you just have to move the decimal point 9 places to the right thats an easy trick to remember 1849900000
Answers:
- <u>24000 dollars</u> invested at 4%
- <u>18000 dollars</u> was invested at 7%
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Work Shown:
x = amount invested at 4%
If she invests x dollars at 4%, then the rest (42000-x) must be invested at the other rate of 7%
She earns 0.04x dollars from that first account and 0.07(42000-x) dollars from the second account
This means we have
0.04x+0.07(42000-x)
0.04x+0.07*42000-0.07x
0.04x+2940-0.07x
-0.03x+2940
This represents the total amount of money earned after 1 year.
We're told the amount earned in interest is $2220, so we can say,
-0.03x+2940 = 2220
-0.03x = 2220-2940
-0.03x = -720
x = -720/(-0.03)
x = 24000 dollars is the amount invested at 4%
42000-x = 42000-24000 = 18000 dollars was invested at 7%
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As a check, we can see that
18000+24000 = 42000
and also
0.04x = 0.04*24000 = 960 earned from the first account
0.07*18000 = 1260 earned from the second account
1260+960 = 2220 is the total interest earned from both accounts combined
This confirms our answers.
To help you with it, plug-in 15 in each equation and see what you get!
Answer:
AB/DE=BC/EF=AC/DF
Step-by-step explanation:
Corresponding segments are designated by letters in corresponding positions in the triangle names. For example, of one segment is designated using the 1st and 2nd letters of one triangle name (such as AB), then the corresponding segment is designated using the 1st and 2nd letters of the other triangle name (such as DE).
Corresponding segments are proportional in length. Corresponding angles are congruent.




so the characteristic solution is

As a guess for the particular solution, let's back up a bit. The reason the choice of

works for the characteristic solution is that, in the background, we're employing the substitution

, so that

is getting replaced with a new function

. Differentiating yields


Now the ODE in terms of

is linear with constant coefficients, since the coefficients

and

will cancel, resulting in the ODE

Of coursesin, the characteristic equation will be

, which leads to solutions

, as before.
Now that we have two linearly independent solutions, we can easily find more via variation of parameters. If

are the solutions to the characteristic equation of the ODE in terms of

, then we can find another of the form

where


where

is the Wronskian of the two characteristic solutions. We have






and recalling that

, we have