So the Pythagorean triplet is 8,15and 17
Take 36 and add it to 60 it gives you 96 then divide it by 2 and the answer is 48
<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>
Let f be the fraction invested at 10%. So (1-f) is the fraction at 7%. After one year the interest is
664 = 8200 f (.10) + 8200 (1-f) (.07) = 8200(.03)f + 8200(.07)
f = (664 - 8200(.07))/(8200(.03)) = .3659 = 36.59 %
Answer: 36.59%
Check:
8200(.3659)*.1 + 8200(1-.3659)*.07 = 664.01 good
1 batch need 3/4 gallon of milk
She has 1/4 gallon cup
(3/4) divided by (1/4)
A technique in math is just flip the divider which is (1/4) to (4/1)
so it becomes (3/4) multiply (4/1) = (3x4) / (4x1) = 12/4 = 3 times for one batch
She needs three batches so 3 x 3 = 9 times to fill the measuring cup to make all 3 batches of milkshake.
