Hello :
the discriminat of each quadratic equation : ax²+bx+c=0 ....(a <span>≠ 0) is :
</span><span>Δ = b² -4ac
1 ) </span>Δ > 0 the equation has two reals solutions : x = (-b±√Δ)/2a
2 ) Δ = 0 : one solution : x = -b/2a
3 ) Δ <span>< 0 : no reals solutions</span>
Sin³ x-sin x=cos ² x
we know that:
sin²x + cos²x=1 ⇒cos²x=1-sin²x
Therefore:
sin³x-sin x=1-sin²x
sin³x+sin²x-sin x-1=0
sin³x=z
z³+z²-z-1=0
we divide by Ruffini method:
1 1 -1 -1
1 1 2 1 z=1
-------------------------------------
1 2 1 0
-1 -1 -1 z=-1
--------------------------------------
1 1 0 z=-1
Therefore; the solutions are z=-1 and z=1
The solutions are:
if z=-1, then
sin x=-1 ⇒x= arcsin -1=π+2kπ (180º+360ºK) K∈Z
if z=1, then
sin x=1 ⇒ x=arcsin 1=π/2 + 2kπ (90º+360ºK) k∈Z
π/2 + 2kπ U π+2Kπ=π/2+kπ k∈Z ≈(90º+180ºK)
Answer: π/2 + Kπ or 90º+180ºK K∈Z
Z=...-3,-2,-1,0,1,2,3,4....
Answer:
Josh had $500
Karen had $100
Step-by-step explanation:
J = 5K
J - 20 = 6(K - 20)
5K - 20 = 6K - 120
100 = K
J = 500
The total time spent in minutes is 110 minutes
<h3>How to determine the total time?</h3>
The given parameters are:
- Erica = 1 hour, 15 minutes
- Sean = 35 minutes
The total time is calculated as:
Total = Erica + Sean
So, we have:
Total = 1 hour, 15 minutes + 35 minutes
1 hour = 60 minutes
So, we have:
Total = 60 minutes + 15 minutes + 35 minutes
Evaluate the sum
Total = 110 minutes
Hence, the total time spent is 110 minutes
Read more about time at:
brainly.com/question/4931057
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