Answer:
a) v = 12.21m/s
a = 4.07 m/s²
b)v = 11.24m/s
a = 3.75 m/s²
Step-by-step explanation:
a) Dividing the moviment into two parts:
I - With acceleration
v = v₀ + at
s = s₀ + v₀t + at²/2
- v₀ = 0
- s₀ = 0
- a = ?
- v = ?
- t = 3s
- s = x
v = v₀ + at
v = 3a ⇒ a = v/3
s = s₀ + v₀t + at²/2
x = v/3.3²/2
x = 3v/2
II - Uniform
s = s₀ + vt
s = 100
s₀ = x
v = v
t = 9.69 - 3 = 6.69s
s = s₀ + vt
100 = x + v*6.69
100 = x + 6.69v
As x = 3v/2
100 = 3v/2 + 6.69v
100 = 1.5v + 6.69v
100 = 8.19v
v = 12.21m/s
a = v/3 = 4.07 m/s²
b) Dividing the moviment into two parts:
I - With acceleration
v = v₀ + at
s = s₀ + v₀t + at²/2
- v₀ = 0
- s₀ = 0
- a = ?
- v = ?
- t = 3s
- s = x
v = v₀ + at
v = 3a ⇒ a = v/3
s = s₀ + v₀t + at²/2
x = v/3.3²/2
x = 3v/2
II - Uniform
s = s₀ + vt
s = 200
s₀ = x
v = v
t = 19.30 - 3 = 16.30s
s = s₀ + vt
200 = x + v*16.3
100 = x + 16.3v
As x = 3v/2
200 = 3v/2 + 16.3v
200 = 1.5v + 16.3v
200 = 17.8v
v = 11.24m/s
a = v/3 = 3.75 m/s²
Answer: f(120°) = (√3) + 1/2
Step-by-step explanation:
i will solve it with notable relations, because using a calculator is cutting steps.
f(120°) = 2*sin(120°) + cos(120°)
=2*sin(90° + 30°) + cos(90° + 30°)
here we can use the relations
cos(a + b) = cos(a)*cos(b) - sin(a)*sin(b)
sin(a + b) = cos(a)*sin(b) + cos(b)*sin(a)
then we have
f(120°) = 2*( cos(90°)*sin(30°) + cos(30°)*sin(90°)) + cos(90°)*cos(30°) - sin(90°)*sin(30°)
and
cos(90°) = 0
sin(90°) = 1
cos(30°) = (√3)/2
sin(30°) = 1/2
We replace those values in the equation and get:
f(120°) = 2*( 0 + (√3)/2) + 0 + 1/2 = (√3) + 1/2
Answer:
Step-by-step explanation:
1. x+2y=6 or x=6-2y
3x-2y=2
3(6-2y)-2y=2
18-6y-2y=2
18-8y=2
-8y=-18+2
-8y=-16
y=-16/-8
y=2 ans.
x+2*2=6
x+4=6
x=6-4=2 ans.
Proof:
3*2-2*2=2
6-4=2
2=2
I leave the rest for you to practice with.
3. 4x+y=7
2x+5y=-1
5. 3x+2y=-2
6x-y=6
Solve the system using the elimination method. Show all your steps.
7. -3x+3y=3
3x+y=9 add.
---------------------------------
4y=12
y=12/4
y=3 ans.
3x+3=9
3x=9-3
3x=6
x=6/3
x=2 ans.
Proof:
-3*2+3*3=3
-6+9=3
3=3
I'll leave the rest for practice.
9. -5x+12y=20
x-2y=-6
11. 3x+2y=1
4x+ 6y= 7
Answer:
see explanation
Step-by-step explanation:
the equation of parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier.
here (h, k ) = (3, 1 ) , then
y = a(x - 3)² + 1
to find a substitute any other point on the graph into the equation.
using (0, 7 )
7 = a(0 - 3)² + 1 ( subtract 1 from both sides )
6 = a(- 3)² = 9a ( divide both sides by 9 )
= 
= a
y = (x - 3)² + 1 ← in vertex form
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the equation of a parabola in factored form is
y = a(x - a)(x - b)
where a, b are the zeros and a is a multiplier
here zeros are - 1 and 3 , the factors are
(x - (- 1) ) and (x - 3), that is (x + 1) and (x - 3)
y = a(x + 1)(x - 3)
to find a substitute any other point that lies on the graph into the equation.
using (0, - 3 )
- 3 = a(0 + 1)(0 - 3) = a(1)(- 3) = - 3a ( divide both sides by - 3 )
1 = a
y = (x + 1)(x - 3) ← in factored form
