Answer:
7) is 625
8) 169
9) 1.44
10) 180??
11) 1000000
12) 3430
hopefully these are right
Step-by-step explanation:
The wheel has diameter 60 cm = 0.60 m, and thus circumference π(0.60 m) ≈ 5.923 m.
In one complete revolution, a point on the edge of the wheel covers this distance, so that the wheel has an angular speed of
(13.2 m/s) * (1/5.923 rev/m) ≈ 2.229 rev/s
There are 60 seconds to each minute, and 60 minutes to each hour, so converting to rev/h gives
(2.229 rev/s) * (60 s/min) * (60 min/h) ≈ 8024 rev/h
Answer:
The base is decreasing at 2 cm/min.
Step-by-step explanation:
The area (A) of a triangle is given by:
(1)
Where:
b: is the base
h: is the altitude = 10 cm
If we take the derivative of equation (1) as a function of time we have:
![\frac{dA}{dt} = \frac{1}{2}(\frac{db}{dt}h + \frac{dh}{dt}b)](https://tex.z-dn.net/?f=%20%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28%5Cfrac%7Bdb%7D%7Bdt%7Dh%20%2B%20%5Cfrac%7Bdh%7D%7Bdt%7Db%29%20)
We can find the base by solving equation (1) for b:
![b = \frac{2A}{h} = \frac{2*120 cm^{2}}{10 cm} = 24 cm](https://tex.z-dn.net/?f=%20b%20%3D%20%5Cfrac%7B2A%7D%7Bh%7D%20%3D%20%5Cfrac%7B2%2A120%20cm%5E%7B2%7D%7D%7B10%20cm%7D%20%3D%2024%20cm%20)
Now, having that dh/dt = 1 cm/min, dA/dt = 2 cm²/min we can find db/dt:
![2 cm^{2}/min = \frac{1}{2}(\frac{db}{dt}*10 cm + 1 cm/min*24 cm)](https://tex.z-dn.net/?f=%202%20cm%5E%7B2%7D%2Fmin%20%3D%20%5Cfrac%7B1%7D%7B2%7D%28%5Cfrac%7Bdb%7D%7Bdt%7D%2A10%20cm%20%2B%201%20cm%2Fmin%2A24%20cm%29%20)
Therefore, the base is decreasing at 2 cm/min.
I hope it helps you!
Answer:
8
+ 3 + -6x
Step-by-step explanation:
First we need to find the like terms so that we could add them. In this case the like terms are,
1. 6x , -2x , -10x
So, these are the only terms that we can add in this expression.
Hence,
=> 8
+ 3 + (6x - 2x - 10x)
=> 8
+ 3 + -6x
And this is as simple as this expression can go until we find the value of "x" which is not yet told.
Hope my answer helped.