This week in math 10 we learned how to identify functions.
Differences between a function and a relation. A function is the X variable paired with the Y variable And each number must be special meaning that there can’t be to X variables that pair with the same Y variable.
The image above is an example of a function because each X value pairs with Y value, with no number being repeated.
The photo above is an example of a relation because two or more X variables have the same pair as the Y variable.
In the work sheet we had many graphs that represented different real life scenarios. Question “E” represented an oven and the bake time of a cake. In the graph we see the temperature rising and lowering small amounts on the graph. I would have not chose “E” to represent an oven. Because I didn’t know an oven rose and lowered in temperature in the oven. Math has many ways of expressing itself, sometimes you don’t even need to use an equation. Ms. Burton is helping us figure out more ways to solve math.
For question a the question in {x^2 +10x +16} we are going to focus on the last variable, (16) we are going to look at all the numbers that multiply into (16), we have 1*16, 2*8, and 4*4. Then we are going to look at the 10x we are going to look at all the multiples of 16 and see if any equal (10) when added together. 2+8 equals 10, so we all know that, that will be the way we get to 16. now we have to expand these equations out x^2 would look like (x)(x). then we add in our +2 and +8 in no specific order. So the equation no looks like (x +2)(x+8). And that is how we expand our equation. there are many methods to solve this equation if you want to check your answer I prefer the DD rule (double distribution rule) the DD rule is where you take the x and the 2 and multiply them one at a time with the other two variables. (X*X)+(X+8)+(2+X)+(2+8) then we have X^2+8x+2x+16 So our final answer would be x^2+10x+16. Which is the same as our original equation.
In the image we see the Eiffel tower and the shadow it casts onto the person standing at the reference angle. Our job is to figure out the distance the shadow casts along the bottom of the Eiffel tower.
In the image there are two parts to the equation, the first part is figuring out the height of the cliff, the second part is figuring out the distance between the boat and the top of the cliff if the boat was 75m closer. All we get for our information in these questions are the reference angle (16*) and the floor of the triangle (300m, and 225m).
in this equation a totem pole is placed into a 2m hole in the ground and has two guy wires holding it up on either side at an angle of the unknown. We have the opposite and the Hypotenuse, so we will use sign to figure out our missing angle.
in the image we see X is our unknown variable for our reference angle, to determine the reference angle we must use one of the SOH CAH TOA formulas to get our answer, we can use simple process of elimination to figure out which one we must use. We do not have a number for the adjacent so we can rule out cosign and tangent, meaning that we must use sign as our formula to figure out the equation.
We did extra practice to sharpen our skills at solving triangles when you don’t know any of the sides.
And here is another example of how to solve when you don’t know the number for the reference angle. This time we use Cosign and we need to isolate X to get our answer, so we have to do the opposite of cosign which is cosign^-1, which will make the equation {X=cos^-1 (40/41)}.
In the image we see A, H, and O, which stand for Hypotenuse, which is the longest side of the triangle. Opposite, which is the side opposite of the (theta) the theta is that shape that I drew the two lines coming out of, it is used to find the opposite side of the triangle, and A is for adjacent, adjacent is whatever is in between H and O.
Sine Ratio, Cosine Ratio, and Tangent Ratio are all the formulas used to solve a triangle, we take the O, H, and A, and we use these different formulas to solve the answer for the triangles.
In the image we are multiplying (-7 x^3 x^-5)(x^2 x^-3) first I used the power of multiplication to make X all one letter with one exponent, so we add the exponents over all the X’s to get -3. Now we need to make all these numbers positive including the 7, so I divide by -1 to make the 7 positive and the -3 exponent over X positive. The 7 goes on top because the -1 goes invisible so I had to put a number up there, and because a -#/-# equals a positive number we can put the 7 on top, because it has no visible negative exponent.
In the image we see two different bases for the exponent, meaning we can not multiply or divide any of our exponents, the only thing we can do here is make the M^-5 and M^5. To do that we simply divide m^-5/1 to make it 1 over m^5. now n^2 is really n^2/1 so we can multiply n^2 * 1 to get the n^2 on top of our fraction. And of course there is a 1 under our n^2 so we can multiply 1 * m^5, which will stay the same. Thus resulting in our answer being n^2/M^5.
In the image {-7^2 * 8^-2} we can solve the answer by simply doing {-7 * -7} which equals 49 because a negative * a negative = a positive. for the 8^-2 the negative exponent tells us that it is on the wrong side of the fraction which is invisible so we divide one by 8^-2 to get {1/8^-2} and we can multiply that by {49/1} to get {49/8^2} then we can simply do 8^2 which will get you 64.