Numerade

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Use summation properties and formulas to rewrite and evaluate the sum $$\sum_{j=1}^{28} (j^2 - 4j).$$ $$\sum_{j=1}^{28} (j^2 - 4j) =$$

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Factor out the greatest common factor, GCF. 12(5x+3) - 3x^2(-5x-3)

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What is the significance of the Poynting vector in understanding the flow of electromagnetic energy?

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Q3. Consider a processor having 3 level cache hierarchy. The processor has 32-bit address. Assume an exclusive cache implementation. The details of 3 level cache are as below: L1 Cache: Direct Mapped, 4 lines, 2 words/line (1word=4bytes) L2 Cache: 2 way set associative, 8 lines, 2 words/line (1word=4bytes), LRU replacement policy L3 Cache: Fully associative, 16 lines, 2 words/line (1word=4bytes), LRU replacement policy Given that the processor generates block addresses in the following order: 9,8,0,8,8,4,9,12,5,8,12,0,8,4,8 Determine the level from which each reference is serviced by filling M(for miss), H(for hit), NA(if memory reference does not reach that level) in the table below. Assume that all caches are initially empty.

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(a) Consider the following function f(t)=f(t+4)fffffff(t)=a_(0)+sum_(n=1)^(infty ) a_(n)cos((npi t)/(L))+b_(n)sin((npi t)/(L)),Lb_(n)a_(n)pi (-8)^(n)-8^(n)b_(n)= 回 (a) Consider the following function (3, 1 < t 1, f(t= 6-3|t|,-2<t<-1and 1<t<2, and f(t) =f(t+4). (i) Choose the correct statement for function f from the following statements O Function f is odd. o Function f is even. O Function f is both even and odd. Function f is neither even nor odd. (ii) Your classmate Edwin wants to approximate f by the Fourier series nTt f(t) =ao+ L an cos(r + bn sin T. where I is the half-period of the function. Help Edwin by finding the values of bn and an and simplifying them. Give your answers in the boxes below. Syntax advice: Use Pi for Tr. Note that (-8) is different to --87 . bn ,forn=1,2,3,.. ao 18/4 an forn=1,2,3,..

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Suppose $f(x) = x^3 + 8$ and $g(x) = \sqrt{x}$. Then $f(g(x)) =$ help (formulas) $g(f(x)) =$ help (formulas)

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Exhibit 2: Price of Calculators $27 Domestic Supply 12 7 World Price 2 Domestic Demand 0 150 300 400 Quantity of Calculators Refer to Exhibit 2. For the country shown, producer surplus before trade is equal to: $375 $1,500 $3,000 $900 $750

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If you take a look at the chart, which of the following could be potential external costs to the consumer's health? Select all that apply, then click Submit below Increased risk of infections Increased risk of cancer Potential skin, nervous, and reproductive problems

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6. Consider the finite field $F_2[\alpha]$ where $\alpha$ is a root of the irreducible polynomial \newline $p(x) = x^3 + x^2 + 1$. \newline a. (10) Find the inverse of $1 + \alpha^2$ in $F_2[\alpha]$. \newline b. (5) How many roots does the equation $x^7 - 1 = 0$ have in $F_2[\alpha]$? Explain.

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B) Consider the system: $x = f(x) = -h(x)$ \\ Then answer the following; \\ 1) State whether $h(x)$ is (a) continuous (b) locally Lipschitz; (c) continuously differentiable; (d) globally Lipschitz. \\ 2) State whether the solution exist for (a) $t \in [0,\infty)$ (b) $t \in [0,T)$ where T is a finite time. Give the reason. \\ 3) State whether the origin is (a) an asymptotically stable equilibrium point (b) a finite time stable point (c) an unstable equilibrium point. Give the reason.

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