Step-by-step explanation:
common ratio is usually used for geometric sequences.
every term is created by multiplying the previous term by a certain constant factor (= common ratio).
this factor or common ratio is in our case 4.
such a sequence is a function f(x) for x being whole numbers.
a0 = 1
a1 = a0×4 = 1×4 = 4
a2 = a1×4 = 4×4 = 16
...
an = 4^n
as general function that is then
f(x) = 4^x
a horizontal shift right by 6 units means that now the functional value of x is the same as it was for (x-6) before the shift.
e.g. f_new(6) = f_old(0)
so, the function is
f(x) = 4^(x - 6) or (4^x)/4⁶
Answer:2.625 also 2 5/8
Step-by-step explanation:
(a) The vertical motion equation for the ball is h = 8 + 48t - 16t².
(b) The time for the ball to hit the ground is 3.15 s.
(c) The time for the ball to travel 56 ft above the ground is 0.79 s.
<h3>Vertical motion equation for the ball</h3>
The vertical motion equation for the ball is calculated as follows;
h = h₀ + vt - ¹/₂gt²
h = 8 + 48t - ¹/₂(32)t²
h = 8 + 48t - 16t²
<h3>Time for the ball to hit the ground</h3>
0 = 8 + 48t - 16t²
solve the above quadratic equation with formula method;
a = -16, b = 48, c = 8
t = 3.15 s
<h3>Time for the ball to be 56 ft above the ground</h3>
- let upward motion be positive
h = 8 + 48t + 16t²
56 = 8 + 48t + 16t²
0 = -48 + 48t + 16t²
solve the above quadratic equation with formula method;
a = 16, b = 48, c = -48
t = 0.79 s
Learn more about equation of motion here: brainly.com/question/25951773
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7a = 63
Inverse operation
7a/7 = 63/7
a= 63/7
a= 9
Answer: a = 9
Answer: length = 14 meters
Width = 10 meters
Step-by-step explanation:
The rectangular tennis court has two equal lengths,L and two equal widths,W
The area of the tennis court is expressed as
Area = Length × width
The area is given as 140 square meters. It means that
L× W = 140
It's length is 6 meters less than twice it's width. It means that
L = 2W - 6
Substituting L = 2W - 6 into LW = 140, it becomes
W(2W - 6) = 140
2W^2 - 6W = 140
2W^2 - 6W - 140 = 0
W^2 - 3W - 70 = 0
W^2 + 7W - 10W - 70 = 0
W( W + 7 ) - 10( W + 7) = 0
( W + 7 )(W - 10) = 0
( W + 7 ) = 0 or W - 10 = 0
W= -7 or W = 10 meters
The value cannot be negative so W = 10
L = 2W - 6 = 2×10 - 6
L = 20 - 6 = 14 meters
