Answer: Identify which of the following functions are eigenfunctions of the operator d/dx: (a) eikx, (b) cos kx, (c) k, (d) kx, (e) e−ax2
Step-by-step explanation: First, we going to apply the operator derivate to each item. Remember that a function f is an eigenfunction of D if it satisfies the equation
Df=λf, where λ is a scalar.
a) D(eikx)/dx= ik*eikx, then the function is a eigenfunction and the eingenvalue is ik.
b) D(cos kx)/dx= -ksen kx, then the funcion is not a eigenfunction.
c) D(k)/dx=0, then the funcion is not a eigenfunction.
d) D(kx)/dx=k, then the funcion is not a eigenfunction.
e) D(e-ax2)/dx= -2ax*e-ax2, then the function is a eigenfunction and the eingenvalue is -2ax
Answer:
The monthly payment for this loan is $127.80
Step-by-step explanation:
The formula of the monthly payment is
- P is the initial amount of the loan
- n is the period of the time
- t is the time of the loan
∵ Mario is taking a $2,900, 2-year loan with an APR of 5.44%
∴ P = 2,900
∴ t = 2
∵ ART means annual percent rate
∴ r = 5.44% = 5.44 ÷ 100 = 0.0544
∴ n = 12
→ Substitute all these values in the formula above
∵ M.P = 
→ use your calculator to find the answer
∴ M.P = 127.7992528
→ Round it to the nearest cent ⇒ 2d.p
∴ M.P = 127.80
∴ The monthly payment for this loan is $127.80
Answer:
3 bars
Step-by-step explanation:
Total no. of gold bars = 24.
Fraction of bar captain allocated to himself = 1/3 of the bars
no. of bars he allocated to himself = 1/3 of 24 = 1/3 * 24 = 8
Fraction of bar captain allocated to his friend bill = 1/4 of the bars
no. of bars he allocated to his friend bill = 1/4 of 24 = 1/4 * 24 = 6
No . of bars captain allocated to rest of crew = 7
Total no of bars which are allocated altogether =
no. of bars he allocated to himself +no. of bars he allocated to his friend bill +No . of bars captain allocated to rest of crew
substituting the value of above summation variable as calculated above we have
Total no of bars which are allocated altogether = 8+6+7 = 21
No. of bars left = total no. of bars - Total no of bars which are allocated altogether = 24 - 21 = 3
Thus 3 gold bars are left.
Answer:
equation involves an equal sign, ' = '
while expression does not have an equal sign.
for example:
an equation is 5x² × 3 = y
an expression is 2xy + 3
