Answer:
C (2, -1)
Step-by-step explanation:
C has the same x coordinate as A = 2
that eliminates A and B.
and the y value of C has to be closer to the y value of B than to the y value of A (due to the 5:3 ratio).
so, without spending unnecessary effort on actual calculation, we can directly derive the correct answer to be C.
but to show in numbers, the "coordinate triangle" of the difference between D and B is a similar triangle to ACD. and so, the ratio of one side pair applies then to all other sides too. including the individual coordinate differences.
so, also the y difference of A to D relates to the y difference between D and B in the same ratio of 5:3 of the overall y difference of A to B.
the y difference A to B is 2 - -6 = 8
the 5/3 split of 8 units is actually 5 and 3.
so, the y coordinate of D is -6 + 5 = -1
and C must have the same y coordinate.
therefore, it is proven that answer C (2, -1) is the right answer.
Send me your email I will send the working.
The answers:
x = 1
y = -5
Answer:
1. 625,000 J
2. 100 J
4. 5 kg
5. √5 ≈ 2.236 m/s
Step-by-step explanation:
You should be aware that the SI derived units of Joules are equivalent to kg·m²/s².
To reduce confusion between <em>m</em> for mass and m for meters, we'll use an <em>italic m</em> for mass.
In each case, the "find" variable is what's left after we put the numbers into the formula. It is what the question is asking for. The "given" values are the ones in the problem statement and are the values we put into the formula. The formula is the same in every case.
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1. KE = (1/2)<em>m</em>v² = (1/2)(2000 kg)(25 m/s)² = 625,000 kg·m²/s² = 625,000 J
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2. KE = (1/2)<em>m</em>v² = (1/2)(0.5 kg)(20 m/s)² = 100 kg·m²/s² = 100 J
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4. KE = (1/2)<em>m</em>v²
250 J = (1/2)<em>m</em>(10 m/s)² = 50 m²/s²
(250 kg·m²/s²)/(50 m²/s²) = <em>m</em> = 5 kg
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5. KE = (1/2)<em>m</em>v²
2000 kg·m²/s² = (1/2)(800 kg)v²
(2000 kg·m²/s²)/(400 kg) = v² = 5 m²/s²
v = √5 m/s ≈ 2.236 m/s
Answer:
The Car.
Step-by-step explanation:
We need to find the unit rate for each vehicle to figure out who is traveling faster or slower.
Car: 600/20 = 30 ft per second
Motorcycle: 300/12 = 25 ft per second
So, the Car is faster
