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sin θ = 4/7, θ in quadrant II. Find the remaining five trigonometric functions (cos θ, tan θ, csc θ, sec θ, cot θ).
2. Given that $x = x(t)$ and $y = y(t)$ are two functions in the variable $t$ and that $xy^2 = 3x + 2y$, find $\frac{dy}{dt}$ at $x = 1$, $y = 3$ and $\frac{dx}{dt} = 5$.
Example 5.5.3 Find the velocity of the system shown in Figure 5.6a when the applied force is $f(t) = e^{-t}u(t)$. Assume zero initial conditions. Solve the same problem using convolution techniques. The input is the force and the output is the velocity. Solution The controlling equation is, from Figure 5.6b, $\frac{dv}{dt} + 5v + 4 \int_0^t v \, dt = e^{-t}u(t)$. Laplace transform this equation and then solve for $F(s)$. We obtain
The time required for an automotive center to complete an oil change service on an automobile approximately follows a normal distribution, with a mean of 17 minutes and a standard deviation of 2 minutes (a) The automotive center guarantees customers that the service will take no longer than 20 minutes. If it does take longer, the customer will receive the service for half-price. What percent of customers receive the service for half-price? (b) If the automotive center does not want to give the discount to more than 4% of its customers, how long should it make the guaranteed time limit? Click here to view the standard normal distribution table (page 1) Click here to view the standard normal distribution table (page 2) (a) The percent of customers that receive the service for half-price is % (Round to two decimal places as needed) (b) The guaranteed time limit is minutes. (Round up to the nearest minute.)
For PbCl$_2$, K$_{sp}$ = 0.0000128 Determine the molar solubility of PbCl$_2$. Hint: Write the ICE table and K$_{sp}$ expression out and be careful of exponents. Report your answer with 4 places past the decimal point. Do not use scientific notation.
1. Use the table of Laplace transforms to find the inverse Laplace transform.\\ (a) \frac{3}{(s-7)^4}\\ (b) \frac{2s-4}{s^2-4s+13}\\ (c) \frac{1}{s^2+4s+20}\\ (d) \frac{2}{s^2+9}\\ (e) \frac{s^2-1}{(s^2+1)^2}\\ (f) \frac{1}{(s-2)^2-4}\\ (g) \frac{12s-24}{(s^2-4s+85)^2}\\ (h) \frac{2}{(s-3)^2-9}\\ (i) \frac{s^2-4s+3}{(s^2-4s+5)^2}
Solve the wave equation for a potential of the form $V = -V_0(1 + i\zeta)$, where $V_0$ and $\zeta$ are positive constants. If $\zeta << 1$, show that there are stationary state solutions that represent plane waves with exponentially attenuated amplitude, describing absorption of the waves. Calculate the absorption coefficient.
Obtain the transfer function $Y(s)/X(s)$ of the system in figure 4. (20 Marks)
Counting Evaluate the following combinations. Check your results using the combinations calculator. Combinations on Calculator Find the number of combinations of 6 objects taken 4 at a time. Find the number of combinations of 16 objects taken 5 at a time. Evaluate: ${16}C_1$ Evaluate: ${7}C_7$