
Substituting this into the other ODE gives

Since
, it follows that
. The ODE in
has characteristic equation

with roots
, admitting the characteristic solution

From the initial conditions we get



So we have

Take the derivative and multiply it by -1/4 to get the solution for
:

Answer:
George has 64 nickel and 32 dimes.
Step-by-step explanation:
Normally, we have:
One nickel = 5 cents
One dime = 10 cents
One dollar = 100 cents
Therefore, total number of cents that George has can be calculated as follows:
Total number of cents = $6.40 * 100 = 640 cents
Based on the above, we have:
640 cents = 640 / 5 = 128 nickel
640 cents = 640 / 10 = 64 dimes
Therefore, we have:
128 nickel = 64 dimes
Divide through by 2 in order to share 640 cents equally, we have:
128 nickel / 2 = 64 dimes / 2 => 64 nickel = 32 dimes
Since 64 minus 32 is equal to 32, it therefore implies that George has 64 nickel and 32 dimes.
Answer:
A. A reflection over the x-axis
Answer:
5·7
Step-by-step explanation:
From your knowledge of multiplication tables, you know that ...
5×7 = 35
Both 5 and 7 are prime numbers, so that is the prime factorization.