Hello the answer should be 4√10
Since this problem talks about rates of change, then the concept of calculus is very useful. But first, let's find at least two equations in order to solve this system. The first one is the area of a triangle written as
A = 1/2 ab sin θ, where a and b are the sides that from the angle θ. So, we substitute a=6 and b=10. That makes it:
A = 1/2 (6)(10)sin θ = 30 sin θ
Now, you differentiate implicitly (both sides simultaneously) with respect to time.
dA/dt = 30 cosθ (dθ/dt)
We replace dθ/dt = 0.06 rad/s, as mentioned in the problem. Then, the rate of change of the area of the triangle when θ = π/3 rad with respect to time is
dA/dt = 30cos(π/3) (0.06)
dA/dt = 1.8 m²/s
Therefore, the rate of change of the area of the triangle is 1.8 m² per second.
Answer:
3.14159... is irrational. Is that what you mean? What you put right now is rational
Step-by-step explanation:
Irrational = infinite
Rational = Not infinite
Step-by-step explanation:
Break down every term into prime factors. ...
Look for factors that appear in every single term to determine the GCF. ...
Factor the GCF out from every term in front of parentheses, and leave the remnants inside the parentheses. ...
Multiply out to simplify each term.
Step-by-step explanation:
d = the distance in one direction.
the time t1 it took group 1 was
t1 = d/6 + d/4
and t2 for group 2 moving with speed2 all the way
t2 = (d+d)/speed2
we know
2d = 24 miles
d = 12 miles
t1 = t2
so,
12/6 + 12/4 = 24/speed2
2 + 3 = 24/speed2
5 = 24/ speed2
5×speed2 = 24
speed2 = 24/5 = 4.8 mph
the second group moved with 4.8 mph.
