F(x)=x^2+1 g(x)=5-x (f+g)(x)=
1 answer:
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Answer:
A. About 4,900 ft
Step-by-step explanation:
We want h such that ...
5 = 10·ln(h) -80
8.5 = ln(h) . . . . . . . add 80, divide by 10
e^8.5 = h ≈ 4914.8 . . . . take the antilog
h ≈ 4900 . . . . feet
We have been given that The boston celtics have won 16 nba championships over approximately 50 years. Therefore, it can be concluded that in any given year the probability of celtics winning the title will be p = 16/50 = 0.32
For Celtics to win eight straight championships in 1959, we will be required to multiply the probability of winning championship in one year to itself 8 times.
Therefore, the required probability is:
Therefore, the required probability is almost 0.00011.
Answer: To know whether a radical expression is in simplest form or not you should put the numbers and letters inside the radical in terms of prime factors. Then, the radical expression is in the simplest form if all the numbers and letters inside the radical are prime factors with a power less than the index of the radical
Explanation:
Any prime factor raised to a power greater than the index of the root can be simplified and any factor raised to a power less than the index of the root cannot be simplified
For example simplify the following radical in its simplest form:
![\sqrt[5]{3645 a^8b^7c^3}](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7B3645%20a%5E8b%5E7c%5E3%7D%20)
1) Factor 3645 in its prime factors: 3645 = 3^6 * 5
2) Since the powr of 3 is 6, and 6 can be divided by the index of the root, 5, you can simplify in this way:
- 6 ÷ 5 = 1 with reminder 1, so 3^1 leaves the radical and 3^1 stays in the radical
3) since the factor 5 has power 1 it can not leave the radical
4) the power of a is 8, then:
8 ÷ 5 = 1 with reminder 3 => a^1 leaves the radical and a^3 stays inside the radical.
5) the power of b is 7, then:
7 ÷ 5 = 1 with reminder 2 => b^1 leaves the radical and b^2 stays inside the radical
6) the power of c is 3. Since 3 is less than 5 (the index of the radical) c^3 stays inside the radical.
7) the expression simplified to its simplest form is
![3ab \sqrt[5]{3.5.a^3b^2c^3}](https://tex.z-dn.net/?f=3ab%20%5Csqrt%5B5%5D%7B3.5.a%5E3b%5E2c%5E3%7D%20)
And you know it cannot be further simplified because all the numbers and letters inside the radical are prime factors with a power less than the index of the radical.
Explanation:
Any prime factor raised to a power greater than the index of the root can be simplified and any factor raised to a power less than the index of the root cannot be simplified
For example simplify the following radical in its simplest form:
1) Factor 3645 in its prime factors: 3645 = 3^6 * 5
2) Since the powr of 3 is 6, and 6 can be divided by the index of the root, 5, you can simplify in this way:
- 6 ÷ 5 = 1 with reminder 1, so 3^1 leaves the radical and 3^1 stays in the radical
3) since the factor 5 has power 1 it can not leave the radical
4) the power of a is 8, then:
8 ÷ 5 = 1 with reminder 3 => a^1 leaves the radical and a^3 stays inside the radical.
5) the power of b is 7, then:
7 ÷ 5 = 1 with reminder 2 => b^1 leaves the radical and b^2 stays inside the radical
6) the power of c is 3. Since 3 is less than 5 (the index of the radical) c^3 stays inside the radical.
7) the expression simplified to its simplest form is
And you know it cannot be further simplified because all the numbers and letters inside the radical are prime factors with a power less than the index of the radical.