Answer:
Step-by-step explanation:
A boat leaves the harbor entrance and travels 28 miles in the direction N 43° E.
Displacement in vector form
= 28 cos43 i + 28sin43j
= 20.47 i + 19.1 j
The captain then turns the boat 90° and travels another 15 miles in the direction S 47° E
Displacement
= 15 cos47 i - 15 sin47 j
= 10.22 i - 10.97 j
Total displacement
= 20.47 i + 19.1 j + 10.22 i - 10.97 j
= 30.69 i - 8.13 j
Magnitude of displacement
= 31.75 miles
Angle with east direction
TanФ = - 8.13 / 30.69
Ф = 15 degree south of east.
Each coin has a head and a tail, therefore when you toss two coins, you have 4 possible outcomes. You have two heads in only one of these outcomes, while the other three have at least one tail.
The expected value of the game is the price paid/gained times the probability of loss/victory:
E = (1 / 4) · (-6) + (3 / 4) · (2)
= -3 / 2 + 3 / 2
= 0
Bob expects to tie with Will.
5x = 2x + 9, where 5x > 0 and 2x + 9 > 0 ;
Then, 3x = 9 ;
Then, x = 3 ;
Verify : 5 × 3 = 2 × 3 + 9 ;correct !
5 × 3 > 0 ; correct !
2 × 3 + 9 > 0; correct !
Answer: (-2,1)
Step-by-step explanation:
So first you need to factor and get 8( t-1 ) (2t+1)=0. Then you need to divide both sides by 8 to isolate the equation. 0/8=0 so ( t-1 ) (2t+1)=0. Next set each of the factors = to 0 and get t-1=0 and 2t+1=0. Solve, and get t=1 and t=-1/2. The negative does not apply so you know it takes 1 second for the ball to hit the ground.
