The diameters of two circles are in the ratio 2 5 The area of the larger circle is 450 cm?
Work out the area of the smaller circle
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72 cm²

Step-by-step explanation:

Given the ratio of diameters = a : b , then

ratio of areas = a² : b²

Here the ratio of diameters = 2 : 5 , then

ratio of areas = 2² : 5² = 4 : 25

let x be the area of smaller circle then using proportion

= ( cross- multiply )

25x = 1800 ( divide by 25 )

x = 72

That is the area of the smaller circle is 72 cm²

The correct answer is a) R = = - + 30x; b) $ 1120; c) Maximum quantity is 75 units with maximum revenue being $1125; d) p = $15.

Step-by-step explanation:

Demand equation: p = - x + 30 , 0 x 150 ; where p is the price of the product and x is the quantity sold.

a) Revenue function by the problem is given to be R= p × x = - + 30x.

b) Revenue at x = 70 is given by 2100 - 980 = $ 1120.

c) For maximizing the R we differentiate it with respect to x and equate it to zero.

⇒ - x + 30 =0

⇒ x = 75.

As the second order derivative is negative at this point, this is the value of x that maximizes the revenue.

Maximum Revenue is at x = 75 and is equal to $1125.

d) Price charged by the company for maximum revenue is $15.