- <span>A </span>projectile<span> is </span>thrown upward so<span> that </span>its distance above<span> the </span>ground after t seconds<span> is </span>given<span> by the </span>function h(t<span>) = - 16t² + </span>640t<span>. </span>After<span> how </span>many seconds<span> does the </span>projectile<span>take</span><span> to reach </span>its<span> maximum height? I made the </span>function<span> .</span>
Answer:
The "operations" are addition, subtraction, multiplication, division, exponentiation, and grouping; the "order" of these operations states which operations take precedence (are taken care of) before which other operations.
Step-by-step explanation:
Sin 2x - sin x=0
Using the trigonometric identity: sin 2x=2 sinx cosx
2 sinx cosx - sinx =0
Common factor sinx
sinx ( 2 cosx -1)=0
Two options:
1) sinx=0
on the interval [0,2π), the sinx=0 for x=0 and x=<span>π=3.1416→x=3.14
2) 2 cosx - 1=0
Solving for cosx
2 cosx-1+1=0+1
2 cosx = 1
Dividing by 2 both sides of the equation:
(2 cosx)/2=1/2
cosx=1/2
cosx is positive in first and fourth quadrant:
First quadrant cosx=1/2→x=cos^(-1) (1/2)→x=</span><span>π/3=3.1416/3→x=1.05
Fourth quadrant: x=</span>2π-π/3=(6π-π)/3→x=5<span>π/3=5(3.1416)/3→x=5.24
Answer: Solutions: x=0, 1.05, 3.14, and 5.24</span>
