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4 years ago

9

A perfume is to be mixed in the ratio of 3 drops of pure essence to 7 drops of alcohol. How many drops of pure essence should be

mixed with 56 drops of alcohol?

1 answer:

Lemur [1.5K]4 years ago

7 0

the anwser is 24 drops of essentail oil

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Find the general solution of the nonhomogeneous differential equation x^2y''-2y=3(x^2) -1, (x>0).

Ira Lisetskai [31]

Answer:

G.S= $C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}$

Step-by-step explanation:

We are given that non-homogeneous differential equation

$x^2y''-2y=3(x^2)-1$

It is Cauchy Euler equation

Substitute x=e^t x>0

Auxillary equation

$D'(D'-1)-2=0$

$D'^2-D'-2=0$

$(D'-2)(D'+1)=0$

$D'-2=0 \implies D'=2$

$D'+1=0\implies D'=-1$

Complementary solution

$y=C_1e^{-t}+C_2e^{2t}$

$y=C_1\frac{1}{x}+C_2x^2$

Particular solution

$y_p=\frac{3e^{2t}}{D'^2-D'-2}-\frac{e^{0t}}{D'^2-D'-2}$

$y_p=te^{2t}+\frac{1}{2}=x^2logx+\frac{1}{2}$

G.S= $C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}$

Hence, general solution G.S= $C_1\frac{1}{x}+C_2x^2+x^2logx+\frac{1}{2}$

6 0

4 years ago

The graphs of f(x) and g(x) are shown below. On a coordinate plane, a straight line with negative a slope represents f (x) = neg

juin [17]

Graph it to a then to b then to c and you will have your answer sikew

6 1

3 years ago

A store gives a discount of $20 for every purchase above 100. A customer buys clothes worth $78.04, groceries worth &24.81 a

Nadya [2.5K]

First figure out his total bill by adding up what he buys.

$\sf 78.04+24.81+17.96=\$120.81$

Now subtract the discount of $20 since his purchase was above $100:

$\sf 120.81-20=\boxed{\sf\$100.81}$

7 0

3 years ago

Read 2 more answers

PLEASE HELP!!! I NEED HELP URGENTLY

kirill [66]

Answer:

You would click (1,-5)

Step-by-step explanation:

The absolute minimum is the lowest point of the graph.

In all graphs, if it says minimum, it almost certainly means that lowest point, and if there are more than one, you would simply click on those.

It does not matter how many points there are, only that they are the lowest.

Therefore, it would be 1,-5.

3 0

3 years ago

Read 2 more answers

Georgia [21]

Answer:

see explanation

Step-by-step explanation:

The average rate of change over the closed interval [ a, b ] is

$\frac{f(b)-f(a)}{b-a}$

here [ a, b ] = [ 0, 8 ]

f(b) = f(8) = $\frac{16-2}{40-6}$ = $\frac{14}{34}$ = $\frac{7}{17}$

f(a) = f(0) = $\frac{-2}{-6}$ = $\frac{1}{3}$

f(b) - f(a) = $\frac{7}{17}$ - $\frac{1}{3}$ = $\frac{4}{51}$

average rate of change = $\frac{\frac{4}{51} }{8}$ = $\frac{1}{102}$

7 0

3 years ago