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Home Question Bank Math Archive 2024 December 20

Math Questions from Dec 20,2024

Browse the Math Q&A Archive for Dec 20,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Solve, finding all solutions in \( [0,2 \pi) \) or \( \left[0^{\circ}, 360^{\circ}\right) \). \( 2 \boldsymbol{s i n}^{2} x+\sqrt{2} \sin x=0 \) The solution(s) in \( \left[0^{\circ}, 360^{\circ}\right) \) is/are \( x=\square \). (Type your answer in degrees. Do not include the degree symbol in your answer. Use a comma to separate answers as needed.) The solution(s) in \( [0,2 \pi) \) is/are \( x=\square \). (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.). Solve, finding all solutions in \( [0,2 \pi) \) or \( \left[0^{\circ}, 360^{\circ}\right) \). \( -\boldsymbol{\operatorname { s i n }} 2 \mathrm{x} \boldsymbol{\operatorname { s i n }} \mathrm{x}+\boldsymbol{\operatorname { c o s } x}=0 \) The solution(s) in \( \left[0^{\circ}, 360^{\circ}\right) \) is/are \( x=\square \). (Type your answer in degrees. Do not include the degree symbol in your answer. Use a comma to separate answers as needed.) The solution(s) in \( [0,2 \pi) \) is/are \( x=\square \). (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) Rewrite \( \frac{1}{\sqrt[4]{y}} \) using rational exponents. Sossible \( 4 \cos ^{2} x=3 \) The solution(s) in \( \left[0^{\circ}, 360^{\circ}\right) \) is/are \( x=\square \). (Type your answer in degrees. Do not include the degree symbol in your answer. Use a comma to separate answers as needed.) The solution(s) in \( [0,2 \pi) \) is/are \( x=\square \) (Simplify your answer. Type an exact answer, using \( \pi \) as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) Solve, finding all solutions in \( [0,2 \pi) \) or \( \left[0^{\circ}, 360^{\circ}\right) \). \( 4 \cos ^{2} x=3 \) The solution(s) in \( \left[0^{\circ}, 360^{\circ}\right) \) is/are \( x=\square \). (Type your answer in degrees. Do not include the degree symbol in your answer. Use a comma to separate answers as needed.) The solution(s) in \( [0,2 \pi) \) is/are \( x=\square \) (Simplify your answer. Type an exact answer, using \( \pi \) as néeded. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) What is the formula for calculating the surface area of a rectangular prism? 11. Si \( x \) y y son enteros positivos, encuentra los valores que satisfagan siguiente ecuación \( x^{2}-9 y^{2}=43 \). Determine if the functions \( f(x) = 3x + 1 \) and \( g(x) = \frac{x - 1}{3} \) are inverse functions. Describe the steps involved in finding the inverse of a function algebraically. Hallar las trayectorias ortogonales de la familia de parábolas con eje de simetría vertical que pasan por el vértice \( (-4,3) \). a. Escriba la ecuación de la familia de cruvas \( F(x, y, u)=0 \) ( \( u \) es la constante que genera la familia de cruvas). b. Escriba la ecuación diferencial de la familia de curvas, \( \frac{d y}{d x}=f(x, y) \) c. Escriba la EDO que representa la pendiente ortogonal de la familia de curvas dada \( \frac{d y}{d x}=g(x, y) \). d. Escriba la ecuación que representa la trayectoria ortogonal \( G(x, y, v)=0 \) (coloque \( v \) como la constante de integración obtenida al resolver la EDO) -
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