There are two -main- approaches to answer this problem. By using the sine identity, or applying law of sines.
We'll do the sine trig. identity, as it is the most effective.
Given an angle '
' in a right triangle, '
' is defined as the opposite side of the triangle to the given angle, over the triangle's hypotenuse.
So, for this setup:
Now, we solve for x:
So, answer is 3.4
The answer is 140
140 x 0.1 (10% as a decimal) = 14
Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:
| 2 -7 8 -3
<u>1 | 2 -5 3</u>
| 2 -5 3 0
<u> 1 | 2 -3 </u>
2 -3 0
So the factorization is (x-1)² (2x-3)=0. So:
Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:
| 1 -1 0 -4
<u>2 | 2 2 </u>
1 2 2 0
So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.
Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:
| 6 7 9 2
<u>-2 | -12 10 -2</u>
6 -5 1 0
So the factorization is (x+2)(6x²-5x+1)=0 . The quadratic equation is solved by the general formula:
The
second projectile was travelling 1.4 times faster than the first. I
am hoping that this answer has satisfied your query and it will be able to help
you in your endeavor, and if you would like, feel free to ask another question.
First of all, let's find the slope of line L. To find the slope of a line, you write it in the explitic form 
, and consider the coefficient 
. So, we have
So, the slope of line L is 2/3.
Two lines are parallel if they have the same slope. So, line M has slope 2/3 as well, and we know that it passes through the point (3, -10).
When you are given the slope and a point 
of a line, its equation is given by
So, if you plug your values, you have
which you can simplify into
