Math Semester 1 Unit 2 Flashcards

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Questions and Answers

What is the equation solved for C when converting Kelvin to Celsius?

C = K - 273.15

What is the solution for w in the equation 5w + 9z = 2z + 3w?

w = -7/2z

Which are equivalent equations for the lateral area of a right cone, LA = pi rs? (Select two correct answers)

  • s = r/LA pi
  • s = LA/pi r (correct)
  • r = LA/(pi s)
  • r = LA/pi r (correct)

What is the equivalent equation solved for r from the formula C = 2 pi r?

<p>r = c/2 pi</p> Signup and view all the answers

Which are equivalent equations for the area of a rhombus, A = 1/2 d1 d2? (Select two correct answers)

<p>d1 = 2A/d2 (B), d2 = 2A/d1 (C)</p> Signup and view all the answers

What is the acceleration of an object with F = 7.92 newtons and m = 3.6 kilograms?

<p>2.2 m/s^2</p> Signup and view all the answers

What is the result when solving the equation S = 2Ï€rh + 2Ï€r^2 for h?

<p>h = s/(2 pi r) - r</p> Signup and view all the answers

What is the equivalent equation solved for t in the equation f = v + at?

<p>t = (f - v)/a</p> Signup and view all the answers

What is the value of r if the circumference of a circle is C = 2 pi r?

<p>r = 8</p> Signup and view all the answers

What is the equivalent equation solved for the slope, m, from the slope-intercept form y = mx + b?

<p>m = (y - b)/x</p> Signup and view all the answers

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Study Notes

Temperature Conversion

  • Temperature in Kelvin (K) can be calculated from Celsius (C) using K = C + 273.15.
  • To convert from K to C, the equation is C = K - 273.15.

Algebraic Manipulation

  • To solve for w in the equation 5w + 9z = 2z + 3w, the result is w = -7/2z.

Lateral Area of a Cone

  • The lateral area (LA) of a right cone is given by LA = Ï€rs, where r is the radius and s is the slant height.
  • Equivalent expressions for s are: s = LA / (Ï€r) and re-arranging yields proper forms.

Circle Circumference

  • Circumference (C) of a circle is calculated via C = 2Ï€r.
  • When solving for the radius (r), the equivalent equation is r = C / (2Ï€).

Area of a Rhombus

  • The area (A) of a rhombus is given by A = 1/2 * d1 * d2, where d1 and d2 are diagonal lengths.
  • Solving for d1 gives d1 = 2A / d2, and for d2 gives d2 = 2A / d1.

Newton's Second Law

  • Force (F) is defined by the equation F = ma, where m is mass and a is acceleration.
  • For an object with F = 7.92 N and m = 3.6 kg, the calculated acceleration is 2.2 m/s².

Surface Area of a Cylinder

  • The equation for the surface area of a cylinder is S = 2Ï€rh + 2Ï€r².
  • Solving for height (h) results in h = S / (2Ï€r) - r.

Final Velocity Formula

  • The final velocity formula is f = v + at, where f is final velocity, v is initial velocity, a is acceleration, and t is time.
  • Rearranging to solve for time (t) yields t = (f - v) / a.

Circle Radius Confirmation

  • The radius can also be determined using the circumference formula C = 2Ï€r, leading to r = C / (2Ï€).
  • When C is specifically given as 16Ï€, then r = 8.

Slope-Intercept Form

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

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