Answer:
The answer to the problem is C
Answer:
1. 1
2. 1/12
3. 3 1/6
Step-by-step explanation:
Solution for #1. First, you have to get a common denominator. Here, that would be 6. In order to give 1/2 a denominator of 6, you will need to multiply the numerator and the denominator by 3. That will give you 3/6. Add that to the other 3/6 (3/6+3/6) which equals 6/6 which can be simplified to 1.
Solution for #2. This is just like #1. First, you have to get a common denominator. Here, that would be 12. In order to give 1/3 a denominator of 12, you will need to multiply the numerator and the denominator by 4. That will give you 4/12. Then, to give 1/4 a denominator of 12, you will need to multiply the numerator and the denominator by 3. That will give you 3/12. Then, subtract (4/12-3/12). You will get an answer of 1/12.
Solution for #3. This is slightly different from the others, I has two more steps. First, you need to changed the mixed fractions into improper fractions. You will get 17/3 and 5/2. Then, you have to get a common denominator. Here, that would be 6. In order to give 17/3 a denominator of 6, you will need to multiply the numerator and the denominator by 2. That will give you 34/6. Then, to give 5/2 a denominator of 6, you will need to multiply the numerator and the denominator by 3. That will give you 15/6. After that, subtract (34/6-15/6). You should get 19/6. Finally, divide 19/6 and you should get 3R1. So, the mixed fraction version of 19/6 is 3 1/6 (I did this by using the 3 from 3R1 as the whole number and I just put the remainder of 1 over 6 as the fractional part). You can multiply to check your answer.
I think I know what it forms - a cone!!
I'm guessing that the angles at the end are 10 degrees so that would make angle CAB equal 5 degrees.
Line AB would be the radius of the "upper cone".
Line BC is 12/2 or 6
tangent (A) = BC / AB
tangent (5) = 6 / AB
AB = 6 / tan(5)
AB = 6 / 0.087489
AB =
<span>
<span>
<span>
68.58 which is the radius of the "upper cone".</span></span></span>
Cone Volume = (PI * radius^2 * height) / 3
Cone Volume = (PI * 68.58 * 68.58 * 6) / 3
Cone Volume =
<span>
<span>
<span>
29,551
That is just the "upper cone volume. So, we multiply </span></span></span><span><span>
<span>
<span>
29,551 * 2
and get 59,102 which is the volume of the entire solid.
</span></span></span> </span>
Source for cone volume:
http://www.1728.org/volcone.htm
Answer:
Step-by-step explanation:
Add and subtract the square of half the x-coefficient:
x² -10x +(-5)² -(-5)² +15
Express the first three terms as a square; simplify the remaining terms.
(x -5)² -10
This expression describes a parabola that opens upward and has its vertex at (x, y) = (5, -10). The minimum value is -10.
