<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>
Answer:
x² + 4x + 20 = 12x - 5
x² + 4x - 12x + 20 + 5 = 0
x² - 8x + 25 = 0
Δ = √b² - 4ac
= √(-8)² - 4×1×25
= √64-100
= √(-36)
x ∉ R
Answer:
(A ∪ B) = {15, 17, 19, 20, 21, 23, 25}
Step-by-step explanation:
Multiples of 5:
{0, 5, 10, 15, 20, 25, ...}
So between 14 and 26:
A = {15, 20, 25}
Odd numbers between 14 and 26:
B = {15, 17, 19, 21, 23, 25}
(A ∪ B)
All numbers that are part of at least one of these sets. So
(A ∪ B) = {15, 17, 19, 20, 21, 23, 25}
2 sack of cement is needed to cover entire floor of Joel
<em><u>Solution:</u></em>
Given that a sack of cement is enough to cover a floor with a total area of 45 sqft
Joel’s floor length is 8ft by 7ft
To find: Number of sacks needed to cover entire floor of Joel
Let us first find area of Joel's floor
Since the floor is generally of rectangular, we can use area of rectangle
<em><u>So the total area of floor with length 8 feet and width 7 feet is:</u></em>
Thus the total area of floor is 56 square feet
<em><u>Let us now find number of sacks needed to cover entire floor</u></em>
Given that, one sack of cement covers 45 square feet
Since Sack of cement cannot be in point value hence we can say 2 sack of cement is required.
Answer:
x=5
Step-by-step explanation:
Step 1: you want to have x alone on one side so I will subtract one x from both sides (to remove the 1 x on the right side). Now we're left with 3x=15.
Step 2: Divide both sides by 3 (to remove the 3 in front of 3x). Now we have x=5.
