Answer:
Mona will save a total of $7 by going to Carpet World.
Step-by-step explanation:
First, we need to calculate the total area of the floor by multiplying the width by the length...
5m * 8m = 40m
Now we calculate the amount that it would cost to buy the carpet from each of the establishments. For the first establishment, we can buy 16
and get the next 8 half off and that would leave another 16 at full price. The second establishment we have a 5% off (0.95 of official price) for every 8, since out total area is 5 times this amount then our total will have a 5% off.
Establishment 1: (16 * 2.20) + (8 * 1.10) + (16 * 2.20) = $79.20
Establishment 2: (40 * 1.90) * 0.95 = $72.20
Difference: 79.20 - 72.20 = $7
Mona will save a total of $7 by going to Carpet World.
<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:
For the first part
1.) Negative
2.)zero
3.) undefined
4.) positive
The point slope formula is y-y1=m(x-x1). It is best to use if you already know the slope and one other point on the line. It is used to find another point on the line.
The slope-intercept form is used to show a line. To use this form, you need to know the slope and the y-intercept.
The slope formula is y=mx+b. M is the slope while b is the y-intercept.
Answer:
p = 16
Step-by-step explanation:
Given p is directly proportional to (q + 2)² then the equation relating them is
p = k(q + 2)² ← k is the constant of proportion
To find k use the condition when q = 1, p = 1
1 = k(1 + 2)² = k × 3² = 9k ( divide both sides by 9 )
= k
p = (q + 2)² ← equation of proportion
When q = 10 , then
p = × (10 + 2)² = × 12² = × 144 = 16
