Tutor profile: Jackie W.
What is the area of a circle with a diameter of 18?
The area formula for a circle is πr^2. If we know the diameter is 18 we divide that in 2 to find the radius. 18/2 = 9. We know that r = 9, so we take 9^2 = 81. We now have our final answer of 81π. In short: D = 18, πr^2 r = 18/2 = 9 9^2 = 81 81π = area of the circle
What is the antiderivative of the equation below? ∫3x^2dx?
To find the anti-derivative your brain has to work backwards. In the equation above we are trying to figure out what 3x^2 used to be. First step is to add an +1 onto the exponent of the x. Therefore we know x^2 was x^3. Secondly the number out front is the exponent * what number was there before. In this case since the number is 3, we know the number there before was 1, hence 1*3. We now have our answer that the antiderivative was x^3 + c. You always will add a "+c" because if there was no variable (x, y, z) attached to the number it will disappear when you take the derivative, so there could have been a number there before. In short: ∫3x^2dx = x^3 + c
Last Monday, Emma played 4 more tennis games than Jenny did. Together they play 10 games. How many games did Jenny play?
We know the E + J = 10. We also know that E = 4 + J. If we sub the E = 4 + J equation into the E + J = 10 equation we get, 4 + J + J = 10. Next we combine like terms, 2J + 4 = 10. Using PEMDAS we then subtract 4 from each side giving us, 2J = 6. We then divide each side by 2 giving us J =3. You then have your answer that Jenny played 3 games! 1. E = 4 + J, E + J = 10 2. 4 + J + J = 10 3. 4 + 2J = 10 4. 2J = 6 5. J = 3