Eília convenceu sua mãe a comprar uma zaixa enorme de seu cereal preferido. Sua nãe acha que a caixa não vai caber na prateleira da cozinha delas. O volume da taixa é \( 10.000 \mathrm{~cm}^{3} \). A base da caixa mede 25 cm por 10 cm . Qual é a altura da caixa de cereal?

Graph the given ellipse. Identify the domain, range, center, vertices, endpoints of the minor axis, and foci in the figure. \( \frac{(x+5)^{2}}{4}+\frac{(y-4)^{2}}{9}=1 \) The center of the ellipse is \( \square \). (Type an ordered pair.) The vertices are \( \square \). (Type ordered pairs. Use a comma to separate answers as needed.) The endpoints of the minor axis are \( \square \). (Type ordered pairs. Use a comma to separate answers as needed.) The foci of the ellipse are \( \square \). (Type ordered pairs. Use a comma to separate answers as needed. Type an exact answer, using radicals as needed.) Graph the ellipse \( \frac{(x+5)^{2}}{4}+\frac{(y-4)^{2}}{9}=1 \). The domain of the graph is \( \square \). (Type your answer in interval notation.) The range of the graph is \( \square \).

What is the slope of the line that passes through the points \( (-10,9) \) and \( (-10,18) \) ? Write your answer in simplest form.

A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 9 feet less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 21 feet. The length of the ladder is

En cada uno de los siguientes pares de rectas, determinar: 1. Cuál par de rectas son paralelas no coincidentes (en cuyo caso, calcular la distancia entre ellas). 2. Cuál par son perpendiculares. 3. Cuál par se intersectan en un punto, en cuyo caso, obtener el punto de intersección. 4. Cuál par son coincidentes, en cuyo caso, calcular su distancia al origen. 5. Cuál par no son paralelas, ni perpendiculares, ni se intersectan en un punto, ni son a) \( \mathrm{L}_{1} \) : coincidentes (en cuyo caso, calcular el ángulo entre ellas). \( \mathrm{L}_{2} \) : contiene al punto \( (0,-2,1) \) y es paralela al vector \( \bar{u}=-10 i-10 j+4 j \)

What is the slope of the line that passes through the points \( (6,-8) \) and \( (6,-3) \) ? Write your answer in simplest form.