Mathematics Questions & Answers

Hallar la derivada direccional de la función en P en la dirección de v. \( f(x, y)=x y, \quad P(0,-2), \mathbf{v}=\frac{1}{2}(\mathbf{i}+\sqrt{3} \mathbf{j}) \)

4.) The circumference of a circle is 26.8 m . What is the radius and diameter of the circle?

Find the complement angle of \( 43^{\circ} \)

ify the following: \[ (2 x-5)\left(x^{2}-6 x+4\right) \]

Ejercicio 1 \( f(x)=\sqrt{\left(3 x^{2}-x\right)} \)

6. The foot of a ladder is 1.2 m from a fence that is 1.8 m high. The ladder touches the fence and re against a building that is 1.8 m behind the fence. Draw a diagram, and determine the height on the building reached by the top of the ladder.

The hour hand of a clock, centred at the origin, has equation \( y=0,839 x \). 1) What is the time? 2) What is the equation of the minute hand?

Susan has a collection of 60 nickels and dimes. If the number of nickels is four times the number of dimes, how many nickels and how many dimes does she have? Susan has 48 nickets and 12 dimes.

Actividad 9.8 Calculen las siguientes integrales definidas \( \begin{array}{lll}\text { a) } \int_{-1}^{2}\left(x^{3}-2 x\right) d x & \text { b) } \int_{-2}^{5} 6 d x & \text { c) } \int_{1}^{4}\left(5-2 t+3 t^{2}\right) d t \\ \text { d) } \int_{0}^{1} x^{4 / 5} d x & \text { e) } \int_{1}^{8} \sqrt[3]{x} d x & \text { f) } \int_{1}^{2} \frac{3}{t^{4}} d t \\ \text { g) } \int_{0}^{2 \pi} \cos (\theta) d \theta & \text { h) } \int_{0}^{\pi / 4} \sec ^{2}(t) d t & \text { i) } \int_{1}^{9} \frac{2}{x} d x \\ \text { j) } \int_{-3}^{-1} \frac{2}{x} d x & \text { k) } \int_{0}^{1} 10^{x} d x & \text { l) } \int_{1 / 2}^{\sqrt{3} / 2} \frac{6}{1+t^{2}} d t\end{array} \)

cargar el paso a paso en el desarrollo el siguiente ejercicio: \( f(x)=-6 x^{3}-2 x^{2}+x \) y \( g(x)=7 m x^{2}-5 x+1 \) Hallar \( f(x) \cdot g(x) \)