Since length of diagonal ( 
) is less than diameter of circle ( 11 cm ) , Therefore , the square will fit inside the circle without touching the edge of the circle.
<u>Step-by-step explanation:</u>
Here we have , A circle has diameter of 11 cm A square has side length of 7 cm . Use Pythagoras’ Theorem to show that the square will fit inside the circle without touching the edge of the circle . Let's find out:
We know the concept that for any square to fit inside the circle without touching the edge of circle , diagonal of square must be less than diameter of circle . Let's find out length of diagonal by using Pythagoras Theorem :
For a square , 
⇒ 
⇒ 
⇒ 
⇒
Since length of diagonal ( ) is less than diameter of circle ( 11 cm ) , Therefore , the square will fit inside the circle without ruching the edge of the circle.
Answer:
area of the circular plate =πr²
50.24 =3.14×r²
r² =50.24/3.14
r² =16
radius =4 inch
If you put this info into a distance/rate/time table, you would have "against the wind" and "with the wind" as your 2 situations. If the distance from PA to AZ is 1800 miles, then the distance backwards, from AZ to PA is 1800 miles also. That number would go into the distance category for both situations. The rate is what we are looking for. The rate for "against the wind" is the speed of the plane minus the speed of the wind since the wind is blowing into the plane, slowing it down a bit. That looks like this: p - w where p is the speed of the plane and w is the speed of the wind. The rate for "with the wind" is p + w since the wind is pushing the plane along with it, making it fly faster. It took 3.6 hours to get from PA to AZ (you have to convert the 36 minutes into hours) and it took 3 hours to go from AZ to PA. In table form that looks like this:
distance = rate x time
against wind 1800 = p - w x 3.6
with wind 1800 = p + w x 3
Since distance = rate times time, then the first equation going along in the first row is 1800 = 3.6(p - w) and
1800 = 3.6p - 3.6w
Going along in the second row we have 1800 = 3p + 3w. Let's solve this equation for p: 1800 - 3w = 3p and dividing everything by 3 we have
600 - w = p. Now we have a viable substitution to make into the first equation we wrote. If p = 600 - w, then 1800 = 3.6(600 - w) - 3.6w
and 1800 = 2160 - 3.6w - 3.6w. Combining like terms we have
-360 = -7.2w and solving for w we have that w = 50. That means that the speed of the wind is 50 mph. Now we can sub that value in for w to solve for p. 600 - w = p so 600 - 50 = p. That means that p = 550mph. The wind blows at a rate of 50 mph while the plane travels at a rate of 550 mph. There you go!
Y=2x is an equation that passes through those points
Hey!
Hope this helps...
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
To solve this, we will be doing a semi-alternate route, but it will get us to our answer...
400 / 100 = 4
30 / 4 = 7.5 seconds
60 * 60 * 7.5 = 27,000 meters per hour
<em></em><em>Lets plug it into our meters to miles formula...</em>
27,000 / 1,609.344 ~ 16.777 miles per hour
So...
The answer is: The Polar Express was going 27,000 meters per hour (or roughly close to 16.777 miles per hour)...
