Numerade

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When you are 18 years old you have a hair that is 19 centimeters long, and your hair grows about 12 centimeters each year. Let H(t) be the length, in centimeters, of that hair t years after age 18. (a) Find a formula that gives H as a linear function of t. H = (b) How long will it take for the hair to reach a length of 101 centimeters? (Round your answer to two decimal places.) yr

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Problem 3 Let G be the grammar below G: S -> E E->E+EE*E|(E) E-> abc | D D -> 0| 1| 2| 3| 4| 5| 6| 7| 8 | 9 a. Show that G is ambiguous by finding two different parse trees for w = (b+5)* c + b. Label and paste your parse trees into Homework 5. How many leaves are in your parse tree? b. Draw a parse tree for w = 5* (a + 2*b) starting from S. Paste your parse tree into Homework 5. How many leaves are in your parse tree?

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The greater the MPC, 1) the greater the expenditure multiplier. 2 the larger the change in equilibrium income for a given change in spending. 3) neither A nor B is correct. 4) both A and B are correct.

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you conduct a series of five, 1:10 dilutions. you plate 1 ml from your last dilution tube, and count 65 colonies on a plate. what is your starting concentration of your original culture

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In 2020, Moderna developed an effective mRNA based vaccine against COVID-19. The mRNA causes the body to make viral proteins that then elicit a strong immune response. The vaccine consists of a suspension containing 0.25 mg/mL of the mRNA. The required dose of the mRNA is 103.0 µg. Part A What volume of the vaccine suspension must be injected to achieve the required dose of mRNA? Express the volume in milliliters to two significant figures.

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(11%) Problem 4: An airplane starts at rest and accelerates at 6.3 m/s² at an angle of 31° south of west. ? 50% Part (a) After 7 s, how far, in meters, in the westerly direction has the airplane traveled? Xwest = m sin() cos() tan() cotan() asin() acos() atan() acotan() sinh() cosh() tanh() cotanh() Degrees Radians Submit Hint Feedback I give up! Feedback: 2% deduction per feedback. ints: 0 for a 0% deduction. Hints remaining: 0 50% Part (b) After 7 s, how far, in meters, in the southerly direction has the airplane traveled?

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4. Synchrotron radiation. Taking $\boldsymbol{\beta} = \beta \hat{\mathbf{e}}_z, \dot{\boldsymbol{\beta}} = \beta \hat{\mathbf{e}}_x, \mathbf{R} = \frac{\mathbf{r} - \mathbf{r}'}{|\mathbf{r} - \mathbf{r}'|} = \sin \theta \cos \phi \hat{\mathbf{e}}_x + \sin \theta \cos \phi \hat{\mathbf{e}}_y + \cos \theta \hat{\mathbf{e}}_z,$ a) Show that $\frac{dP}{d\Omega} = \frac{q^2}{4\pi} \beta^2 \frac{(1 - \beta \cos \theta)^2 - (1 - \beta^2)}{(1 - \beta \cos \theta)^5},$ $P = \frac{2}{3} q^2 \beta^2 \gamma^4,$ Where \(\gamma = 1/(1 - \beta^2)^{1/2},\ b) Estimate the line width due to radiation losses.

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Problem 10. Shortest Road Trip. Mary and Tom are taking a road trip from New York City to San Francisco. Because it is a 44-hour drive, Mary and Tom decide to switch off driving at each rest stop they visit. However, because Mary has a better sense of direction than Tom, she should be driving both when they depart and when they arrive (to navigate the city streets). Given a route map represented as a weighted undirected graph $G = (V, E, w)$ with positive edge weights, where vertices represent rest stops and edges represent routes between rest stops, devise an efficient algorithm to find a route (if possible) of minimum distance between New York City and San Francisco such that Mary and Tom alternate edges and Mary drives the first and last edge. [Hint: one way to solve this problem is to construct a new graph $G'$ to represent the alternate driving]

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Find the first partial derivatives of \frac{2x - y}{2x + y} f(x, y) = \frac{2x - y}{2x + y} at the point (x, y) = (1, 1). \frac{\partial f}{\partial x}(1, 1) = 0 \frac{\partial f}{\partial y}(1, 1) =

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Consider two identical masses m connected together with a spring and attached with another spring to a moving support. The support is oscillating vertically by an external drive and its position is given by $h(t) = A \cos(\omega_d t)$. The spring constant for the both springs is k. Ignore effects of damping. A. Find the equations of motion for the vertical displacements of the two masses $y_1(t)$ and $y_2(t)$. B. Find the steady state response for $y_1(t)$ and $y_2(t)$. Plot the amplitude as a function of the driving frequency $\omega_d$ for each of the masses. C. By inspecting the results of (B), find the frequencies and amplitude ratios for the normal modes of the undriven system.

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nicol-s s.