Terms: 3n, 5p, 3, n
Coefficients: 3, 4, 1
Constants: 3
Simplified: 4n+5p+n
Answer:
x=12 and y=6
Step-by-step explanation:
because the angle are same and equal
Let <em>f(x)</em> = (<em>x</em> ² - 1)³. Find the critical points of <em>f</em> in the interval [-1, 2]:
<em>f '(x)</em> = 3 (<em>x</em> ² - 1)² (2<em>x</em>) = 6<em>x</em> (<em>x </em>² - 1)² = 0
6<em>x</em> = 0 <u>or</u> (<em>x</em> ² - 1)² = 0
<em>x</em> = 0 <u>or</u> <em>x</em> ² = 1
<em>x</em> = 0 <u>or</u> <em>x</em> = 1 <u>or</u> <em>x</em> = -1
Check the value of <em>f</em> at each of these critical points, as well as the endpoints of the given domain:
<em>f</em> (-1) = 0
<em>f</em> (0) = -1
<em>f</em> (1) = 0
<em>f</em> (2) = 27
So max{<em>f(x)</em> | -1 ≤ <em>x </em>≤ 2} = 27.
Answer:
The crossover point for Time 
Step-by-step explanation:
From the question we are told that
The total rooms rented for the year is 
Time's fixed cost is r = $61,000
Time's variable cost is 
$12.5 per room
Duffy's Maid Service fixed cost is 
$25,000
Duffy's Maid Service variable cost is 
$18.00 per room
The cross over point for Time is mathematically represented as
substituting values
Present value, PV = $500
Future value, FV = 2*PV = 2*500 = $1,000
Rate, r = 4% = 0.04
Compounding times in a year, n = 4 (compounded quarterly)
Time, t = ??
The future value expression is stated as:
FV = PV (1+r/n)^nt
Substituting;
1000 = 500 (1+0.04/4)^4t
2 = (1.01)^4t
ln 2 = 4t ln 1.01
0.6931 = 4t* 0.00995
0.6931 = 0.0398t
t = 17.414 years
Time required for the amount to double is 17.41 years.
