Answer:
- r(0) = <0, 100> . . . . . . . .meters
- r'(0) = <7.071, 7.071> . . . . meters per second
Step-by-step explanation:
<u>Initial Position</u>
The problem statement tells us we're measuring position from the ground at the base of the building where the projectile was launched. The initial horizontal position is presumed to be zero. The initial vertical position is said to be 100 meters from the ground, so (in meters) ...
r(0) = <0, 100>
<u>Initial Velocity</u>
The velocity vector resolves into components in the horizontal direction and the vertical direction. For angle α from the horizontal, the horizontal component of velocity is v₁·cos(α), and the vertical component is v₁·sin(α). For v₁ = 10 m/s and α = π/4, the initial velocity vector (in m/s) is ...
r'(0) = <10·cos(π/4), 10·sin(π/4)>
r'(0) ≈ <7.071, 7.071>
Answer:
63 ft
Step-by-step explanation:
Multiply your yard value by 3 to find it's value in feet.
<em>(Remember that 1 yard = 3 feet.)</em>
21<em>y</em> x 3 = 63<em>ft</em>
Answer: Part 1: 111.24
Part 2: 9.27
Part 3: 54 minutes
Step-by-step explanation:
Part 1: Since you already know that the total bill increases by 3%, you just have to find 103% of 180.
1.03*108= 111.24; your answer would be 111.24 pounds
Part 2: Since you already know yearly, 111.24 divided by 12= 9.27 per month
Part 3: First find 73% of 200 which is 146. Then subtract that from 200 which is 54. So you have 54 minutes left.
If the amount of monkeys is m, lions is a, and lizards is b, then a+b+m=151, 17+a=m (since there are 17 more monkeys than lions), and 30+a=b. Substituting those values in (17+a=m and 30+a=b), we have 30+17+a+a+a=151=47+3a. Subtracting 47 from both sides, we get 104=3a. Next, we can divide both sides by 3 to get 104/3=a (the number of lions), 104/3+17=the number of monkeys, and 104/3+30=the number of lizards. Somehow we end up with a fraction (not a whole number), so there are 2/3rds of monkeys floating around using this logic.
