If we do not care about order, then a combination is an arrangement of r objects chosen from n distinct objects. It can often be seen written as:
or
Its factorial form is:
In any linear equation the coefficient of the x-term represents ALWAYS the slope.
So it is B. The slope of the line
<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>
3 Hours
4 People does the job in 6 hours if there are twice as many people it gets done twice as fast
9514 1404 393
Answer:
4.9% weekly
Step-by-step explanation:
The compound interest formula is ...
A = P(1 +r/n)^(nt)
where A is the account balance that results from investing P at rate r compounded n times per year for t years.
Filling in the values for the two scenarios, we find ...
A = 10,000(1 +0.04/365)^(365·3) ≈ 11,274.89
A = 10,000(1 +0.049/52)^(52·3) = 11,582.74
The higher interest rate will earn Mr. Larson the most money in three years. (4.9% weekly)
