A manufacturing company plans to progressively increase its production capacity over the next few quarters. (A quarter is a peri
od of three months.) The increase in production can be modeled by the equation y = x6 − 25x4 + 199x2, where x is the number of quarters. What is the minimum duration required for the company to reach a production capacity of 4,975 units?
1 answer:
Answer:
5 months
Step-by-step explanation:
We assume that y represents production capacity, rather than <em>increase</em> in production capacity. Then we want to solve the 6th-degree equation ...
x^6 -25x^4 +199x^2 -4975 = 0
This can be factored in groups as ...
x^4(x^2 -25) + 199(x^2 -25) = 0
(x^4 +199)(x^2 -25) = 0
This has 4 complex solutions and 2 real solutions.
x^2 = 25
x = ±5
The duration required for capacity to reach 4975 units is 5 months.
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Hello,
1)
I suppose we must write correcty and corrects the mistakes!
f(x)=x+3
y=x+3
->x=y+3 exchange x and y
->y=x-3 solve for y
f^(-1)(x)=x-3=g(x)
Here are the mistakes:
(fog)(x)=f(g(x))=f(x-3)=(x-3)+3=x and not -x !
(gof)(x)=g(f(x))=g(x+3)=(x+3)-3=x and not -x!!
f(x) and g(x) ARE inverses each another.
2)
f(x)=1/(4x) x≠0
y=1/(4x)
->x=1/(4y)
->y=1/(4x)
g(x)=f^(-1)(x)=1/(4x)=f(x), x≠0
1)
I suppose we must write correcty and corrects the mistakes!
f(x)=x+3
y=x+3
->x=y+3 exchange x and y
->y=x-3 solve for y
f^(-1)(x)=x-3=g(x)
Here are the mistakes:
(fog)(x)=f(g(x))=f(x-3)=(x-3)+3=x and not -x !
(gof)(x)=g(f(x))=g(x+3)=(x+3)-3=x and not -x!!
f(x) and g(x) ARE inverses each another.
2)
f(x)=1/(4x) x≠0
y=1/(4x)
->x=1/(4y)
->y=1/(4x)
g(x)=f^(-1)(x)=1/(4x)=f(x), x≠0
Answer:
X-5Y-4Z+12=0
Step-by-step explanation:
Plan P1 = 3x-y+2z=1. with A=(1,1,2); B=(2,2,1); we must will find V1 from P1,
V1 =(3,-1,2) and AB = (2-1,2-1,1-2) = (1,1,-1) now we find V2 by vector product.
V2 =V1.X,AB =; (aplying sarrus method)
according to general plan formula a(X-Xo)+b(Y-Yo)+c(Z-Zo); V=(a,b,c)
V2=(-1,5,4) ; A=(1,1,2); so -(X-1)+5(Y-1)+4(z-2)=0 → -X+1+5Y-5+4Z-8=0 →
-X+5Y+4Z+1-5-8=0 → -X+5Y+4Z-12=0 (-1) → Plan equation X-5Y-4Z+12=0