9514 1404 393
Answer:
C: 5 inches
Step-by-step explanation:
The length of the sides of the new square is the square root of the area:
s = √A = √49 = 7
The original square had sides 2 inches shorter, so they were ...
7 in -2 in = 5 in . . . . side length of original square
Answer:
Price = $4.50
Maximum revenue = $2,430
Step-by-step explanation:
The concession stand sells 600 bags of peanut at $4.00 (600, $4.00).
If there is a $1 increase in price, the number of bags old will decrease by 120, which mens that 480 bags of peanuts will be sold at $5.00 (480, $5.00).
Tracing a linear relationship between price and quantity sold with the two given points:
![m = \frac{5-4}{480-600}\\ m=-\frac{1}{120}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B5-4%7D%7B480-600%7D%5C%5C%20m%3D-%5Cfrac%7B1%7D%7B120%7D)
![P - P_0=m*(Q-Q_0)\\P-4.00=-\frac{1}{120} (Q-600)\\P= -\frac{1}{120}Q +9](https://tex.z-dn.net/?f=P%20-%20P_0%3Dm%2A%28Q-Q_0%29%5C%5CP-4.00%3D-%5Cfrac%7B1%7D%7B120%7D%20%28Q-600%29%5C%5CP%3D%20-%5Cfrac%7B1%7D%7B120%7DQ%20%2B9)
The revenue function is given by the price multiplied by the quantity sold:
![R=Q*P= (-\frac{1}{120}Q +9)*Q\\R=-\frac{1}{120}Q^2 +9Q](https://tex.z-dn.net/?f=R%3DQ%2AP%3D%20%28-%5Cfrac%7B1%7D%7B120%7DQ%20%2B9%29%2AQ%5C%5CR%3D-%5Cfrac%7B1%7D%7B120%7DQ%5E2%20%2B9Q)
The value of 'Q' for which the derivate of the revenue function is zero, is the output level for which revenue is maximum:
![R'=0=-\frac{2}{120}Q+9\\Q_{max} = 540\\P_{max} = -\frac{540}{120} +9\\P_{max} =\$4.50](https://tex.z-dn.net/?f=R%27%3D0%3D-%5Cfrac%7B2%7D%7B120%7DQ%2B9%5C%5CQ_%7Bmax%7D%20%3D%20540%5C%5CP_%7Bmax%7D%20%3D%20-%5Cfrac%7B540%7D%7B120%7D%20%2B9%5C%5CP_%7Bmax%7D%20%3D%5C%244.50)
The total revenue of 540 units at $4.50 per unit is:
![R = \$4.50*540\\R=\$2,430](https://tex.z-dn.net/?f=R%20%3D%20%5C%244.50%2A540%5C%5CR%3D%5C%242%2C430)
Answer:
x = 30/π, in general case x=30/π +2πn
Step-by-step explanation:
30 cos(30x) + 14 = -16
30 cos(30x) = -16 - 14
30 cos(30x) = -30
cos(30x)= - 1
30x = π
x = 30/π, in general case x=30/π +2πn
Answer:
654
Step-by-step explanation:
109 x =16 x 2 + 43 + 32
109 x 6 = 654
654 / 3 = 218
Answer:
329.91 cm^2
Step-by-step explanation:
A ring-shaped region is shown below. Its inner radius is 8m, and its outer radius is 11m. 8m 11m Find the area of the shaded region. Use 3.14 for π. Do not round your answer.
Your answer
Given data
inner radius= 8cm
area= πr^2
area= 3.142*8^2
area= 3.142*16
area= 50.272 cm^2
outer radius= 11cm
area= πr^2
area= 3.142*11^2
area= 3.142*121
area= 380.182 cm^2
Hence the area of the shaded part is
=380.182-50.272
=329.91 cm^2