A particle P moves in a straight line with position given by $s(t)=80 e^{-\frac{t}{10}}-40 t \mathrm{m}$ where t is the time in seconds, $t \geqslant 0$. Find the initial position, velocity, and acceleration of P.

Rewrite the expression as a sum of terms.

$$\dfrac{\sqrt{b}-2b^{-3}}{4b^2}=$$

Another unproven conjecture is that there are an infinitude of primes that are 1 less than a power of $2,$ such as $3=2^{2}-1$. (a) Find four more of these primes. (b) If $p=2^{k}-1$ is prime, show that $k$ is an odd integer, except when $k=2$ . [Hint: $3 | 4^{n}-1$ for all $n \geq 1.1$

Bigger animals tend to carry their young longer before birth. The length of horse pregnancies from conception to birth varies according to a roughly Normal distribution with mean 336 days and standard deviation 3 days. Use the 68-95-99.7 rule to answer the following question. What percent of horse pregnancies are longer than 339 days? Show your work.

Find the area of each triangle. $b=5, c=5, A=20^{\circ}$

Prove that if a statement can be proved by ordinary mathematical induction, then it can be proved by the well-ordering principle.

Draw the anomers of D-erythrofuranose.

Solve the equation by using three methods. (A) Factoring and applying the zero product property. (B) Completing the square and applying the square root property. (C) Applying the quadratic formula.

x^2-10x=-9

Write each rational number as a decimal. Then tell whether each decimal is a terminating or a repeating decimal. $\frac { 89 } { 100 } =$

Use the discriminant to determine the number of real solutions of the equation. $2 x^{2}-6 x=-9$

Choose the letter that best answers the question or completes the statement. Which law states that the angle of incidence equals the angle of reflection? a. law of refraction b. law of diffraction c. law of reflection d. law of images

What atoms have the configuration (a) $4 s^{2} 4 p^{4}$, (b) $4 p^{6} 4 d^{10} 5 s$ , (c) $5 s^{2} 5 p^{6} 4 f^{12}$. Explain.

A series RLC circuit has a 200 kHz resonance frequency. What is the resonance frequency if the capacitor value is doubled and the inductor value is halved?

(a) Prove that if f(r) is a scalar point function then curl grad f = 0 (b) Prove that if v = grad [zf(r)] + α f(r)k and $\nabla^{2} f=0$, where α is a constant and f is a scalar point function, then $\operatorname{div} v=(2+\alpha) \frac{\partial f}{\partial z}, \quad \nabla^{2} v=\operatorname{grad}\left(2 \frac{\partial f}{\partial z}\right)$