Consider the following hypotheses: 12:V ) >(x)) Use rules of inference to prove that the following conclusion follows from th
ese hypotheses: Clearly label the inference rules used at every step of your proof 2. Consider the following hypotheses: H1 Vr (C()--A(x)) H2 : Vr (A() Vy B(y)) Use rules of inference to prove that the following conclusion follows C: 3r (B(x) AC()) H3: Br A(a) from these hypotheses: Clearly label the inference rules used at every step of your proof. 3. Consider the following predicate quantified formula: r y (P(x, y)P(, y)) Prove the unsatisfiability of this formula using rules of inference.
1 answer:
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Answer: D. 0.29 m
Explanation:
We will use the following equations to describe the leap of the cat:
(1)
(2)
Where:
is the height of the cat
is the cat's initial velocity
is the acceleration due gravity
is the time
is the y-component of the velocity
Now the cat will have its maximum height when
. So equation (2) is rewritten as:
(3)
Finding :
(4)
(5)
(6)
Substituting (6) in (1):
(7)
Finally:
(8)
Answer:
a) 17.8 m/s
b) 28.3 m
Explanation:
Given:
angle A = 53.0°
sinA = 0.8
cosA = 0.6
width of the river,d = 40.0 m,
the far bank was 15.0 m lower than the top of the ramp h = 15.0 m,
The river itself was 100 m below the ramp H = 100 m,
(a) find speed v
vertical displacement
putting values h=15 m, v=0.8
............. (1)
horizontal displacement d = vcosA×t = 0.6×v ×t
so v×t = d/0.6 = 40/0.6
plug it into (1) and get
solving for t we get
t = 3.734 s
also, v = (40/0.6)/t = 40/(0.6×3.734) = 17.8 m/s
(b) If his speed was only half the value found in (a), where did he land?
v = 17.8/2 = 8.9 m/s
vertical displacement =
⇒
t = 5.30 s
then
d =v×cosA×t = 8.9×0.6×5.30= 28.3 m