Answer:
Step-by-step explanation:
(5^3/2)^-2/3 = 0.2 ⇒ E
(256^0.5)^1.25 = 32 ⇒ C
(81^1/6)^3/2 = 3 ⇒ F
(1024^0.03)^20 = 64 ⇒ D
(1000^4/7)^7/3 = 10,000 ⇒ B
(49^5/2)^0.2 = 7 ⇒ A
Step-by-step explanation:
* Lets explain how to solve the problem
- If we have base x to a power n and all to the power of m then we
multiply the two powers to be one power on the base
- [(x^n)^m] = x^(nm)
* Lets solve the problem
∵
∴ (5^3/2)^-2/3 = 0.2 ⇒ E
∵
∵ 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^8
∴
∴ (256^0.5)^1.25 = 32 ⇒ C
∵
∵ 81 = 3 × 3 × 3 × 3 = 3^4
∴
∴ (81^1/6)^3/2 = 3 ⇒ F (answer F must be 3 not 0.333)
∵
∵ 1024 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2^10
∴
∴ (1024^0.03)^20 = 64 ⇒ D
∵
∵ 1000 = 10 × 10 × 10 = 10³
∴
∴ (1000^4/7)^7/3 = 10,000 ⇒ B
∵
∴ (49^5/2)^0.2 = 7 ⇒ A
Answer:
see explanation
Step-by-step explanation:
let w represent the width then length = w + 7
The perimeter of the rectangle = 2w + 2(w + 7) = 2w + 2w + 14 = 4w + 14
The perimeter is given as 54 m, thus
4w + 14 = 54 ( subtract 14 from both sides )
4w = 40 ( divide both sides by 4 )
w = 10
Thus
width of playground = w = 10 m
length of playground = w + 7 = 10 + 7 = 17 m
Answer:
N(x) = 40 - 2x
P(x) = -2x² + 52 x - 240
maximum profit = 13
Step-by-step explanation:
given data
feeder cost = $6
average sell = 20 per week
price = $10 each
solution
we consider here price per feeder = x
and profit per feeder id here formula = x - 6
so that here
total profit will be
P (x) = ( x - 6 ) Nx
here N(x) is number of feeders sold at price = x
so formula for N (x) is here
N(x) = 20 - 2 ( x - 10 )
N(x) = 40 - 2x
so that
P(x) = (x-6) ( 40 - 2x)
P(x) = -2x² + 52 x - 240
since here
a = -2
b = 52
c = -240
a < 0
so quadratic function have maximum value of c - 
so it will be
maximum value = -240 - 
maximum value = 98
so here maximum profit attained at
x = 
x = 
x = 13
maximum profit = 13
