Find f(a), f(a + h), and the difference quotient $\frac{f(a+h)-f(a)}{h},$ where $h \neq 0.$ $f(x)=3 x^{2}+2$

The resistance R of a wire varies directly as its length L and inversely as the square of its diameter d. (a) Write an equation that expresses this joint variation. (b) Find the constant of proportionality if a wire 1.2 m long and 0.005 m in diameter has a resistance of 140 ohms. (c) Find the resistance of a wire made of the same material that is 3 m long and has a diameter of 0.008 m. (d) If the diameter is doubled and the length is tripled, by what factor is the resistance changed?

Arrange these numbers in order from least to greatest: 0, -1, 2, -3

The heat experienced by a hiker at a campfire is proportional to the amount of wood on the fire and inversely proportional to the cube of his distance from the fire. If the hiker is 20 ft from the fire and someone doubles the amount of wood burning, how far from the fire would he have to be so that he feels the same heat as before?

A toy gun uses a spring to project a 5.3-g soft rubber sphere horizontally. The spring constant is 8.0 N/m, the barrel of the gun is 15 cm long, and a constant frictional force of 0.032 N exists between barrel and projectile. With what speed does the projectile leave the barrel if the spring was compressed 5.0 cm for this launch?

Escribe la forma correcta del verbo entre paréntesis para completar cada oración.

1. Mi prima BLANK los rápidos el año pasado. (navegar)
2. El albergue juvenil BLANK un descuento a los estudiantes. (ofrecer)
3. Ustedes BLANK el sendero para observar los árboles. (seguir)
4. Yo BLANK un guía para la excursión. (buscar)
5. Ellos BLANK una caminata cuando fueron de excursión. (hacer)

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

How do Anzac biscuits compare nutritionally to other cookies? What changes could you make to improve the nutrient profile?

Exchange of gases occurs between capillaries and which of the following structures? A) alveoli B) bronchi C) bronchioles D) trachea

Yes or No? If No, give an example. (a) If x(x + 1) > 0, does it follow that x is positive? (b) If x(x + 1) > 5, does it follow that x > 5?

Vocabulary: Integrated pest management (IPM)

Evaluate the expression without using a calculator. $\left(\sin \frac{\pi}{3} \cos \frac{\pi}{4}-\sin \frac{\pi}{4} \cos \frac{\pi}{3}\right)^{2}$

Find the domain and range of the function. $f(x)=3 x, \quad-2 \leq x \leq 6$

Draw a graph that contains the points (-2, -1), (0, 1), (1, 3), and (3, 5). Compare your graph with those of other students. Are most of the graphs almost straight lines? How many are “curved”? Discuss the various ways that these points might be connected.