1. m • (n • p) 2. (q ⊃ ~t) • (~m v q) 3. ~t...

1. m •   (n • p)
2. (q   ⊃ ~t) • (~m v q)
3.   ~t ⊃ z     : .     z

Expert Solution

Colby Messinger answered 2 years ago

Prove via induction the following properties of Pascal’s Triangle: •P(n,2)=(n(n-1))/2 • P(n+m+1,n) = P(n+m,n)+P(n+m−1,n−1)+P(n+m−2,n−2)+···+P(m,0) for all...

Prove via induction the following properties of Pascal’s Triangle: •P(n,2)=(n(n-1))/2 • P(n+m+1,n) = P(n+m,n)+P(n+m−1,n−1)+P(n+m−2,n−2)+···+P(m,0) for all m ≥ 0

Prove that (((p v ~q) ⊕ p) v ~p) ⊕ (p v ~q) ⊕ (p ⊕...

Prove that (((p v ~q) ⊕ p) v ~p) ⊕ (p v ~q) ⊕ (p ⊕ q) is equivalent to p ^ q. Please show your work and name all the logical equivalence laws for each step. ( v = or, ~ = not, ⊕ = XOR) Thank you

V = X'(t) = -t^2 + 6 m/s Implies X(t) = -(1/3)t^3 + 6t The initial...

V = X'(t) = -t^2 + 6 m/s Implies X(t) = -(1/3)*t^3 + 6*t The initial position is zero in this case. This function will initially increase (this means the object is moving forward), then the negative force will be too strong, so the object will start moving backwards. calculate the maxima and minima. Graph the function X(t). Describe the motion. Every detail.

For problems 1-4 the linear transformation T/; R^n - R^m is defined by T(v)=AV with A=[-1 -2...

For problems 1-4 the linear transformation T/; R^n - R^m is defined by T(v)=AV with A=[-1 -2 -1 -1 2 1 0 -4 4 6 1 15] 1. Find the dimensions of R^n and R^m (3 pts) 2. Find T(<-2, 1, 4, -1>) (5 pts) 3. Find the preimage of <-6, 12, 4> (8 pts) 4. Find the Ker(T) (8 pts)

Calculus dictates that (∂U/∂V) T,Ni = T(∂S/∂V)T,Ni – p = T(∂p/∂T)V,Ni – p (a) Calculate (∂U/∂V)...

Calculus dictates that (∂U/∂V) T,Ni = T(∂S/∂V)T,Ni – p = T(∂p/∂T)V,Ni – p (a) Calculate (∂U/∂V) T,N for an ideal gas [ for which p = nRT/V ] (b) Calculate (∂U/∂V) T,N for a van der Waals gas [ for which p = nRT/(V–nb) – a (n/V)2 ] (c) Give a physical explanation for the difference between the two. (Note: Since the mole number n is just the particle number N divided by Avogadro’s number, holding one constant is equivalent...

(1) T(n)=9⋅T(n3)+n2⋅(log⁡(n))2 (2) T(n) = 10 * T(n/3) + n^2 One of these can be solved...

(1) T(n)=9⋅T(n3)+n2⋅(log⁡(n))2 (2) T(n) = 10 * T(n/3) + n^2 One of these can be solved using the Master Theorem; the other cannot. Which one can be solved using the Master Theorem? Compute the solution to this recurrence relation. Which one cannot be solved using the Master Theorem? Carefully explain why not. (NOTE: A complete solution will use the definition of big-O.) Use another method to solve this recurrence relation. To make this a bit easier, you may assume that...

A bulldozer’s velocity (in m/s) at a time t is given by v(t)=t^2-t+3. (a)Estimate the displacement...

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Show that if P;Q are projections such that R(P) = R(Q) and N(P) = N(Q), then...

Show that if P;Q are projections such that R(P) = R(Q) and N(P) = N(Q), then P = Q.

An aircraft is in level flight at airspeed v(t) m/s with thrust T(t) N at cruising...

An aircraft is in level flight at airspeed v(t) m/s with thrust T(t) N at cruising altitude. Suppose that at v0 = 250 m/s, the aerodynamic drag experienced by the aircraft at this altitude is: Fd(v) = 0.25v 2 . (1) Then, an extremely simplified model relating v(t) to T(t) is: mv˙(t) + Fd(v(t)) = T(t), (2) where m = 25000 kg. Assume v(t) is always positive. Question 1. Linearize (2) at v0 = 250 m/s, and an appropriate nominal...

The demand for T-shirts is Q=20 – (P/2), where Q is the number of t-shirts and...

The demand for T-shirts is Q=20 – (P/2), where Q is the number of t-shirts and P is the price. The private cost of producing t-shirts is C(Q) = Q^2, with the private marginal cost being MC(P) = 2Q. Washing and dyeing t-shirts causes water pollution with marginal external costs of MC(E) = Q. A) Based on the above information, net welfare: consumer surplus + producer surplus - damages of consumption at market equilibrium is ______(no decimal point)...(numeric answer). Hint:...

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