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:
5.5 units
Step-by-step explanation:
Arc length is given by ...
s = rθ
s = (3.5)(π/2) ≈ 5.5 . . . units
Answer:
Explained below.
Step-by-step explanation:
A graph is formed using the height of students in Diego's math class.
It is provided that he arranges the students from shortest to tallest and measures the height in inches of each student in the class.
A distribution is known as to be skewed to the right, or positively skewed, when maximum of the data are collected on the left of the distribution and the graph has a longer tail towards the right.
For a positively skewed data: Mean > Median
A distribution is said to be skewed to the left, or negatively skewed, if maximum of the data are collected on the right of the distribution and the graph has a longer tail towards the left.
For a negatively skewed data: Mean < Median
A distribution is said to be symmetric, if maximum of the data are collected in the middle of the distribution and the graph has equal proportion of tails on both sides.
For a symmetric data: Mean = Median
One bowl needs 3/5 of a pound. Knowing that, we just need to find out how many 3/5s may fit in 10:
10 ÷ 3/5 =
= 10 * 5/3 =
= 50/3 =
= 16 2/3
Assuming the potter can't make a 2/3 of a bowl, he'll be able to make 16 bowls from 10 pounds.
