Factor each polynomial. $3 x^{2}+4 x+1$

Describe how the focal length of a convex lens changes as the lens becomes more curved.

The product of two consecutive even integers is 224. Find the integers.

Prove that if p ones and q zeros are placed around a circle in an arbitrary manner, where p, q, and k are positive integers satisfying p$\geq$kq, the arrangement must contain at least k consecutive ones.

Suppose that electricity is draining from a capacitor at a rate that is proportional to the voltage V across its terminals and that, if t is measured in seconds, dV/dt = -V/40. Solve this equation for V, using V_0 to denote the value of V when t = 0. How long will it take the voltage to drop to 10% of its original value?

Write the decimal as a fraction or a mixed number.

$$- 1 . \overline { 63 }$$

A function f has derivative

$$f ^ { \prime } ( x ) = \frac { 1 } { x ^ { 4 } + 1 }.$$

Where on the interval [1, 4] does f take on its maximum value?

State the instructions of the function in words. R(r) = 3(2r + 5)

Find the exact value of each of the remaining trigonometric functions. $\csc \theta=-4,\ \pi<\theta<\frac{3 \pi}{2}$

Solve equation $s-5=3$ and check your answer.

Simplify. Then write a word problem involving the given numbers and operation.

$$\$ 64.32 \div 16$$

Hay que buscar ayuda para la fiesta de fin de año de tu clase. ¿Qué pregunta el presidente de la clase en la reunión? 1.desear ser el anfitrión (la anfitriona) 2.conocer a un disc jockey 3.saber bailar salsa. 4.cocinar comida puertorriqueña

Answer with “converges,” “diverges” or “can’t tell.” If $\lim _{k \rightarrow \infty} a_{k}=1$, then $\sum_{k=1}^{\infty} a_{k}$ ____.

Multiply.

$$35.15\times3.7$$