The diameter is equal to 12.
Answer:
y =
x + 7
Step-by-step explanation:
Given
x = 3t ( divide both sides by 3 )
x = t
Substitute this value into y = 2t + 7
y = 2 ×
x + 7 =
x + 7
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:
8%
Step-by-step explanation:
Initial attendance = 2000
New attendance record = 1840
Percentage decrease in attendance :
((Initial - new attendance record) / initial attendance) * 100%
((2000 - 1840) / 2000) * 100%
(160 / 2000) * 100%
0.08 * 100%
8%
8% decrease in attendance
Answer:
(7,2)
Step-by-step explanation:
Multiply the first equation by -3
(x-3y=1) = -3x+9y=-3
Combine like terms with the new equation and the second equation
(-3x+9y=-3) + (3x-5y=11) = 4y=8
Divide each side by 4
4y/4=8/4
y=2
Plug in 2 for y in any equation. It doesn’t matter which one
x-3(2)=1
Distribute
x-6=1
Add 6 to both sides
x-6=1
+6 +6
x=7