Answer:
a) the trigonometric function is;
b) 
( to two decimal places)
Step-by-step explanation:
This data can be represented by the sinusoidal function of the form :
where A = amplitude and which can be determined via the formula:
A = 7.5° C
where B = the frequency;
Since the data covers a period of 3 days ; then 
( where 365 is the time period )
The vertical shift is found by the equation D;
D = 
D = 
D = 21.5
Replacing the values of A ; B and D into the above sinusoidal function; we have :
From the question; when it is 7th of the year ( i.e January 7);
t = 7 and the temperature (y) = 29° C
replacing that too into the above equation; we have:
Thus; the trigonometric function is;
Similarly; to determine the temperature o Jan 31; i.e when t= 31 ; we have :
( to two decimal places)
Answer:
62.8
Step-by-step explanation:
Answer:
x=-6,x=3
Step-by-step explanation:
x^2-x-18=-4x
Adding both sides by 4x
x^2+3x-18=0
Factoring
(x+6)(x-3)=0
x=-6,x=3
The answer to your question is "C. 4 feet/ 1 second."
When the rate has a quantity of 1, it is a unit rate. So if the rate is 4 feet to 1 second (or four feet per second), it would be considered a unit rate.
Answer:
1. The equation represent an exponential decay
2. The rate of the exponential decay is -3×2.5ˣ·㏑(2.5)
Step-by-step explanation:
When a function a(t) = a₀(1 + r)ˣ has exponential growth, the logarithm of x grows with time such that;
log a(t) = log(a₀) + x·log(1 + r)
Hence in the equation -3 ≡ a₀, (1 + r) ≡ 2.5 and y ≡ a(t). Plugging in the values in the above equation for the condition of an exponential growth, we have;
log y = log(-3) + x·log(2.5)
Therefore, since log(-3) is complex, the equation does not represent an exponential growth hence the equation represents an exponential decay.
The rate of the exponential decay is given by the following equation;
Hence the rate of exponential decay is -3×2.5ˣ × ㏑(2.5)
