Answer:
5. 49, (x+7)²
6. 36, (x-6)²
7. 81/4, [x-(9/2)]²
Step-by-step explanation:
5. x² + 2(x)(7) + 7² = (x + 7)²
6. x² - 2(x)(6) + 6² = (x - 6)²
7. x² - 2(x)(9/2) + (9/2)² = (x - 9/2)²
<span>2π m2 and 200π m2
so ratio is 1:100</span>
x - 27 = 62 → ( add 27 to both sides )
x - 27 + 27 = 62 + 27
x = 89
drag first box then box with x = 89
To find the angle of the helicopter, we are going to take advantage of the fact the the sum of the interior angles of a triangle is always 180°. Lets denote that angle with
![h](https://tex.z-dn.net/?f=h)
, so:
![h+60+30=180](https://tex.z-dn.net/?f=h%2B60%2B30%3D180)
![h+90=180](https://tex.z-dn.net/?f=h%2B90%3D180)
![h=180-90](https://tex.z-dn.net/?f=h%3D180-90)
![h=90](https://tex.z-dn.net/?f=h%3D90)
Look what we have here: a angle of 90°, so our triangle is a right triangle.
Now, let
![x](https://tex.z-dn.net/?f=x)
be the distance between Amanda and the helicopter. Using the law of sines:
![\frac{x}{sine(30)} = \frac{4000}{sine(90)}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7Bsine%2830%29%7D%20%3D%20%5Cfrac%7B4000%7D%7Bsine%2890%29%7D%20)
Remember that sine of 90 ° is equal to 1, so:
![\frac{x}{sine(30)} = \frac{4000}{1}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7Bsine%2830%29%7D%20%3D%20%5Cfrac%7B4000%7D%7B1%7D%20)
![x=4000sine(30)](https://tex.z-dn.net/?f=x%3D4000sine%2830%29)
![x=2000](https://tex.z-dn.net/?f=x%3D2000)
We can conclude that the distance between Amanda and the helicopter is
2000 feet.