9514 1404 393
Answer:
- see below for a sketch
- 12 km
Step-by-step explanation:
The distance can be calculated using the Law of Cosines. The angle internal to the triangle at Q is (180°-(146° -65°)) = 99°. Then the distance PR can be found from ...
PR² = PQ² +QR² -2·PQ·QR·cos(∠PQR)
PR² = 6² +10² -2·6·10·cos(99°) ≈ 154.77
PR ≈ √154.77 ≈ 12.44 . . . . km
The distance PR is about 12 km.
Answer:
• for x = 2a√t, make t the subject:
![{ \tt{x = 2a \sqrt{t} }} \\ \\ { \tt{ \sqrt{t} = \frac{x}{2a} }} \\ \\ { \boxed{ \tt{t = \frac{ {x}^{2} }{4 {a}^{2} } }}}](https://tex.z-dn.net/?f=%7B%20%5Ctt%7Bx%20%3D%202a%20%5Csqrt%7Bt%7D%20%7D%7D%20%5C%5C%20%20%5C%5C%20%7B%20%5Ctt%7B%20%5Csqrt%7Bt%7D%20%20%3D%20%20%5Cfrac%7Bx%7D%7B2a%7D%20%7D%7D%20%5C%5C%20%20%5C%5C%20%7B%20%5Cboxed%7B%20%5Ctt%7Bt%20%3D%20%20%5Cfrac%7B%20%7Bx%7D%5E%7B2%7D%20%7D%7B4%20%7Ba%7D%5E%7B2%7D%20%7D%20%7D%7D%7D)
• then find y:
![{ \tt{y = {ar}^{2} - 2at}} \\ \\ { \tt{y = {ar}^{2} - 2a( \frac{ {x}^{2} }{4 {a}^{2} } ) }} \\ \\ { \boxed{ \tt{y = {ar}^{2} - \frac{ {x}^{2} }{2a} }}}](https://tex.z-dn.net/?f=%7B%20%5Ctt%7By%20%3D%20%20%7Bar%7D%5E%7B2%7D%20%20-%202at%7D%7D%20%5C%5C%20%20%5C%5C%20%7B%20%5Ctt%7By%20%3D%20%20%7Bar%7D%5E%7B2%7D%20-%202a%28%20%5Cfrac%7B%20%7Bx%7D%5E%7B2%7D%20%7D%7B4%20%7Ba%7D%5E%7B2%7D%20%7D%20%29%20%7D%7D%20%5C%5C%20%20%5C%5C%20%7B%20%5Cboxed%7B%20%5Ctt%7By%20%3D%20%20%7Bar%7D%5E%7B2%7D%20-%20%20%5Cfrac%7B%20%7Bx%7D%5E%7B2%7D%20%7D%7B2a%7D%20%20%7D%7D%7D)
It'd be clearer if you'd write: "How many tenths are there in 2 3/5?"
2 3/5 13/5
---------- = ---------- = 26
(1`/10) 1/10
There are 26 tenths in 2 3/5.