ and }a+3b = -1 \\\\ \implies a=\frac{13}2\text{ and }b=-\frac52$

So the integral becomes

$\displaystyle \int \left(1 + \frac{13}{2(x+3)} - \frac{5}{2(x+1)}\right) \,\mathrm dx = \boxed{x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C}$

We can simplify the result somewhat:

$\displaystyle x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C \\\\ = x + \frac12 \left(13\ln|x+3| - 5\ln|x+1|\right) + C \\\\ = x + \frac12 \left(\ln\left|(x+3)^{13}\right| - \ln\left|(x+1)^5\right|\right) + C \\\\ = x + \frac12 \ln\left|\frac{(x+3)^{13}}{(x+1)^5}\right| + C \\\\ = \boxed{x + \ln\sqrt{\left|\frac{(x+3)^{13}}{(x+1)^5}\right|} + C}$

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How do you use trigonometric ratios to solve for a missing side or angle of a right triangle?

Kisachek [45]

Answer:

the sine of the angle of one corner equals the opposite side divided by the hypotenuse.

the cosine of the angle of one corner equals the adjacent side divided by the hypotenuse.

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3 0

3 years ago

Read 2 more answers

$13:50 to 6 pounds what the ratio

AleksAgata [21]

Answer:

$2.25: 1 pound

Step-by-step explanation:

13.50 divided by 6= 2.25

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3 years ago

Priscilla is on her school’s swim team. Her coach has noted the number of laps Priscilla and five of her teammates can swim with

ruslelena [56]

Answer:

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Step-by-step explanation:

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Median: 5

3, 4, 5, 5, 6, 7,

Mode: 5

3, 4, 5, 5, 6, 7

2 fives

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2 years ago

A family went to a baseball game. The cost to park cars was $5 and the cost per ticket was $21. Write a linear function in the f

Sophie [7]

Answer:

The total cost $y$ in dollars of going to the baseball game for $x$ people of a family can be given as:

$y=21x+5$

Step-by-step explanation:

Given:

At a baseball game:

Cost of car parking = $5

Cost per ticket = $21

To write an equation in the form of $y=mx+b$ representing the total cost of going to the baseball game.

Solution:

The total number of people in the family is = $x$

Using unitary method to find the cost of tickets for $x$ persons.

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Thus, the total cost $y$ in dollars of going to the baseball game for $x$ people of a family can be given as:

$y=21x+5$

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