You mean what's the answer as a fraction or the equation as a fraction?
4/1 would be the answer as a fraction. 2/1 + 2/1 would be the equation as a fraction.
Answer:
2.38 miles
Step-by-step explanation:
From Given diagram:
In ΔABC,
AC=2.5 miles
BC= 3.7 miles
∠BCA= 39.4°
Now as we have two sides and an angle, using law of cosines to find the third side:
c= √(a^2+b^2-2abcosα
AB=√(AC)^2 + (BC)^2 - 2(AC)(BC)cosα
=√(2.5)^2 + (3.7)^2 - 2(2.5)(3.7)cos(39.4°)
=√(2.5)^2 + (3.7)^2 - 2(2.5)(3.7)(0.77)
=√(5.695)
= 2.38 !
A
The velocity is found by differentiating the given cubic.
x'(t) = 2t^3 - 15t^2 + 24t This is the distance
x'(t) = 6t^2 - 20t + 24 This is the velocity (first derivative)
x"(t) = 12t - 20 This is the acceleration (second derivative)
x'(2) = 6(2)^2 - 20*2 + 24
x'(2) = 24 - 40 + 24
x'(2) = 48 - 40
x'(2) = 8 units per second.
x"(2) = 12(2) - 20
x"(2) = 24 - 20
x"(2) = 4 units per second^2
B
at t = 2 the acceleration is positive. That's a pretty good indication that the velocity is increasing.
C
When x(t) is minus, then the particle is moving left.
At t = 0 the object is not moving (x(t) = 0)
Any value less than 0 and the object is moving left. Try a couple of values.
x(-1) = 2(-1)^3 - 15(-1)^2 +24(-1) Whatever that is is minus.
t < 0 will make the object move left.
The minimum number of degrees that a hexagram can be rotated so that it is carried onto itself is 60 degrees.