An incompressible liquid flows through a straight horizontal pipe. Friction of the fluid within the pipe causes a small amount of heat to be transferred from the fluid; to compensate, flow work must be done on the fluid to move it through the system (so W(dot)fl is greater than zero.

a) How are V(dot)in and V(dot)out related, where V(dot) is the volumetric flow rate of the liquid? (Remember, fluid is incompressible)

b) How must the pressures of Pin and Pout be related?

Any help is appreciated, I don't understand this at all.

A 130.0 mL sample of 0.070 M Ca 2 + is titrated with 0.070 M EDTA at pH 9.00. The value of log K f for the Ca 2 + − EDTA complex is 10.65 and the fraction of free EDTA in the Y 4 − form, α Y 4 − , is 0.041 at pH 9.00. What is K ′ f , the conditional formation constant, for Ca 2 + at pH 9.00?

What is the equivalence point volume, Ve, in milliliters?

Calculate the concentration of Ca2+ at V=(1/2)Ve.

Calculate the concentration of Ca2+ at V=Ve.

Calculate the concentration of Ca2+ at V=1.1Ve.

Calculate the mass percent (m/m) of a solution prepared by dissolving 49.94 gg of NaClNaCl in 173.6 gg of H2OH2O.

Express your answer to four significant figures.

Vinegar is a solution of acetic acid in water. If a 125 mLmL bottle of distilled vinegar contains 27.6 mLmL of acetic acid, what is the volume percent (v/v) of the solution?

Express your answer to three significant figures.

Calculate the mass/volume percent (m/v) of 20.5 gg NaClNaCl in 60.5 mLmL of solution.

Express your answer to three significant figures.

1) There is a continuous function from [1, 4] to R that is not uniformly continuous. True or False and justify your answer.

2) Suppose f : D : →R be a function that satisfies the following condition: There exists a real number C ≥ 0 such that |f(u) − f(v)| ≤ C|u − v| for all u, v ∈ D. Prove that f is uniformly continuous on D

Definition of uniformly continuous: A function f: D→R is called uniformly continuous iff for all sequences {a_n} and {b_n} in D if (a_n) - (b_n)→ 0 then f(a_n) - f(b_n)→ 0

Let R be the two-dimensional region in the first quadrant of the xy- plane bounded by the lines y = x and y = 3x, and by the hyperbolas xy = 1 and xy = 3. Let (x,y) = g(u,v) be the two-dimensional transformation of the first quadrant defined by x = u/v, y = v.

a) Compute the inverse transformation g−1.

b) Draw the region R in the xy-plane and the region g−1(R) in the uv-plane

c) Use the transformation to compute the value of the double integral xy dx dy

Q3. A)

I. Put the following sentences into their Clausal Elements:

Eg. John / danced / yesterday. S V A

i. Seeing is believing.

ii. I wish you good luck.

iii. What he said at the meeting was completely balderdash.

iv. Out of joy, the lecturer appointed Collins the course representative immediately.

v. Gyesi scores the third goal for Oasis FC in every competition.

II. Construct a Meaningful Sentence for EACH of the Following Patterns

i. SAVC

ii. ASVOC

iii. SVOA

iv. SVOCA

v. AASVC

Let A ∈ Mat n×n(R) be a real square matrix.

(a) Suppose that A is symmetric, positive semi-definite, and orthogonal. Prove that A is the identity matrix.

(b) Suppose that A satisfies A = −A^T . Prove that if λ ∈ C is an eigenvalue of A, then λ¯ = −λ.

From now on, we assume that A is idempotent, i.e. A^2 = A.

(c) Prove that if λ is an eigenvalue of A, then λ is equal to 0 or 1.

(d) Set V1 = {v ∈ C n | Av = v} and V0 = {v ∈ C n | Av = 0}. Show that im A = V1 and ker A = V0.

(e) Prove that A is diagonalizable.

You are testing a new GPS system for general aviation aircraft and have encountered some unexplained heating. Modeling the circuit as three resistors in series, R₁ (2 Ω) is known while R₂ and R₃ are not. We measure voltage drops of V₁= 1 V, V₂ = 50 V, and V₃ = 100 V respectively across the three resistors. Determine the resistance of the unknown resistors.

In addition to the above calculations, explain to a member of upper management why anomalous heating in this circuit is related to determining these values and hence may be beneficial to the future design operations.  

The grammar below generates a tiny subset of English sentences, without worrying much about subject-verb agreement:

G = {

S → NP VP

NP → the Adj N | N

VP → V | V NP

Adj → happy | angry | ε |

V → chases | growls | purrs

N → cat | dog

}

Convert G into Chomsky Normal Form. When eliminating rules that mix terminals and non-terminals on the RHS of a rewrite rule, add needed rules only, and please use the form X_word → word (e.g., X_the → the).

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