Answer:
Distance = 8
![Formula =\\\sqrt{(x_2-x_1)^2+(y_2-y_2)^2}](https://tex.z-dn.net/?f=Formula%20%3D%5C%5C%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_2%29%5E2%7D)
Step-by-step explanation:
![(17,3)=(x_1 , y_1 )\\ (17,-5)=(x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\d = \sqrt{(17-17)^2+(-5-3)^2}\\\\ d = \sqrt{(0 )^2+(-8)^2}\\\\d = \sqrt{0 +64}\\\\ d = \sqrt{64} \\\\d = 8](https://tex.z-dn.net/?f=%2817%2C3%29%3D%28x_1%20%2C%20y_1%20%29%5C%5C%20%2817%2C-5%29%3D%28x_2%2Cy_2%29%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D%20%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B%2817-17%29%5E2%2B%28-5-3%29%5E2%7D%5C%5C%5C%5C%20d%20%3D%20%5Csqrt%7B%280%20%29%5E2%2B%28-8%29%5E2%7D%5C%5C%5C%5Cd%20%3D%20%5Csqrt%7B0%20%2B64%7D%5C%5C%5C%5C%20d%20%3D%20%5Csqrt%7B64%7D%20%5C%5C%5C%5Cd%20%3D%208)
Answer:
He played 40 matches in total, scoring 32 goals.
Step-by-step explanation:
Since after a certain number of football matches, a footballer averages 1 goal per game, and he only scored 2 goals in the next 10 games and his average dropped to 0.8 goals per game, to determine how many football matches did he play altogether you must perform the following calculation:
10/10 + 2/10 = 12/20 = 0.6
8/8 + 2/10 = 10/18 = 0.55
12/12 + 2/10 = 14/22 = 0.64
20/20 + 2/10 = 22/30 = 0.73
24/24 + 2/10 = 26/34 = 0.76
30/30 + 2/10 = 32/40 = 0.8
Thus, he played 40 matches in total, scoring 32 goals.
Answer:
The 10th term of the sequence is:
Step-by-step explanation:
Given the number
729, 243, 81, 27...
A geometric sequence has a constant ratio 'r' and is defined by
![a_n=a_0\cdot r^{n-1}](https://tex.z-dn.net/?f=a_n%3Da_0%5Ccdot%20r%5E%7Bn-1%7D)
Computing the ratio of all the adjacent terms
![\frac{243}{729}=\frac{1}{3},\:\quad \frac{81}{243}=\frac{1}{3},\:\quad \frac{27}{81}=\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B243%7D%7B729%7D%3D%5Cfrac%7B1%7D%7B3%7D%2C%5C%3A%5Cquad%20%5Cfrac%7B81%7D%7B243%7D%3D%5Cfrac%7B1%7D%7B3%7D%2C%5C%3A%5Cquad%20%5Cfrac%7B27%7D%7B81%7D%3D%5Cfrac%7B1%7D%7B3%7D)
The ratio of all the adjacent terms is the same and equal to
![r=\frac{1}{3}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B1%7D%7B3%7D)
also
![a_1=729](https://tex.z-dn.net/?f=a_1%3D729)
Therefore, the nth term is computed by:
![a_n=729\left(\frac{1}{3}\right)^{n-1}](https://tex.z-dn.net/?f=a_n%3D729%5Cleft%28%5Cfrac%7B1%7D%7B3%7D%5Cright%29%5E%7Bn-1%7D)
Putting n = 10 to find the 10th term
![a_{10}=729\left(\frac{1}{3}\right)^{10-1}](https://tex.z-dn.net/?f=a_%7B10%7D%3D729%5Cleft%28%5Cfrac%7B1%7D%7B3%7D%5Cright%29%5E%7B10-1%7D)
![=729\cdot \frac{1}{3^9}](https://tex.z-dn.net/?f=%3D729%5Ccdot%20%5Cfrac%7B1%7D%7B3%5E9%7D)
![=\frac{1\cdot \:729}{3^9}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%5Ccdot%20%5C%3A729%7D%7B3%5E9%7D)
![=\frac{729}{3^9}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B729%7D%7B3%5E9%7D)
![=\frac{3^6}{3^9}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3%5E6%7D%7B3%5E9%7D)
![=\frac{1}{3^3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B3%5E3%7D)
![a_{10}=\frac{1}{27}](https://tex.z-dn.net/?f=a_%7B10%7D%3D%5Cfrac%7B1%7D%7B27%7D)
Therefore, the 10th term of the sequence is:
Answer:
5 if its a dice.
Step-by-step explanation:
So the formula for the circumference of a circle is π x diameter
Since we know the the circumference already, we just divide that by π:
12π / π = 12
Now we halve the diameter to get the radius:
12 / 2 = 6
The area of a circle is π x radius²
So the area is:
·π x 6² = 36π· (or 113 not in terms of π)