Answer: ??
Step-by-step explanation:
This might help :/
Area of a circle = pie r^
Circumference = 2pie r
Answer:
8:1
Step-by-step explanation:
the actual table's height in inches is 4*12 = 48 inches.
48/6 = 8
so the ratio is 8:1.
Answer:
The angle between the given vectors u and v is ![\theta=cos^{-1}\left[\frac{3}{\sqrt{10}}\right]](https://tex.z-dn.net/?f=%5Ctheta%3Dcos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B3%7D%7B%5Csqrt%7B10%7D%7D%5Cright%5D)
Step-by-step explanation:
Given vectors are
and 
Now compute the dot product of u and v:




Now find the magnitude of u and v:









To find the angle between the given vectors

![\theta=cos^{-1}\left[\frac{\overrightarrow{u}.\overrightarrow{v}}{|\overrightarrow{u}|\overrightarrow{v}|}\right]](https://tex.z-dn.net/?f=%5Ctheta%3Dcos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B%5Coverrightarrow%7Bu%7D.%5Coverrightarrow%7Bv%7D%7D%7B%7C%5Coverrightarrow%7Bu%7D%7C%5Coverrightarrow%7Bv%7D%7C%7D%5Cright%5D)
![=cos^{-1}\left[\frac{15}{5\times \sqrt{10}}\right]](https://tex.z-dn.net/?f=%3Dcos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B15%7D%7B5%5Ctimes%20%5Csqrt%7B10%7D%7D%5Cright%5D)
![=cos^{-1}\left[\frac{15}{5\times \sqrt{10}}\right]](https://tex.z-dn.net/?f=%3Dcos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B15%7D%7B5%5Ctimes%20%5Csqrt%7B10%7D%7D%5Cright%5D)
![\theta=cos^{-1}\left[\frac{3}{\sqrt{10}}\right]](https://tex.z-dn.net/?f=%5Ctheta%3Dcos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B3%7D%7B%5Csqrt%7B10%7D%7D%5Cright%5D)
Therefore the angle between the vectors u and v is
![\theta=cos^{-1}\left[\frac{3}{\sqrt{10}}\right]](https://tex.z-dn.net/?f=%5Ctheta%3Dcos%5E%7B-1%7D%5Cleft%5B%5Cfrac%7B3%7D%7B%5Csqrt%7B10%7D%7D%5Cright%5D)
Answer:
for (−4/5)x + 3/10 < 8/10: solution is x > -5/8
for −4/(5x) + 3/10 < 8/10: solution is x > -8/5
Step-by-step explanation:
I'm not exactly sure if you mean -4 divided by 5x or (-4/5)x, so I've done both! :)

subtract 3/10 from both sides: 
Divide both sides by 4/5: 
Divide both sides by -1 (reverse sign): 

subtract 3/10 from both sides: 
Multiply both sides by 5x: 
Divide both sides by 5/2: 
Answer:
It takes 27 minutes for the element to decay to 35 grams
Step-by-step explanation:
Given:
Initial amount = 790 grams
Final amount = 35 grams
Half life = 6 minutes
To find:
Time taken for the element to reduce into 35 grams = ?
Solutions
Time taken = 
On substituting the values given, Time taken
= 
= 
= 
= 26.97
= 27 minutes