3 Hours
4 People does the job in 6 hours if there are twice as many people it gets done twice as fast
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
Answer:
The difference in the populations of the cities when t=4 is 25,800.
Step-by-step explanation:
Given equations each of the city:
-150t+50,000
and
50t+75,000
To find the difference between the population when t=4, we first have to solve both equation when t=4.
For both equations, substitute 4 into t:
-150(4) + 50,000 = 49,400
50(4) + 75,000 = 75,200
Now subtract 49,400 from 75,200 and you get 25,800.
The difference in the populations of the cities when t=4 is 25,800.
Answer:
9.9 meters
Step-by-step explanation:
Given that the distance between Kelly and launching point was 7m and also the distance between launching point and Dennis was also 7m, to calculate for the distance between Kelly and denise is done by applying the formula used for calculating the hypotenuse in a right angle triangle (the shape that was created)
PICTURE ATTACHED IS A DETAILED STEP BY STEP PROCESS OF HOW 9.9m WAS GOTTEN.
First find the slope using the formula

Substitute the values in:

Point-slope form is

Substitute (it doesn't matter which point you choose; I chose (4,5):
Therefore, the answer is D.