If f(x) = 3x – 2 and g(x) = x2 + 1, find f [g(-3)] and g[1–3)].
1 answer:
You might be interested in
$4,000 is invested in ABC's stock and $11,000 is invested in her market account
Step-by-step explanation:
Susan purchased company ABC's stock and invested the balance in her money market account
- ABC's stock yielded 13% last year and her money market account yielded 5% last year
- Susan's initial investments amount to $15000, and the annual income is $1070
We need to find how much money is invested in stock and how much is invested in her money market account
Assume that she invested $x in ABC's stock and $y in her money market account
∵ She invested $x in ABC's stock
∵ She invested $y in her market account
∵ Her initial investments amount is $15000
∴ x + y = 15000 ⇒ (1)
The interest formula is I = Prt, where P is the initial investment, r is the rate of interest in decimal and t is the time
In ABC's stock:
∵ She invested $x
∴ P = x
∵ The rate is 13%
∴ r = 13% = 13 ÷ 100 = 0.13
∵ t = 1
- Substitute all of these values in the formula of interest above
∴ = x(0.13)(1)
∴ = 0.13x
In her market account:
∵ She invested $y
∴ P = y
∵ The rate is 5%
∴ r = 5% = 5 ÷ 100 = 0.05
∵ t = 1
- Substitute all of these values in the formula of interest above
∴ = y(0.05)(1)
∴ = 0.05y
∵ Her annual income is $1070
- Add the interest of ABC's stock and the interest of her market
account, equate the sum by 1070
∴ 0.13x + 0.05y = 1070 ⇒ (2)
Now we have a system of equations to solve it
Multiply equation (1) by -0.05 to eliminate y
∵ -0.05x - 0.05y = -750 ⇒ (3)
- Add equations (2) and (3)
∴ 0.08x = 320
- Divide both sides by 0.08
∴ x = 4000
- Substitute value of x in equation (1) to find y
∵ 4000 + y = 15000
- Subtract 4000 from both sides
∴ y = 11000
$4,000 is invested in ABC's stock and $11,000 is invested in her market account
Learn more:
You can learn more about the system of equations in brainly.com/question/2115716
#LearnwithBrainly
Answer:
x(t) = 2000 - e^(-k*t)
Step-by-step explanation:
Interpretation:
No . infected student = x
Total student = 2000
rate of infected students = dx / dt
not-infected student = 200 - x
The general rate at which student are infected can be expressed as below:
dx / dt = k * ( 2000 - x )
To develop an expression of x(t) we integrate the above expression by separating variables:
dx / (2000 - x ) = k * dt
Now integrate:
@ t = 0 , infected students x = 0
Hence,
C = - ln (2000)