Literal Equations Test Flashcards

Density Calculation

• Density (d) is calculated from mass (m) and volume (v) using the formula d = m/v.
• Rearranging this equation for volume gives V = m/d.

Right Cone Geometry

• The lateral area (LA) of a right cone is given by LA = πrs.
• This formula can be rearranged to find slant height (s) as s = LA / (πr) and radius (r) as r = LA / (πs).

Temperature Conversion

• Kelvin (K) is derived from Celsius (C) using the equation K = C + 273.15.
• The rearranged formula for Celsius is C = K - 273.15.

Motion Formula

• The formula for final velocity is f = v + at.
• To solve for time (t), the equivalent formula is t = (f - v) / a.

Hockey Goalie Statistics

• Goals against average (A) is calculated with A = g / t * 60, where g is goals scored against the goalie and t is time in minutes.
• Rearranging for goals gives g = (A * t) / 60.

Slope-Intercept Form

• The slope-intercept form of a linear equation is y = mx + b, with m representing the slope.
• To find slope (m), rearranged equation is m = (y - b) / x.

Algebraic Rearrangement

• From the equation 7a - 2b = 5a + b, rearranging yields a = (3/2)b.

Ellipse Area Calculation

• The area (a) of an ellipse is calculated by a = πxy, where x and y are half the lengths of the respective diameters.
• Rearranging for y gives y = a / (πx).

Rectangular Prism Volume

• The volume (V) of a rectangular prism is determined by V = lwh, where l, w, and h are length, width, and height.
• For a prism with V = 138.24 in³, h = 9.6 in, and l = 3.2 in, the width (w) is found to be 4.5 in.

Physics: Force and Acceleration

• The relationship of force (F) to mass (m) and acceleration (a) is expressed as F = ma.
• Rearranging for acceleration gives a = F / m. For F = 7.92 N and m = 3.6 kg, acceleration results in approximately 2.2 m/s².

Circumference and Radius

• The circumference (C) of a circle is formulated as C = 2πr.
• Rearranging for radius (r) gives r = C / (2π). For a circle with C = 16, the radius is calculated as r = 8.

Slope From Ordered Pairs

• Slope (m) between two points can be found using m = (y2 - y1) / (x2 - x1).
• To find y2 based on known values, rearranging results in y2 = m(x2 - x1) + y1.

Additional Algebraic Rearrangements

• From 5w + 9z = 2z + 3w, solving for width (w) yields w = -7/2z.
• From K = 4a + 9ab, when solving for a, the formula is a = K / (4 + 9b).
• For the surface area equation S = 2πrh + 2πr² rearranging to solve for height (h) results in h = (S/(2πr)) - r.