Tutor profile: Alex A.
In a right triangle, the hypotenuse is 30 units and one of it's adjacent angles is 25 degrees. What are the values of the other two sides to two decimal places?
The first thing we need to do is calculate both the sine and cosine of 25: sin(25): 0.42261826 cos(25): 0.90630779 Next we need to set up two different equations involving the length of the hypotenuse that will help us: sin(25) = opp/hyp sin(25) = opp/30 cos(25) = adj/hyp cos(25) = adj/30 Finally, some quick multiplication: sin(25) = opp/30 0.42261826 = opp/30 12.68 = opp cos(25) = adj/30 0.90630779 = adj/30 27.19 = adj The lengths of our other sides of the triangle are 12.68 and 27.19 units
How do we create major and natural minor scales? What are the notes in an E Major scale? What are the notes in an F Minor scale?
In music, we use whole steps (w) and half steps (h) to build major and minor scales. The major scale is made up of these steps: W W H W W W H The natural minor scale looks like this: W H W W H W W Knowing this we can build major and minor scales starting from any pitch. E Major: E F# G# A B C# D# E F Minor: F G Ab Bb C Db Eb F
John sells Ice Cream on the beach every afternoon. He sells small cones for $2 and large cones for $3. Yesterday, John sold a total of 25 cones and earned $60. If John sold 5 more small cones than large cones, then how many large cones did he sell?
We need to use two different equations to help solve this. Let's say (x) represents the number of small cones and (y) is the number of large cones. We know that there are 5 more small cones than large so we can set our first equation to be: x - 5 = y Our next equation incorporates the price of each cone as well as the total price for the day: 2x + 3y = 60 We can substitute our value of (y) from the first equation into the second: 2x + 3(x - 5) = 60 Now let's solve for (x): 2x + 3x - 15 = 60 5x - 15 = 60 5x = 75 x = 15 Now that we have our value for x, we can substitute it back into our first equation: x - 5 = y 15 - 5 = y 10 = y This means that John sold 10 large cones.
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