Answer:
Size of each monthly payment = $161.69 per month
Step-by-step explanation:
Given:
Value of property = $20,000
Downpayment = 20%
Number of payment = 12 x 10 = 120
Interest rate = 4% = 4% / 12 = 0.33 %
Computation:
Loan balance = 20,000 - 20%
Loan balance = $16,000
A] Size of each monthly payment [In Excel]
Size of each monthly payment = PMT(0.33%,120,16000,0)
Size of each monthly payment = $161.69 per month
Steps:
1) determine the domain
2) determine the extreme limits of the function
3) determine critical points (where the derivative is zero)
4) determine the intercepts with the axis
5) do a table
6) put the data on a system of coordinates
7) graph: join the points with the best smooth curve
Solution:
1) domain
The logarithmic function is defined for positive real numbers, then you need to state x - 3 > 0
=> x > 3 <-------- domain
2) extreme limits of the function
Limit log (x - 3) when x → ∞ = ∞
Limit log (x - 3) when x → 3+ = - ∞ => the line x = 3 is a vertical asymptote
3) critical points
dy / dx = 0 => 1 / x - 3 which is never true, so there are not critical points (not relative maxima or minima)
4) determine the intercepts with the axis
x-intercept: y = 0 => log (x - 3) = 0 => x - 3 = 1 => x = 4
y-intercept: The function never intercepts the y-axis because x cannot not be 0.
5) do a table
x y = log (x - 3)
limit x → 3+ - ∞
3.000000001 log (3.000000001 -3) = -9
3.0001 log (3.0001 - 3) = - 4
3.1 log (3.1 - 3) = - 1
4 log (4 - 3) = 0
13 log (13 - 3) = 1
103 log (103 - 3) = 10
lim x → ∞ ∞
Now, with all that information you can graph the function: put the data on the coordinate system and join the points with a smooth curve.
Answer:
7
Step-by-step explanation:
Add 10,11, and 5
10+11+5=26
subtract 26 from 33
33-26=7
1) -3(5x+2y=-3)⇒ -15x-6y=9
⇒ -9x=27
2(3x+3y=9)⇒ 6x+6y=18
2) -9x/-9=27/-9 ⇒ x=-3
3) 3(-3)+3y=9⇒ -9+9+3y=9+9⇒ 3y/3=18/3⇒ y=6
Answer: (-3,6)
Reasoning:
Step 1) In order to eliminate, first I had to multiple the first equation by -3 and the second by 2 so that when combining the equations y would cancel each other out so that I could solve for x. <em>Note: There are many combinations as to how you could multiple the equations so that either the x or y would cancel out.
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Step 2) Once y is eliminated, solve for x.
Step 3) Now plug x back into one of the original equations and solve for y. <em>Note: Plug x back into one of the original equations, not the equations that were changed by multiplication,</em>
Answer:
4 cm
Step-by-step explanation:
The equation of a parabola with its vertex at the origin can be written as ...
y = 1/(4p)x^2
The problem statement tells us that one point on the parabola is (x, y) = (12, 9). We can put these values into the equation and solve for p, the distance from the focus to the vertex.
9 = 1/(4p)(12^2)
9×4/144 = 1/p = 1/4 . . . . . . . . multiply by the inverse of the coefficient of 1/p
Then p = 4, and the bulb is 4 cm from the vertex.
