We know that Frank is 1/4 Dana's age, so if Frank is represented by f, and Dana is represented by d, then the equation would be
1/4d = f
<span>Secondly, we know that Neil's age is one-half the difference between Dana's and Frank's ages. Because of we learned that Frank is a fraction of Dana's age, we can infer that he is younger than Dana. So, if Neil's age is represented by the variable n, then the equation would be
1/2(d - f) = n
Finally, if we know that Dana is 16 years old, we can find out the other siblings ages using the equations we made above.
d=16
1/4d = f
1/4(16) = f
4 =f
</span>1/2(d - <span>f) = n
</span>1/2(16-4) = n
1/2(12) = n
6=n
Therefore, Frank is 4 years old and Neil is 6 years old.
Answer:
Step-by-step explanation:
14.
by pythagoras,s theorem
15.
first perpendicular=y(say)
and second perpendicular=z (say)
y²=9²+7²=81+49=130
z²=y²+5²=130+25=155
x²=z²+4²=155+16=171
x=√(171)
Answer:
C, just got it on edgenuity.
Step-by-step explanation:
Answer:
15 dollers
Step-by-step explanation:
<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>
