X = k/p^3
125 = k/10^3 = k/1000
1000 x 125 = k
k = 125000
x = 125000/p^3
The profit is given by G = px - (125 + 2x) = p(125000/p^3) - 125 - 2(125000/p^3) = 125000/p^2 - 250000/p^3 - 125
For maximum profit:
dG/dp = 0
dG/dp = -250000/p^3 + 750000/p^4 = 0
750000 - 250000p = 0
p = 750000/250000 = 3
Therefore the price that will yeaild maximum profit is $3.
Answer:
m∠3 = 119°
Step-by-step explanation:
All the angles must equal 360° when added together. You have two known angles that are right next to each other. If you add m∠1 and m∠2, 119 + 61, it is equal to 180°. This means that m∠3 and m∠4 must be equal to 180° as well and since there are only two lines, it is safe to assume that opposing angles are the same so m∠1 = m∠3 and m∠2 = m∠4.
Answer:
x+3y=-1
Step-by-step explanation:
y=3x-2 so m=3 old slope
the new slope must be -1/3 (opposite reciprocal of the old slope).
y-y0=m*(x-x0)
y-2=-1/3*(x-(-7))
y-2=-1/3x-1/3*7
y-2=-1/3x-7/3
3y-6=-x-7
The standard form for linear equations in two variables is Ax+By=C.
x+3y=6-7
x+3y=-1
The solution to given system of equations is (x, y) = (2, -1)
<em><u>Solution:</u></em>
Given system of equations are:
-1x + 2y = -4 -------- eqn 1
4x + 3y = 5 ------- eqn 2
We can solve the above system of equations by elimination method
<em><u>Multiply eqn 1 by 4</u></em>
4(-1x + 2y = -4)
-4x + 8y = -16 ------ eqn 3
<em><u>Add eqn 2 and eqn 3</u></em>
4x + 3y = 5
-4x + 8y = -16
( + ) --------------------
0x + 11y = -16 + 5
11y = -11
y = -1
<em><u>Substitute y = -1 in eqn 1</u></em>
-1x + 2(-1) = -4
-x -2 = -4
-x = -4 + 2
-x = -2
x = 2
<em><u>Check the answer:</u></em>
Substitute x = 2 and y = -1 in eqn 2
4x + 3y = 5
4(2) + 3(-1) = 5
8 - 3 = 5
5 = 5
Thus the obtained answer is correct
Thus the solution to given system of equations is (x, y) = (2, -1)
