As stated in (i), the equation of the line is: ln y = -0.015x + .26
(By the way, I checked your answers for parts (i) and (ii) and they are both correct)
(iii)
Plug in (1.1) for y and solve:
ln (1.1) = -0.015x + .26
0.095 = -0.015x + .26
-0.165 = - 0.015x
10.979 = x
Answer: x = 10.979
Answer:
![20a^3b^3](https://tex.z-dn.net/?f=20a%5E3b%5E3)
Step-by-step explanation:
<u>Binomial Series</u>
![(a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n](https://tex.z-dn.net/?f=%28a%2Bb%29%5En%3Da%5En%2B%5Cdfrac%7Bn%21%7D%7B1%21%28n-1%29%21%7Da%5E%7Bn-1%7Db%2B%5Cdfrac%7Bn%21%7D%7B2%21%28n-2%29%21%7Da%5E%7Bn-2%7Db%5E2%2B...%2B%5Cdfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7Da%5E%7Bn-r%7Db%5Er%2B...%2Bb%5En)
<u>Factorial</u> is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.
Example: 4! = 4 × 3 × 2 × 1
Therefore, the fourth term in the binomial expansion (a + b)⁶ is:
![\implies \dfrac{n!}{3!(n-3)!}a^{n-3}b^3](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7Bn%21%7D%7B3%21%28n-3%29%21%7Da%5E%7Bn-3%7Db%5E3)
![\implies \dfrac{6!}{3!(6-3)!}a^{6-3}b^3](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B6%21%7D%7B3%21%286-3%29%21%7Da%5E%7B6-3%7Db%5E3)
![\implies \dfrac{6!}{3!3!}a^{3}b^3](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B6%21%7D%7B3%213%21%7Da%5E%7B3%7Db%5E3)
![\implies \left(\dfrac{6 \times 5 \times 4 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}{3 \times 2 \times 1 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}\right)a^{3}b^3](https://tex.z-dn.net/?f=%5Cimplies%20%5Cleft%28%5Cdfrac%7B6%20%5Ctimes%205%20%5Ctimes%204%20%5Ctimes%20%5Cdiagup%5C%21%5C%21%5C%21%5C%213%20%5Ctimes%20%5Cdiagup%5C%21%5C%21%5C%21%5C%212%20%5Ctimes%20%5Cdiagup%5C%21%5C%21%5C%21%5C%211%7D%7B3%20%5Ctimes%202%20%5Ctimes%201%20%5Ctimes%20%5Cdiagup%5C%21%5C%21%5C%21%5C%213%20%5Ctimes%20%5Cdiagup%5C%21%5C%21%5C%21%5C%212%20%5Ctimes%20%5Cdiagup%5C%21%5C%21%5C%21%5C%211%7D%5Cright%29a%5E%7B3%7Db%5E3)
![\implies \left(\dfrac{120}{6}\right)a^{3}b^3](https://tex.z-dn.net/?f=%5Cimplies%20%5Cleft%28%5Cdfrac%7B120%7D%7B6%7D%5Cright%29a%5E%7B3%7Db%5E3)
![\implies 20a^3b^3](https://tex.z-dn.net/?f=%5Cimplies%2020a%5E3b%5E3)
Answer:
4√10
Step-by-step explanation:
Hello!
Let's first simplify the radical.
We can do this by expanding the radical:
We need to pull out a perfect square factor to expand a radical and simplify it. In 45, we have 9 and 5 multiplied, and 9 is a perfect square.
Let's work with √45:
- √45 can be written as √9 * √5 (using the rule √ab = √a * √b)
- √9 simplifies to 3, so it is 3√5
Now we can simplify the operation in the parenthesis by combining like terms:
- 3√5 + √5
- √5 + √5 + √5 + √5
- 4√5
Now using the same rule as above, we can multiply the values:
Your solution is 4√10