Using translation concepts, it is found that the transformations to create function d are given as follows:
- Horizontal shift right 1 unit.
- Vertical shift up 5 units.
- Frequency multiplied by 2.
<h3>What is a translation?</h3>
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent cosine function is given by:
f(x) = cos(x).
The translated function is given by:
d(x) = cos(2x - 1) + 5.
Which means that:
- 1 was subtracted in the domain, hence the was a horizontal shift right 1 unit.
- 5 was added in the range, hence there was a vertical shift up 5 units.
- There was a multiplication by 2 in the domain, hence the frequency is multiplied by 2.
More can be learned about translation concepts at brainly.com/question/4521517
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Answer:
Hi,
Step-by-step explanation:
PR²=PQ²+QR²-2*PQ*QR*cos(51°)
=15²+12²-2*15*12*cos(51°)
=142,444659....
PR=11.9350...
PQ²=QR²+PR²-2*QR*PR*cos(R)
cos(R)=(12²+142.444...-15²)/(2*12*11.9350...)=0,21451112....
angle R=77,61315...°≈77.6°
angle P=180°-51°-77.6°≈51,4°
For this problem, we have to set up the formula for the equation first. The equation should help us predict how long would it take to reach a life expectancy of 130 years. Let's start by denoting variable to present them in algebraic equations. Let x be the number of decades, while y is the number of years for life expectancy. The base year used here is 2009 with a life expectancy of 80 years. So, we will expect that 80 is a constant in the expression. We will add to this the number of decades multiplied by 5.4, because it stands for 5.4 additional years per decade. When you write this in an equation, it would be
y = 80 + 5.4x
Now, we substitute y=130.
130 = 80 + 5.4x
x = (130 - 80)/5.4
x = 9.259
Therefore, it would take approximately more than 9 decades. Projecting this amount of time from 2009, the year would be:
Projected year = 2009 + 9 decades * (10 years/1 decade)
Projected year = 2101
It would be in year 2101.
If a number can be represented by a fraction, it is a rational number. So yes, 1815 is a rational number
Answer: the simplify anwser is 64a^ 6 - 27b^6
Step-by-step explanation:
