5510 = x + (x + 100) + (x + 200) + (x + 300) + (x + 400) + (x + 500) + (x + 600) + (x +700) + (x + 800) + (x + 900) = 10x + 4500
=> 10x = 5510 - 4500 = 1010
=> x = 1010 / 10 = 101
=> least prize = 101 and greatest prize = 101+ 900 = 1001.<----- answer
Hi
I have to write at least 20 words to say hello.
Answer:
.
Step-by-step explanation:
The given expression is
We need to simplify the expression such that answer should contain only positive exponents with no fractional exponents in the denominator.
Using properties of exponents, we get
![[\because a^ma^n=a^{m+n}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20a%5Ema%5En%3Da%5E%7Bm%2Bn%7D%5D)
![[\because a^{-n}=\dfrac{1}{a^n}]](https://tex.z-dn.net/?f=%5B%5Cbecause%20a%5E%7B-n%7D%3D%5Cdfrac%7B1%7D%7Ba%5En%7D%5D)
We can not simplify further because on further simplification we get negative exponents in numerator or fractional exponents in the denominator.
Therefore, the required expression is .
Answer: 1
Step-by-step explanation:
Area is equal to length times width. The perimeter (the amount of rope) has to equal twice the length added to twice the width so we're left with:
A = l * w
200 = 2l + 2w
solve for either l or w
l = 100 - w
plug into the area equation to get one equation with two variables
A = w(100 - w)
A = -w^2 + 100w
take the derivative
A' = -2w + 100
set the derivative equal to zero
0 = -2w + 100
2w = 100
w = 50
This is the width that maximizes the area
with a width of 50, the length must also be 50 to have a perimeter of 200
therefore, they can rope up to 50 * 50 = 2500 ft^2
