2x(3×2 – 2x – 8)
Susan has 10 pockets and 44 dollar bills. She wants to arrange the money so that there are a different number of dollars in each
1 answer:
You might be interested in
This question is incomplete, the remaining part of the question is upload as an image alongside this answer.
Answer:
Width = 2x = 2( r/√2 ) = √2 r units
Height = 2y = 2( r/√2 ) = √2 r units
Step-by-step explanation:
From the Figure on the image; lets consider the circle of radius r, centered at the origin.
let ABCD be the largest rectangle that can be inscribed inside the circle.
Let the half width of the rectangle be x, then in right triangle ONB using Pythagorean theorem,
half height of rectangle y = √(r² - x²)
Thus the width of the inscribed rectangle = 2x and height of the inscribed rectangle = 2√(r² - x²)
thus the area of the inscribed rectangle = length × width
⇒ A(x) = 2x(2√(r² - x²))
⇒ A(x) = 4x√(r² - x²)
now in order to maximize the area, we find critical points.
so we find the derivative and set that zero, that is Ai(x) = 0.
so using product rule, we get
A'(x) = 4x × ( -2x / 2√(r² - x²) ) + ( 4 × √(r² - x²) )
A'(x) = ( -4x² / √(r² - x²) ) + ( 4√(r² - x²) )
Now for critical points, set A'(x) = 0
so
( -4x² / √(r² - x²) ) + ( 4√(r² - x²) ) = 0
( 4x² / √(r² - x²) ) = ( 4√(r² - x²) )
x² = r² - x²
2x² = r²
x² = r²/2
x = ±√(r²/2)
Now since x represent the with, it cannot be negative, Thus
x = r/√2
hence
y = √(r² - x²) = √(r² - r²/2) = √(r²/2) = r/√2
Therefore, the dimensions of the rectangle of largest area will be;
Width = 2x = 2( r/√2 ) = √2 r units
Height = 2y = 2( r/√2 ) = √2 r units
Answer:
w =
Step-by-step explanation:
The question is
We can first use distributive property to simplify, the distributive property is
Thus we have:
<em>Now we combine like terms and simplify to get the final answer for w</em><em>.</em>
Thus, w =
An equation that shows the relationship between speed and time is
<u>Given the following data:</u>
- Distance = 100 miles.
- Time = 45 minutes.
To write an equation that shows the relationship between speed and time:
<h3>What is speed?</h3>Speed can be defined as the distance covered by a physical object per unit of time. Thus, the cyclist's speed can be measured as miles per minutes.
Mathematically, speed is given by this formula;
Substituting the given parameters into the formula, we have;
Read more on speed here: brainly.com/question/10545161