Answer:
4x-y+1=0
Step-by-step explanation:
here,given equation of a line id
4x-y-2=0.. eqn(i)
equation of any line parallel to line (i) is
4x-y+k=0...eqn(ii)
since, the line(ii) passes through (1,5)[replacing x=1 and y=5 in eqn(ii), we get]
4*1-5+k=0
or, 4-5+k=0
or,-1+k=0
•°•k=1
substituting the value of k=1 in eqn(ii),
4x-y+1=0 is the required equation 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>
Answer:
²⁵C₅ = 53130
Step-by-step explanation:
number of people in the club = 25
number of people to be selected in the group to attend conference = 5
number of ways of selecting this group from 25 people is same as selecting 5 objects from 25 distinct objects = ²⁵C₅ (Selection)
= 
= 
= 21×22×23×5
= 53130
∴ <u>Number of ways of selecting this group from 25 people = 53130</u>
Answer:
at twice the father's rate of speed. At this rate; how many miles would the bicycle rider travel in 9 hours?
Step-by-step explanation:
at twice the father's rate of speed. At this rate; how many miles would the bicycle rider travel in 9 hours?
