Find the difference?<br> (2-5i) - (3+4i)

How many kilograms of a 5% salt solution and how many kilograms of a 15% salt solution must be mixed together to make 45kg of an

JulsSmile [24]

Answer:

31.5 kilograms of a 5% salt solution and 13.5 kilograms of a 15% salt solution must be mixed together to make 45kg of an 8% salt solution .

Step-by-step explanation:

Let us assume that the number of kilograms of a 5% salt solution used be x .

Let us assume that the number of kilograms of a 15% salt solution used be y .

As given

A 5% salt solution and 15% salt solution must be mixed together to make 45kg of an 8% salt solution .

Equation becomes

x + y = 45

5% is written in the decimal form .

$= \frac{5}{100}$

= 0.05

15% is written in the decimal form .

$= \frac{15}{100}$

= 0.15

8% is written in the decimal form .

$= \frac{8}{100}$

= 0.08

Thus

Concentration of 5% salt solution × Number of kilograms of 5% salt solution used + Concentration of 15% salt solution × Number of kilograms of 15% solution used = Concentration of 8% salt solution × Number of kilograms of 8% salt solution

Thus

0.05x + 0.15y = 0.08 × 45

Simplify the above

$\frac{5x}{100} + \frac{15y}{100} = \frac{8\times 45}{100}$

5x + 15y = 360

Thus two equations becomes

x + y = 45

5x + 15y = 360

Multiply x + y = 45 by 5 and subtracted from 5x + 15y = 360 .

5x - 5x + 15y - 5y = 360 - 225

10y = 135

$y = \frac{135}{10}$

y = 13.5 kilograms

Put value of y in the equation

x + 13.5 = 45

x = 45 - 13.5

x = 31.5 kilograms

Therefore the 31.5 kilograms of a 5% salt solution and 13.5 kilograms of a 15% salt solution must be mixed together to make 45kg of an 8% salt solution .

5 0

3 years ago

Whats the intrgral of <img src="https://tex.z-dn.net/?f=%20%5Cint%20%20%5Cfrac%7Bx%5E2%2Bx-3%7D%7B%28x%5E3%2Bx%5E2-4x-4%29%5E2%7

rosijanka [135]

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

Notice that $x^3+x^2-4x-4=x^2(x+1)-4(x+1)=(x-2)(x+2)(x+1)$ . Decompose the integrand into partial fractions:

$\dfrac{x^2+x-3}{(x-2)^2(x+2)^2(x+1)^2}$
$=\dfrac1{3(x+1)}-\dfrac{11}{32(x+2)}-\dfrac1{3(x+1)^2}-\dfrac1{16(x+2)^2}+\dfrac1{96(x-2)}+\dfrac1{48(x-2)^2}$

Integrating term-by-term, you get

$\displaystyle\int\frac{x^2+x-3}{(x^3+x^2-4x-4)^2}\,\mathrm dx$
$=-\dfrac1{48(x-2)}+\dfrac1{3(x+1)}+\dfrac1{16(x+2)}+\dfrac1{96}\ln|x-2|+\dfrac13\ln|x+1|-\dfrac{11}{32}\ln|x+2|+C$

5 0

4 years ago

The data set shows the numbers of hours students study the week before a test. Find and interpret the mean absolute deviation of

patriot [66]

Step-by-step explanation:

3 + 4 + 5 + 6 + 6 + 7 + 8 + 8 + 9 + 9 / total of numbers or 10 = 65 ÷ 10 = 6.5 This is the mean.

3 - 6.5 = 3.5

4 - 6.5 = 2.5

5 - 6.5 = 1.5

6 - 6.5 = 0.5

7 - 6.5 = 0.5

8 - 0.5 = 7.5

9 - 0.5 = 8.5

MAD = 1.7

4 0

3 years ago

Bobby is helping buy meats for grilling for the school picnic he bought 10 pounds of a dollar and 1.69per pound 100 pounds of ha

lions [1.4K]

The hot dogs...1000x 2.09 is $2090

5 0

3 years ago

Evan earns $21.50 per hour for 25 hours and time and a half for overtime. If he worked 5 hours

Andrei [34K]

21.50 x 25 = 537.50
10.75 x 5 = 53.75

537.50 + 53.75 = 591.25

4 0

3 years ago

Find the difference? (2-5i) - (3+4i) - (-2+i)