Tutor profile: Cameron S.

Convert the measure $$225^{\circ}$$ to radians. Leave your answer in terms of $$\pi$$.

When converting from degrees to radians, we can use the the formula: " $$(degree$$ $$measure) \cdot (\frac{\pi}{180^{\circ}})$$ " So, since our degree measure is $$225^{\circ}$$, we will use the formula above to get: $$(225^{\circ}) \cdot (\frac{\pi}{180^{\circ}})$$ = $$\frac{225^{\circ}{\pi}}{180^{\circ}}$$ = $$\frac{5{\pi}}{4}$$ . Thus, the radians of $$225^{\circ}$$ is $$\frac{5{\pi}}{4}$$ .

What is $$7 \div 3?$$

We can think about this question is asking us "How many times does 3 go into 7 without going over? Are there any left overs?" Well, 3 goes into 7 twice without going over since $$3\cdot2=6$$ . And we can see that we are off by 1 since $$7-6=1$$ . So 3 goes into 7 twice with 1 left over. We can write this as $$2$$$$\frac{1}{3}$$ . Thus, $$7 \div 3 = 2 \frac{1}{3}$$ .

Solve for x in the equation $$| x | + 2 = 8.$$

Since we are asked to solve for the variable $$x$$, we want to isolate the variable. Right now, we have with the variable $$x$$ with a 3 multiplied to the variable, and the absolute value. Let's go step-by-step to have $$x$$ by itself. 1) To remove the 2, we want to the opposite operation of how 2 is attached to x on both sides. Since 2 is being added, the opposite operation would be subtraction. So we have: $$| x | + 2 = 8$$ $$- 2$$ $$-2$$ -------------------- $$| x | = 6$$ 2) Now, look at the absolute value, Know that the absolute value represents the distance 0. Because of this, we can use the rule that: "If $$|x|=a$$ (where $$a$$ is a positive number), then $$x=a$$ or $$x=-a$$." So, in our equation $$| x | = 6$$, we can use the rule to remove the absolute value to have: $$x = 6$$ or $$x=-6$$ So we have two solutions; $$x=6$$ and $$x=-6$$.