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robin carroll

robin c.

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A laboratory exercise on the concept of static equilibrium uses an apparatus called a force table. The force table consists of a round, level platform marked in degree increments about its circumference. In the center of the table sits a massless ring, to which three strings are tied. Each string is strung over a separate pulley clamped to the edge of the platform and then tied to a freely hanging mass, so that each string is under tension and the ring is suspended parallel to the table surface. There is a mass of $m_1 = 145$ g located at $\theta_1 = 24.5^\circ$ and a second mass of $m_2 = 215$ g located at $\theta_2 = 291^\circ$. Calculate the mass $m_3$ and the location $\theta_3$ (in degrees) that will balance the system and hold the ring stationary over the center of the platform. $m_3 =$ 167 g Incorrect Answer $\theta_3 =$ 296.5 Incorrect Answer

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Institutional investors are accurately described by which statement? Banks and student loans are examples of institutional investors. The number of institutional investors in the United States has declined since the 1960s. Institutions account for over 90 percent of total U.S. equity value. Institutions invest their funds by purchasing shares of stock in corporations.

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Which of the following has the faster potential rate of evolution? a bacterium a fly a human all the above evolve at the same rate there is no pattern

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Which method of the Thread class is used to start a new thread of execution? Question 33Answer a. start() b. run() c. execute() d. begin()

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\( \lim _{x \rightarrow 1} \frac{1-x^{2}}{2+\sqrt{x^{2}+3}} \)

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[12] 1. Use Fermat's Little Theorem and then a simple calculator to compute the following congruences. (a) 11^(21423)(mod13) (b) 9^(34567)(mod17) [12] 2. For each of the following primes p and ainN, compute a^(-1)(modp) by using the Fermat's Little Theorem and the Fast Powering Algorithm: (a) p=587 and a=345. (b) p=104801 and a=78467. [10] 3. Use Fermat's Little Theorem with a=2 to check whether or not m=574663 is a prime number. Explain. [16] 4. Show how to do all the parts in this problem by hand and explain. (a) Determine if 2 is a primitive root of Z_(13)^(**) ? That is, determine if ord(2)=12 ? Note: You are not required to calculate all powers of 2 . (b) Determine if 2 is a primitive root of Z_(23)^(**). (c) Show that 2 is a primitive root of Z_(19)^(**). (d) Use part (c) to find the order of all elements in Z_(19)^(**). (e) Write down all primitive roots of Z_(19)^(**) using part (d). (No work is required). [12] 1. Use Fermat's Little Theorem and then a simple calculator to compute the following congruences. (a) 1121423 (mod 13) (b) g34567 (mod 17) [12]2 2. For each of the following primes p and a E N, compute a-1 (mod p) by using the Fermat's Little Theorem and the Fast Powering Algorithm: (a) p= 587 and a= 345. (b) p=104801 and a= 78467. [10] 3. Use Fermat's Little Theorem with a = 2 to check whether or not m = 574663 is a prime number Explain. [16] 4. Show how to do all the parts in this problem by hand and explain (a) Determine if 2 is a primitive root of Z13*? That is, determine if ord(2) = 12? Note: You are not required to calculate all powers of 2 (b) Determine if 2 is a primitive root of Z23* (c) Show that 2 is a primitive root of Z19*. (d) Use part (c) to find the order of all elements in Zig* (e) Write down all primitive roots of Zig* using part (d). (No work is required).

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Use the Flow of Information from Gene to Protein tour of the Gene Expression Visual Synthesis Map to answer the question. Which base pairing is incorrect? A-G G-C U-A A-T

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Martha is walking home from work at night, and she hears a noise in a nearby alley. Her pupils dilate, she begins sweating, and her heart rate increases. Which division of the nervous system is responsible for this reaction? Question 7Select one: a. sympathetic b. central c. parasympathetic d. somatic

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When Jenny decided to have a baby before she was married, her parents were very upset. Their reaction may be influenced by which of the following? Cultural norms Attribution bias Systemic thinking The ripple effect

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Problem 5: Let \(\{a_n\}\) be a sequence of non-negative numbers. Let \(E = [0, \infty)\) and define \(f(x) = a_n\), \(x \in [n, n+1)\), \(n = 1, 2, ...\) Show that \(\int_E f = \sum_{n=1}^\infty a_n\). That is, any series of non-negative terms can be represented as a Lebesgue integral.

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