Answer:
1/3 divided by 3/4 = 0.44
Step-by-step explanation:
1/3 (0.33) divide by 3/4 (0.75) = 0.44
For questions 9 through 12, plug in the term you're looking for in for x:
9. y=10(20)-2=298
10. y=10(9)-2=88
11. y=5(2^5)=160
12.y=5(2^7)=640
For questions 13 through 16, plug the values 1 through 5 in for x, one at a time:
13. y=4^1=4, y=4^2=16, y=4^3=64, y=4^4=256, y=4^5=1,024
14. y=(-3)^1=-3, y=(-3)^2=9, y=(-3)^3=-27, y=(-3)^4=81, y=(-3)^5=-243
15. y=-3^1=-3, y=-3^2=-9, y=-3^3=-27, y=-3^4=-81, y=-3^5=-243
16. y=10^1=10, y=10^2=100, y=10^3=1,000, y=10^4=10,000, y=10^5=100,000
For question 17, plug 4 in for n:
17. f(4)=5^4=625
1. Rewrite the expression in terms of logarithms:

Then differentiate with the chain rule (I'll use prime notation to save space; that is, the derivative of <em>y</em> is denoted <em>y' </em>)




2. Chain rule:




Since
, we can cancel one factor of sine:

3. Chain rule:




4. If you're like me and don't remember the rule for differentiating logarithms of bases not equal to <em>e</em>, you can use the change-of-base formula first:

Then

So we have




and we can use the double angle identity and logarithm properties to condense this result:

5. Differentiate both sides:





6. Same as with (5):






7. Looks like

Compute the second derivative:


Set this equal to 0 and solve for <em>x</em> :




