X²+15x+36<0
at first solve quadratic equation
D=b²-4ac= 225-4*1*36= 81
x=(-b+/-√D)/2a
x=(-15+/-√81)/2= (-15+/-9)/2
x1=(-15-9)/2=-12
x2=(-15+9)/2=-3
we can write x²+15x+36<0 as (x+12)(x+3)<0
(x+12)(x+3)<0 can be 2 cases, because for product to be negative one factor should be negative , and second factor should be positive
1 case) x+12<0, and x+3>0,
x<-12, and x>-3
(-∞, -12) and(-3,∞) gives empty set
or second case) x+12>0 and x+3<0
x>-12 and x<-3
(-12,∞) and (-∞,-3) they are crossing , so (-12, -3) is a solution of this inequality
The equation that represents the <em>sinusoidal</em> function is ![x(t) = -8 + 6.5 \cdot \sin \left[\left(\frac{2}{3} \pm \frac{4\cdot i}{3}\right)\cdot t + \left(\frac{2\pi}{3} \pm \frac{7\pi \cdot i}{3} \right)\right]](https://tex.z-dn.net/?f=x%28t%29%20%3D%20-8%20%2B%206.5%20%5Ccdot%20%5Csin%20%5Cleft%5B%5Cleft%28%5Cfrac%7B2%7D%7B3%7D%20%5Cpm%20%5Cfrac%7B4%5Ccdot%20i%7D%7B3%7D%5Cright%29%5Ccdot%20t%20%2B%20%5Cleft%28%5Cfrac%7B2%5Cpi%7D%7B3%7D%20%5Cpm%20%5Cfrac%7B7%5Cpi%20%5Ccdot%20i%7D%7B3%7D%20%20%5Cright%29%5Cright%5D)
, 
.
<h3>Procedure - Determination of an appropriate function based on given information</h3>
In this question we must find an appropriate model for a <em>periodic</em> function based on the information from statement. <em>Sinusoidal</em> functions are the most typical functions which intersects a midline (
) and has both a maximum (
) and a minimum (
).
Sinusoidal functions have in most cases the following form:
(1)
Where:
- Angular frequency
- Angular phase, in radians.
If we know that 
, 
, 
, 
and 
, then the sinusoidal function is:
(2)
(3)
The resulting system is:
(2b)
(3b)
By applying <em>inverse trigonometric </em>functions we have that:
, 
(2c)
, (3c)
And we proceed to solve this system:
, 
By (2c):
The equation that represents the <em>sinusoidal</em> function is , .
To learn more on functions, we kindly invite to check this verified question: brainly.com/question/5245372
Answer:
The correct answer would be the second one: x > - 7
Step-by-step explanation:
Hope this helps!
Answer:
Angle 1: 55 degrees
Angle 2: 55 degrees
Angle 3: 70 degrees
Step-by-step explanation:
<u>Finding angle 1:</u> We know that in a triangle, all three angles must add up to 180 degrees. In the triangle on the left, 2 of the angle measures are already given to us. Therefore, we can simply do 180 - 40 - 85, thus the measure of angle 1 is 55 degrees.
<u>Finding angle 2:</u> We know that opposite angles are congruent. Therefore, angle 2 and angle 1 have the same measure.
<u>Finding angle 3:</u> Using the same thought process as we used when finding the measure of angle 1, we can subtract the other 2 angles. 180 - 55 - 55 is equal to 70.
Answer:
it`s acute because the angle is less than 90 degrees
