Answer:
15% increase
Step-by-step explanation:
2750... 10% of that is 275, add 275 to 2750 is 3025. 1% of 2750 is 27.50, you times that by 5, which is 137.50 and add that to 3025 giving you 3162.50, add the 10% with the 5% gives you 15%, that's the increase.
Answer:
The answer is the third option from the top:
0, 0, 11, 15, 26, 32, 45, 46, 46, 46, 60, 71, 84, 88
Answer:
x = 10 cm, y = 5 cm gives a minimum area of 300 cm^2.
Step-by-step explanation:
V= x^2y = 500
Surface area A = x^2 + 4xy.
From the first equation y = 500/x^2
So substituting for y in the equation for the surface area:
A = x^2 + 4x * 500/x^2
A = x^2 + 2000/x
Finding the derivative:
dA/dx = 2x - 2000x^-2
dA/dx = 2x - 2000/x^2
This = 0 for a minimum/maximum value of A, so
2x - 2000/x^2 = 0
2x^3 - 2000 = 0
x^3 = 2000/ 2 = 1000
x = 10
Second derivative is 2 + 4000/x^3
when x = 10 this is positive so x = 10 gives a minimum value of A.
So y = 500/x^2
= 500/100
= 5.
to find the distance between 2 points we should apply the formula
![d=\sqrt[]{(x_2-x_1)^2+(y_2-_{}y_1)^2_{}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%5B%5D%7B%28x_2-x_1%29%5E2%2B%28y_2-_%7B%7Dy_1%29%5E2_%7B%7D%7D)
call point q as point 1 for reference in the formula and p as point 2
replace the coordinates in the formula
![d=\sqrt[]{(3-(-1))^2+(-4-(-1))^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%5B%5D%7B%283-%28-1%29%29%5E2%2B%28-4-%28-1%29%29%5E2%7D)
simplify the equation
![\begin{gathered} d=\sqrt[]{(3+1)^2+(-4+1)^2} \\ d=\sqrt[]{4^2+(-3)^2} \\ d=\sqrt[]{16+9} \\ d=\sqrt[]{25} \\ d=5 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20d%3D%5Csqrt%5B%5D%7B%283%2B1%29%5E2%2B%28-4%2B1%29%5E2%7D%20%5C%5C%20d%3D%5Csqrt%5B%5D%7B4%5E2%2B%28-3%29%5E2%7D%20%5C%5C%20d%3D%5Csqrt%5B%5D%7B16%2B9%7D%20%5C%5C%20d%3D%5Csqrt%5B%5D%7B25%7D%20%5C%5C%20d%3D5%20%5Cend%7Bgathered%7D)
the distance between the 2 points is 5 units
Using the inequality
2.50x + 3.50y ≤ 30
substituting y with the number of cheeseburgers sold
2.5x + 3.5(4) ≤ 30
x = 6.4
The maximum number of hamburgers he can sell is 6
