Hi!
Square roots where the things under the root are multiplied (for example ) can be split up into .
That's what I'm going to do in this case. I'm going to split into
Now, the cube root of 125 is 5, because 5 * 5 * 5 = 125, and that is the definition of a cube root. (What multiplied 3 times by itself is equal to what's under the root)
Now to look at what the cube root of is.
A cube root can be rewritten as , same as a square root can be rewritten to .
So if you take the cube root of x^12, you can change it to:
If you have a case like this, then you can multiply the two powers (in this case 12 and 1/3) to simplify it. 12 * 1/3 = 4, so you get x^4.
Now putting the two together, you get:
5 as your answer.
Hope this helped!
Volume = area of base * height = 1/2 * 6 * 8 * 12
= 288 ft^3 answer
Answer:
The rate of change of the distance between the cars at that instant is 5.46 meters per second
Step-by-step explanation:
Speed of first car = 7 m/s
Speed of second car = 3 m/s
At instant, distance of first car from intersection = 5 meters
distance of second car from intersection = 12 meters
Therefore, we have
Distance between both cars at intant = √(12² + 5²) = 13 m
Rate of cahnge of distance is given by;
2ddd/dt = d(x² + y²)/dt = 2xdx/dt + 2ydy/dt
= 26dd/dt = 2×5×7 + 2×12×3 = 142
dd/dt = 142/26 = 5.46 m/s.
That is the rate of change of the distance between the cars at that instant = 5.46 meters per second.