y = x³ + 3x² - x - 3
0 = x³ + 3x² - x - 3
0 = x²(x) + x²(3) - 1(x) - 1(3)
0 = x²(x + 3) - 1(x + 3)
0 = (x² - 1)(x + 3)
0 = (x² + x - x - 1)(x + 3)
0 = (x(x) + x(1) - 1(x) - 1(1))(x + 3)
0 = (x(x + 1) - 1(x + 1))(x + 3)
0 = (x - 1)(x + 1)(x + 3)
0 = x - 1 or 0 = x + 1 or 0 = x + 3
+ 1 + 1 - 1 - 1 - 3 - 3
1 = x or -1 = x or -3 = x
Solution Set: {-3, -1, 1}
<h3>
Answer: n+15</h3>
=======================================================
Explanation:
- n = number of minutes
- cost of company X = 3n+30
- cost of company Y = 2n+15
To find out how much more company X charges, we subtract the two cost expressions
CompanyX - CompanyY = (3n+30)-(2n+15) = 3n+30-2n-15 = n+15 which is the final answer.
--------------
An example:
Let's say you talk on the phone for n = 20 minutes.
Company X would charge you 3n+30 = 3*20+30 = 90 cents
Company Y would charge you 2n+15 = 2*20+15 = 55 cents
The difference of which is 90-55 = 35 cents.
If you plugged n = 20 into the n+15 expression we got, then n+15 = 20+15 = 35 matches up with the previous 35 cents.
This example helps confirm the answer. I'll let you try out other examples.
Answer:
Step-by-step explanation:
Given problem: C(x,y) = 36x + 48y
constraint: 100x^0.6y^0.4
Using langrange Multiplier,
36 = 0.6(100)x^-0.4y^0.4λ i
48 = 0.4(100)x^0.6y^-0.6λ ii
dividing the equations we have:
x = 2y
substituting into the constraint
p(x,y) = 100 *(2y)^0.6 y^0.4 = 100*2^0.6 *y
5000 = 151.572y
y = 329.876 labor units
x = 659.752 capital units
Minimum cost = 36(659.752) +48(329.876) = $39585.12
Answer: (4, 3)
Step-by-step explanation:
The formula for coordinate of the mid point is given as :
Mid point = (
, 
)
= 9
= -1
= 9
= -3
Substituting the values into the formula , we have :
Mid-point = (
, 
)
Mid-point = ( 
, 
)
Mid - point = ( 4 , 3)
X +x²= 132
x +x²-132= 132-132
x²+x -132 = 0
(x-11) (x+12) = 0
x-11 = 0 X+12=0
x-11+11 = 0+11 X+12-12=0-12
x =11 x= -12
Check
x +x²= 132 x +x²= 132
-12 +-12²= 132 11 +11²= 132
-12 + 144 = 132 11+ 121=132
132= 132 132=132
Since the problem says positive the answer is (11,121)
