Visualize pi/2 as 90° on the unit circle. this has no real component, only imaginary. same for 3pi/2, or -pi/2 as shown in this equation:
as you move around the unit circle, you'll find that 9pi/2 is the same angle as pi/2.
Thus, the rectangular coordinates are:
Answer: a<13
Step-by-step explanation:
a*(a+1)<a^2+13
a^2+a<a^2+13
subtract a^2 from both sides:
a<13
The scale factor was D. 4. We can figure this out by multiplying 3 by 4 to get 12 and 1 by 4 which is 4 to get the dimensions of the larger triangle.
I hope this helped! :-)
You need to use Pythagoras’ Theorem.
A² + B² = c² and c is the hypotenuse of the right angled triangle.
The height of the tower (5 feet) is A and the distance from the end of the cable and the base of the tower (12 feet) is B. The length of ONE cable is c. So:
A² + B² = c²
5² + 12² = c²
25 + 144 = c²
169 = c²
13 = c. This is the length of one cable.
3 x 13 = 39 therefore the total length of the cables is 39 feet.
25
For a quadratic of the form
, we have the quadratic formula
,
where a is the coefficient (number before the variable) of the squared term, b is the coefficient of the linear term, and c is the constant term.
So, given
, we can get that
, and
. We substitute these numbers into the quadratic formula above.
This is our final answer.
If you've never seen the quadratic formula, you can derive it by completing the square for the general form of a quadratic. Note that the
symbol (read: plus or minus) represents the two possible distinct solutions, except for zero under the radical, which gives only one solution.
