Answer:
18
Step-by-step explanation:
Answer:
x=3/5
Step-by-step explanation:
x^2+4x=5
x+4x=5x
5x+2=5
-2 -2
5x=3
divide 5 from each side
5/5x=3/5
<u>x=3/5</u>
<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:
5 min
Step-by-step explanation:
time taken=distance required to travel/speed of train
total distance train have to cover to just left the tunnel is (lenght of tunnel+length of train) =2km+250m
=2250m
speed of train is 27km/hr
multiply 5/18 to convert in m/s
i.e, (5/18)×27=7.5m/s
now time taken =2250m/(7.5m/s)
=300s
and,300s =5min
Answer:
If ab=12 and a2+b2=25 then,
(a+b)2=a2+b2+2ab
a+b=√25+24
a+b=√49
a+b=7
Step-by-step explanation:
brainliest pls?
