Answer: 113
Step by Step explanation:
12/2=6
inches.π⋅6^2≈113
Answer:
7 < x < 34
Step-by-step explanation:
The answer must be greater than 7, else the two sides are less than or equal to the third. That triangle is impossible. The answer must also be less than 34, because then the two other sides would equal the third, making an impossible triangle.
These are the formulas that will help you determine which type of triangle they are:
a^2+b^2 < c^2 ----> Obtuse Triangle
a^2+b^2 > c^2 ----> Actue Triangle
a^2+b^2 = c^2 ----> Right Triangle
Okay so now that you know that information, lets get into it :)
a. 5 in, 6 in, 7 in
You're going to take the smallest numbers, 5 and 6, and add them, if it equals a larger number than 7 then its a triangle and you have to determine if its an obtuse, right or acute triangle. In this case it is a triangle because 5 + 6 = 11 aka larger than 7.
The way you'll set this up is:
5^2 + 6^2 = 7^2
solve
25+36=49 -----> 25+36=61
61 > 49 or a^2 + b^2 > c^2
61 > is greater than 49
If you look ate the formulas that are above, this is an acute triangle.
b. 18 in, 9 in, 12 in
In this question, 9 and 12 are the smallest numbers that equal 21 and 21 is larger than 18 so, this is a triangle.
9^2 + 12^2 = 18^2
Solve
81 + 144 = 324 ----> 81 + 144 = 225
225 < 324 or a^2+b^2 < c^2
225 < is less than 324
If you look ate the formulas that are above, this is an obtuse triangle.
Something to just remember:
Sometimes you'll get a question which is like,
4 in, 5 in, 10 in
In this situation, if you add the smallest numbers which are, 4 and 5, you get 9, which is less than the larger number you have, 10. That means it is not a triangle. Just something to be aware about :)
I hope this helped you!
Answer:
The roots of f(x) are: -2, 3, (1+3i) and (1-3i)
Step-by-step explanation:
We are given an expression:
(1+3i) is a root of f(x)
We have to find the remaining roots of f(x).
Since, (1+3i) is a root of f(x),
is a factor of given expression.
Now, we check if (1 - 3i) is a root of given function.
Thus, (1-3i) is also a root of given function.
Since, (1-3i) is a root of f(x),
is a factor of given expression.
Thus, we can write:
Dividing f(x) by above expression:
To find the root, we equate it to zero:
Thus, the roots of f(x) are: -2, 3, (1+3i) and (1-3i)
