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:
5/6
Step-by-step explanation:
to add fractions they need to have a common denominator
make 1/3 have a denominator of 18
1/3(6) = 6/18
9/18 + 6/18 = 15/18
15/18 can be simplified to 5/6
Answer:
4. y = 1/2x + 3/2
Step-by-step explanation:
First, we need to change the line that's parallel into slope-intercept form.
-2x + 4y = 8
4y = 2x + 8
y = 1/2x + 2
If it's parallel, then it remains the same. So our slope is 1/2.
To find the y-intercept, you need to plug the coordinates into the equation.
y = 1/2x + b
-1 = 1/2(-5) + b
-1 = -5/2 + b
3/2 = b
y = 1/2x + 3/2
Answer: 
<u>Step-by-step explanation:</u>
G = (-7, 3) H = (1, -2)
