Answer: C. 7/8
Step-by-step explanation: 7/8 simplifies to .875 which terminates. 1/3 is repeating .333333... 1/6 is repeating, .166666... and 11/24 is repeating, .4583333...
<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>
25r^2-4 rewriten in standard polynomial form
Answer:
11 inches
Step-by-step explanation:
A rectangle's perimeter can be found using:
p=2l+2w
We know that the perimeter, p, is 58, and the length/height is 18. Therefore, we can substitute those values in
58=2(18)+2w
Multiply 2 and 18
58=36+2w
Since we want to find the width, we need to get w by itself. First, subtract 26 from both sides
58-36=36-36+2w
22=2w
Since w is being multiplied by 2, divide both sides by 2. This will cancel out the 2, and leave w by itself.
22/2=2w/2
11=w
So, the width is 11 inches
