Answer:
<em>2 1/3, 2 1/4, 2 3/7</em>
Step-by-step explanation:
<u>Mixed Fractions</u>
Mixed fractions are made of an integer part followed by a proper fraction.
Some examples of mixed fractions are:
3 1/2, -4 5/8, 2 2/3
Between two consecutive integers a and a+1, there are infinitely many fractions. The centered number is a 1/2. Any number with its improper fraction part less than 1/2 is closer to a than to a+1.
In our problem, Jayne bought between 2 and 3 pounds of granola. We need to provide a mixed number that is closer to 2 pounds than to 3 pounds.
We can select any number with integer part 2 and a proper fraction less than 1/2.
Examples could be :
2 1/3, 2 1/4, 2 3/7
All of them are less than 2.5
<span>The two points that are most distant from (-1,0) are
exactly (1/3, 4sqrt(2)/3) and (1/3, -4sqrt(2)/3)
approximately (0.3333333, 1.885618) and (0.3333333, -1.885618)
Rewriting to express Y as a function of X, we get
4x^2 + y^2 = 4
y^2 = 4 - 4x^2
y = +/- sqrt(4 - 4x^2)
So that indicates that the range of values for X is -1 to 1.
Also the range of values for Y is from -2 to 2.
Additionally, the ellipse is centered upon the origin and is symmetrical to both the X and Y axis.
So let's just look at the positive Y values and upon finding the maximum distance, simply reflect that point across the X axis. So
y = sqrt(4-4x^2)
distance is
sqrt((x + 1)^2 + sqrt(4-4x^2)^2)
=sqrt(x^2 + 2x + 1 + 4 - 4x^2)
=sqrt(-3x^2 + 2x + 5)
And to simplify things, the maximum distance will also have the maximum squared distance, so square the equation, giving
-3x^2 + 2x + 5
Now the maximum will happen where the first derivative is equal to 0, so calculate the first derivative.
d = -3x^2 + 2x + 5
d' = -6x + 2
And set d' to 0 and solve for x, so
0 = -6x + 2
-2 = -6x
1/3 = x
So the furthest point will be where X = 1/3. Calculate those points using (1) above.
y = +/- sqrt(4 - 4x^2)
y = +/- sqrt(4 - 4(1/3)^2)
y = +/- sqrt(4 - 4(1/9))
y = +/- sqrt(4 - 4/9)
y = +/- sqrt(3 5/9)
y = +/- sqrt(32)/sqrt(9)
y = +/- 4sqrt(2)/3
y is approximately +/- 1.885618</span>
Just copy the triangle but on the opposite side I think. Take the coordinates and flip it onto the other side until its a perfect match
Answer:
Solution given:
length[l]=3x+7
breadth [b]=2x+3
we have
area of rectangle=l×b=(3x+7)(2x+3)
=6x²+14x+9x+21=6x²+23x+21 units ²
