answer:A vector quantity is different from a scalar quantity, which has only magnitude but no direction. For example, mass is a scalar quantity because it has only a value (magnitude) but no direction. Vector quantities are often used to describe physical phenomena that involve motion, such as velocity, acceleration, and force. They can also be used to describe other physical quantities, such as electric fields and magnetic fields. A vector quantity is a physical quantity that has both magnitude and direction. It is represented by an arrow, with the length of the arrow representing the magnitude of the quantity and the direction of the arrow representing the direction of the quantity. For example, velocity is a vector quantity because it has both a speed (magnitude) and a direction.

answer:Integrating both sides of the equation, we get: begin{align*} int (x + x^3)dx &= int (y + sin y)dy frac{x^2}{2} + frac{x^4}{4} + C_1 &= frac{y^2}{2} - cos y + C_2 end{align*} where C_1 and C_2 are constants of integration. Using the initial condition y(0) = 0, we have: begin{align*} frac{0^2}{2} + frac{0^4}{4} + C_1 &= frac{0^2}{2} - cos 0 + C_2 C_1 &= 1 + C_2 end{align*} Substituting this into the general solution, we get: begin{align*} frac{x^2}{2} + frac{x^4}{4} + 1 + C_2 &= frac{y^2}{2} - cos y + C_2 frac{x^2}{2} + frac{x^4}{4} + 1 &= frac{y^2}{2} - cos y end{align*} Therefore, the solution to the differential equation with the given initial condition is: boxed{frac{y^2}{2} - cos y = frac{x^2}{2} + frac{x^4}{4} + 1}

answer:To calculate the long-term debt of Blackwell Automotive, we can use the accounting equation: Assets = Liabilities + Stockholders' Equity Rearranging the equation, we get: Long-term Debt = Assets - Liabilities - Stockholders' Equity First, we need to calculate the total assets and total liabilities: Total Assets = Current Assets + Long-term Assets = (23,015 + 207,798 + 141,258 + 11,223) + (78,656 + 680,348) = 383,294 + 759,004 = 1,142,298 Total Liabilities = Current Liabilities + Long-term Debt = (118,379 + 21,115) + Long-term Debt = 139,494 + Long-term Debt Now, we can substitute the values into the accounting equation: Long-term Debt = 1,142,298 - 139,494 - (313,299 + 512,159) = 1,142,298 - 139,494 - 825,458 = 177,346 Therefore, Blackwell Automotive has 177,346 in long-term debt.

answer:Electrical currents generate magnetic fields. When an electric current flows through a conductor, it creates a magnetic field around the conductor. The strength and direction of the magnetic field depend on the amount of current flowing and the shape of the conductor. Permanent magnets, on the other hand, have a magnetic field that is not caused by an electric current. Instead, the magnetic field of a permanent magnet is caused by the alignment of the atoms in the material.