Step-by-step explanation:
3. Between √9 and √16 or 3 nd 4
5. D
6. 7cubic inches
7. 8/45
8. 0.5 m
9. 4/25
Answer:
x = 250
y = 125
u(x,y) = 3125500
Step-by-step explanation:
As given,
The utility function u(x, y) = 100xy + x + 2y
= 2 ,
= 4
Now,
Budget constraint -
x +
y = 1000
⇒2x + 4y = 1000
So,
Let v(x, y) = 2x + 4y - 1000
Now,
By Lagrange Multiplier
Δu = Δv
⇒< 100y + 1, 100x + 2 > = < 2, 4 >
By comparing, e get
100y + 1 = 2 ........(1)
100x + 2 = 4 .........(2)
Divide equation (2) to equation (1) , we get

⇒2(100y+1) = 1(100x+2)
⇒200y + 2 = 100x + 2
⇒200y = 100x
⇒2y = x
Now,
As 2x + 4y = 1000
⇒2x + 2(2y) = 1000
⇒2x + 2x = 1000
⇒4x = 1000
⇒x = 250
Now,
As 2y = x
⇒2y = 250
⇒y =
= 125
∴ we get
x = 250
y = 125
Now,
u(250, 125) = 100(250)(125) + 250 + 2(125)
= 3125000 + 250 + 250
= 3125000 + 500
= 3125500
⇒u(250, 125) = 3125500
I'm guessing 202.4? Maybe? Sorta?
Anyway, hope it helped.
Answer:
y = (√3)/2
Step-by-step explanation:
The unit circle has equation ...
x^2 +y^2 = 1
For x = 1/2, the value of y can be found to be ...
(1/2)^2 +y^2 = 1
y^2 = 1 - 1/4 = 3/4 . . . . . subtract 1/4
y = √(3/4) . . . . . . . . . . take the square root (y > 0 here)
y = (√3)/2
The question should be accompanied with choices, below are the choices:
a) sqrt(1-x^2)
<span>b) x/sqrt(1-x^2) </span>
<span>c) sqrt(1-x^2)/x </span>
<span>D) 1/sqrt(1-x^2)
</span>
The answer should be <span>c) sqrt(1-x^2)/x .
</span><span>cos u = sqrt (1 - sin^2 u) = sqrt(1 - x^2), and cot u = cos u / sin u.</span>