Numerade

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6. One physical quantity that a vector can represent is a force. In the coming weeks, we will learn how an object moves when a force is applied. We can already understand what happens when multiple forces are applied to an object using the mathematics of vector addition. Use this method to solve the following problem: Two dogs pull on two sleeves that come out of an old, abandoned piece of luggage. They both pull with forces of equal magnitude, $F_A = F_B = 1.00 \times 10^2$ N (Newtons, the SI unit of force), but at different angles, as shown in the figure. A) Determine the vector sum $F_A + F_B$. B) Find the magnitude of the sum, $|F_A + F_B|$. C) Is it equal to the sum of magnitudes, $|F_A| + |F_B|$ (or $F_A + F_B$)?

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Let $\lim_{x \to 3} f(x) = 4$ and $\lim_{x \to 3} g(x) = 2$. Use the limit rules to find the following limit. $\lim_{x \to 3} \frac{f(x) + g(x)}{2g(x)}$ $\lim_{x \to 3} \frac{f(x) + g(x)}{2g(x)} = \square$ (Type an integer or a simplified fraction.)

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What specific type of “thinking” refers to the ability to listen and decipher information in formulating opinions and making decisions in a rational way? a. Crystallized thinking. b. Concrete random thinking. c. Abstract sequential thinking. d. Fluid thinking.

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the muscles of the hand have a higher neuron to muscle fiber ration than muscles of the hip: true or false

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Match the ancient culture and the trained dancers for each culture. Egypt Crete ? [Choose] Male/female dancers attached to temples Pantomime dancers acted and danced to tell a story Bull dancers performed religious and entertaining dances Chorus dancers were amatuers who performed in theatrical performances Greece [Choose] Rome [Choose]

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Rewrite this measurement with a simpler unit, if possible. 1.9 \frac{kg \cdot kg}{kg \cdot m^2}

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Example 6.1 A thin annular disc has an inner radius of 50mm and an outer radius of 150mm and rotating uniformly at 5000 RPM. Determine the hoop $\sigma_\theta$ and radial $\sigma_r$ stresses at the inner and outer radii? Show the variation of these stresses with $r$ and the radius for which $\sigma_r$ is maximum. Assume that the disc is made of steel for which $\rho = 7480 \text{ kg/m}^3$ and $\nu = 0.3$.

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Solve the ODE using the method of power series, with center x_(0)=0 y''+7xy'-6y=3x

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21-31 Find the derivative of the function using the definition of a derivative. State the domain of the function and the domain of its derivative. 21. $f(x) = \frac{1}{2}x - \frac{1}{3}$ 22. $f(x) = mx + b$ 23. $f(t) = 5t - 9t^2$ 24. $f(x) = 1.5x^2 - x + 3.7$ 25. $f(x) = x^2 - 2x^3$ 26. $f(x) = x + \sqrt{x}$ 27. $g(x) = \sqrt{1 + 2x}$ 28. $f(x) = \frac{x^2 - 1}{2x - 3}$ 29. $G(t) = \frac{4t}{t + 1}$ 30. $g(t) = \frac{1}{\sqrt{t}}$ 31. $f(x) = x^4$

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The shown circuit is connected to an input voltage source $V_{in}(t)$. The output voltage $V_{out}(t)$ is taken across the resistor. Find the appropriate value for L and C to set the resonant frequency, $f_o = 5 kHz$. Also, determine the appropriate value of R to set the circuit step response to be critically damped?

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sharon c.