What we learned in this week is to solve problems using SOH, CAH, and TOA. For example, on the problem, we already know what is the adjacent and the hypotenuse, so we can use cosine. We need to find what is a, so the way is
cos a = adjacent/hypotenuse
a = cos-1 adjacent/hypotenuse
The adjacent is 4 and the hypotenuse is 6.
a = cos-1 4/6
so, a is similar to 48.19
What I learned in this week is about right triangles with the Pythagorean theorem.
A lot of people in grade 10 already know the Pythagorean theorem. It is only used in right triangles, and the other theories are even used in only right triangles. There is opposite, adjacent, and hypotenuse in right triangles. They are titles of sides of right triangles, adjacent means which have two angles, 90 degrees, and unknown angle or that we already know. Hypotenuse defines slanted side which does not have 90 degrees. Opposite defines another angle. the formulas of right triangles are 3, they are sin, cos, and tan.
sin = opposite/hypotenuse (SOH), cos = adjacent/hypotenuse (CAH), and tan = opposite/adjacent.
(The opposite is always top, and the hypotenuse is always the bottom.)
What I learned in math 10 class in this week is about formulas of geometric figures using the measurements that we learned last week. How we can find the surface area of a cone is we have to find two parts, the side, and the base.
The base is π×r2 and the side is π×r×s we have to combine them. So, the formula for the surface area of a cone is πr2+πrs.
The formula for the volume of a cone is easier than the surface area, it is just similar to the volume of a cylinder. Just multiplying 1/3 on the formula for the volume of a cylinder, because the same based cylinder is 3 times by the same based cone. So, the formula for the volume of a cone is 1/3×(area of a base=πr2)×height
What I learned in math class in the fifth week is about the measurement. It even starts measurement unit, so we learned about the basic measurement this week. There are a lot of units, for examples, meter(m) and liter (L), and it can get other definition if we add some alphabet on the measurement.
The positive exponent measurements are da, h, and k. da means ×10, h means ×100, and k means ×1,000. There are even negative exponent measurements that are d, c, and m. d means ×1/10. c means ×1/100. m means ×1/1,000. The measurements are memorized by king henry d(a)oesn’t drink chocolate milk.
There are even bigger and smaller exponent measurements. M means ×1,000,000. G means ×1,000,000,000. µ means ×1/1,000,000. n means ×1/1,000,000,000
I learn something that about the fraction exponent and how we can simplify that fraction exponent to an entire radical.
The denominator of the exponent is 3, and it must mean how many times of the root, so it must be cube root. The numerator of the exponent is 4, and it must also mean how many times multiply it.
(-3m2n3)2 (-2m3n) 3(1/72m2n3)
Use PP -3m2n3 must be multiplied 2 times and -2m3n must be multiplied 3 times, but 1/72m2n3 does need to (Because there is no exponent, and that is same as that there is 1).
(9m4n6) (-8m9n3)(1/72m2n3)
It can be multiplied with same bases.
-72m13n9/72m2n3
And it can be divided
-m13-2n9-3= -m11n6
We can get the results that a is -1, b is 11, and c is 6, so -1+11+6 is equal to 16
We learned about what is prime factorization.
It consists of prime factors. We can use them when we should find the prime factors. First of all, it should be divided by the smallest prime number, the number (72 is an example for this explanation) should keep dividing by the smallest prime numbers. Lastly, gather all of the prime numbers if it becomes the prime number, and make a prime factorization.