Tutor profile: Erin H.
Imagine a right angled triangle with side A, side B, and side C where side B is a hypotenuse (side of the triangle opposite the right angle). The side A is equal to 10. The side B is equal to 20. Side A is opposite to angle A. What is the value of angle A?
The first thing we need to determine is all of the factors we already know. We have: Side A = 10 Side B = 20. Now that we have determined this, and we are told we are looking at a right angled triangle, we can use our sine, cosine and tangent rules: 1) sin (angle) = opposite length/hypotenuse length 2) cos (angle) = adjacent length/hypotenuse length 3) tan (angle) = opposite length/adjacent length. The opposite and adjacent lengths refer to the relative position compared with the angle you need to calculate. In this case, length A is our opposite length, and length B is our hypotenuse (as told in the question). To determine our angle we need to pick an equation that uses the hypotenuse and the opposite length, which is rule number 1, the sine rule. Our equation would look like this: sin (angle A) = side A / side B sin (angle A) = 10 / 20. Now we need to use our inverse (arc) sine to get the value of angle A. Angle A = arcsin (10/20) Angle A = 30 degrees.
Subject: Basic Math
Erin has to make pancakes for her family breakfast tomorrow morning. She is part of a family of 6 and they each want 2 pancakes each. Erin usually uses 2 eggs in her pancake mix that gives her 4 pancakes. How many eggs will she need to use to make enough pancakes for her family?
To begin this question, we should figure out how many pancakes Erin will need to make in total! If there are 6 people eating pancakes, and each of them want 2 we need to do 6 x 2 = 12. This gives us our total pancake amount. Erin's usual pancake mix gives her 4 pancakes. We need to figure out how many more mixes she will need to get 12 pancakes. To do this we can divide our total pancake number needed (12) by the total amount 1 mix gives us (4). 12/4 = 3. Erin will need 3 times as much mix as she normally does. If she uses 2 eggs in each mix, to get the total amount of eggs needed we can multiple our number of eggs by the number of mixes we need: 3 x 2 = 6. Erin will need 6 eggs to make enough pancakes for her family!
Find the solution of the following quadratic equation: 2x^2 + 14x + 22 = 2
This question tells us that we are finding a solution for a QUADRATIC equation. So the first thing we need to look at is the quadratic formula: Ax^2 + Bx + C = 0 By putting our quadratic equation in this format, means we can factorise to find our solutions. The quadratic equation we have been given is equal to 2, not 0. In order to rectify this, we can subtract the 2 from the left hand side of the equals sign. So it would look something like this: 2x^2 + 14x + 22 - 2 = 0 Which simplifies to: 2x^2 + 14x + 20 = 0 Now, we can compare our equation to the quadratic formula and we see that: A = 2, B = 14, and C = 20. In order to factorise, which means splitting our equation into two brackets like this: e.g. (x + 3)(x + 5) = 0 To start this we need to calculate the value of A multiplied by C (AC). AC = 2 X 2 = 40 B = 14 Now we can find 2 numbers that multiple to make 40 and add to make 14. The easiest way is to list all factors of 40: 1, 40, 2, 20, 4, 10, 5, 8. Looking at these factors, we can see that 4+10 will give us 14, these are our numbers, and we can put these into our brackets as so: (Ax + 4)(x + 10) = 0 Our A = 2, so we get: (2x + 4)(x + 10) = 0 Since both brackets multiplied together equals 0, one of these brackets HAS to be zero in order for the answer to be zero. So we can equate both brackets to zero: (1) 2x + 4 = 0 and (2) x + 10 = 0 Solving these we get: (1) 2x + 4 = 0 2x = -4 x = -4/2 x = -2 (2) x + 10 = 0 x = -10 Therefore our two solutions are x = -2 and x = -10.
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