Simplify completely x2 + 4x - 45/x2 +10x+9 and find the restrictions on the variable.
1 answer:
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Since these questions all require similar methods of solving, I will only completely work out the first question of each type.
2. To find
as a decimal, all we need to do is complete the fraction by dividing the numerator by the denominator.
= 7 / 10 = 0.7
as a decimal is 0.7.
3. To write a fraction as a percentage, we must first convert it into a decimal, the way we did in problem 2.
Then to change that number into a percentage, we can either multiply it by 100, or (my personal shortcut) just shift the decimal point over two places to the right.
0.65 = 65%
which is the answer to question 3.
written as a percent is 65%.
4. Writing a percentage as a fraction is a bit easier than writing a fraction as a percentage. All you need to do is place the percentage in the numerator's place of a fraction with 100 as the denominator and simplify.
2%5 =
Since 25 goes into 100 four times, we can simplify this fraction.
which is our answer.
25% written as a fraction is
.
5. This is the same as problem 3, so I won't show my work for the sake of time.
as a percentage is 40%.
6. This is the same as problem 1, so I will not show steps again.
as a decimal is 0.15.
7. Done similar problems in past. No work shown.
as a percent is 42%.
8. Same as last problem.
as a percent is 4%.
9. Same as number 4.
6% as a fraction is
.
10. Similar in past.
as a percentage is 60%.
11. Same as 6.
as a decimal is 0.48.
12. Done a lot of these so far.
as a percentage is 30%.
13. Just did one like this.
as a percentage is 75%.
14. Same as 4 and 9.
65% as a fraction is.
15. Plenty of these done in past.
as a percentage is 20%.
16. Last problem, and it's just like the one just before this.
written as a percent is 90%.
So there are the results.
Hope that helped! =)
2. To find
3. To write a fraction as a percentage, we must first convert it into a decimal, the way we did in problem 2.
Then to change that number into a percentage, we can either multiply it by 100, or (my personal shortcut) just shift the decimal point over two places to the right.
0.65 = 65%
which is the answer to question 3.
4. Writing a percentage as a fraction is a bit easier than writing a fraction as a percentage. All you need to do is place the percentage in the numerator's place of a fraction with 100 as the denominator and simplify.
2%5 =
Since 25 goes into 100 four times, we can simplify this fraction.
which is our answer.
25% written as a fraction is
5. This is the same as problem 3, so I won't show my work for the sake of time.
6. This is the same as problem 1, so I will not show steps again.
7. Done similar problems in past. No work shown.
8. Same as last problem.
9. Same as number 4.
6% as a fraction is
10. Similar in past.
11. Same as 6.
12. Done a lot of these so far.
13. Just did one like this.
14. Same as 4 and 9.
65% as a fraction is
15. Plenty of these done in past.
16. Last problem, and it's just like the one just before this.
So there are the results.
Hope that helped! =)
2.8.1
By definition of the derivative,
We have
and
Combine these fractions into one with a common denominator:
Rationalize the numerator by multiplying uniformly by the conjugate of the numerator, and simplify the result:
Now divide this by <em>h</em> and take the limit as <em>h</em> approaches 0 :
3.1.1.
Differentiate one term at a time:
• power rule
The last two terms are constant, so their derivatives are both zero.
So you end up with