Answer:
y = 6cos(π/2)t
Step-by-step explanation:
Given in the question that,
in a simple harmonic motion in which
at t=0 the amplitude is 6 cm, so the simple harmonic motion will be in cosine form. As in case of sine function, the value of function at t=0 is 0.
And,
the period is given as 4 sec
We know that model equation of simple harmonic motion is
<h3>y = a. cosb(t + c) + d</h3>
here,
a is amplitude
c is Horizontal shift or phase shift
d is Vertical shift
<h3>Step1</h3><h3>Find b</h3>
Period = 2 π / b
4 = 2π / b
b = 2π/4
b = 1π/2
<h3>Step2</h3><h3>Find shifts</h3>
Horizontal and vertical shifts are 0.
So, c = 0 and d = 0
<h3>Step3</h3><h3>Plug those values in the above in the equation</h3>
y = 6cos π/2 (t + 0) + 0
y = 6cos(π/2)t
Discount amount:
10% of $10.95 = 10/100 × $10.95
= $1.095
Discounted sales:
$10.95 - $1.095 = $9.855 ≈ $9.86 (2 d.p.)
"Disneyland will never be completed. It will continue to grow as long as there is imagination left in the world." - Bear Grylls
<span>
"M</span>ickey Mouse popped out of my mind onto a drawing pad 20 years ago on a train ride from Manhattan to Hollywood at a time when business fortunes of my brother Roy and myself were at lowest ebb and disaster seemed right around the corner."- Ray Mears
<span>
2 GREAT EXPLORERS!
</span>
Answer:
17.25 years
Step-by-step explanation:
A certain type of conifer hedging increases in height by 17% each year for the first 20 years.When i bought some of this hedging, it was all about 50cm tall. How long will it take to grow 3m tall?
Step 1
We make sure all parameters have the same units, hence:
We convert 3m to cm
1 m = 100cm
3m = x
Cross Multiply
x = 3 × 100cm
x = 300cm
Step 2
To solve this question, we use the formula for Exponential growth =
y = a (1 + r) ^t
Where:
y = Size after time t = 3m = 300cm
a = Initial size of the tree = 20 cm
r = Growth rate = 17%
t = Time in years = ??
300 = 20 (1 + 0.17)^t
300 = 20(1.17) ^t
Divide both sides by 20
300/20 = 20(1.17) ^t/20
15 = 1.17^t
Take the Natural logarithm of both sides
In 15 = 1n 1.17^t
In 15 = t 1n 1.17
t = In 15/In 1.17
t = 17.248315544 years
Approximately = 17.25 years