Answer:
16:3
17:4
18:1
19:1
Step-by-step explanation:
Step-by-step explanation:
f(x) = -0.01x² + 0.7x + 6.1
a) f(x) is a downward facing parabola, so the maximum height is at the vertex. The vertex of a parabola can be found using x = -b/(2a).
x = -0.7 / (2 × -0.01)
x = 35
f(35) = -0.01(35)² + 0.7(35) + 6.1
f(35) = 18.35
The maximum height is 18.35 feet.
b) The maximum horizontal distance is when the ball lands, or when f(x) = 0.
0 = -0.01x² + 0.7x + 6.1
0 = x² − 70x − 610
Solve with quadratic formula:
x = [ -b ± √(b² − 4ac) ] / 2a
x = [ -(-70) ± √((-70)² − 4(1)(-610)) ] / 2(1)
x = (70 ± √7340) / 2
x = 35 ± √1835
x = -7.84, 77.84
x can't be negative, so x = 77.84. The ball's maximum horizontal distance is 77.84 feet.
c) When the ball is first launched, x = 0. The height at that position is:
f(0) = 6.1
The ball is launched from an initial height of 6.1 feet.
Answer:
{3,6,7,10}
Step-by-step explanation:
2/3(3)+1=3
2/3(6)+1=5
2/3(7)+1=17/3
2/3(10)+1=23/3
Answer:
KL ≈ 1.94
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos48° = 
= 
= 
( multiply both sides by KL )
KL × cos48° = 1.3 ( divide both sides by cos48° )
KL = 
≈ 1.94 ( to the nearest hundredth )
Explanation:
A system of equations are two or more equations that has to be valid at the same time. It means that the variables of one equation can be substitute in the other equation.
For example we have <span>y=5x−8</span> and we can substitute this value of y in the other equation
<span>4x+3y=33</span>
<span>4x+3<span>(5x−8)</span>=33</span> we can solve now for x
<span>4x+15x−24=33</span>
<span>19x=33+24</span>
<span>19x=57</span>
<span>x=<span>5719</span>=3</span>.
y can be obtained from the first equation
<span>y=5x−8</span>
<span>y=5⋅3−8=15−8=7</span>
Then <span>x=3</span> and <span>y=7</span>.
