The measure of an angle is the coterminal angle with a 45A°+360A° and can be determined by using the measurement of coterminal angles.
<h2>We have to
determine</h2>
Which expression finds the measure of an angle that is coterminal with a 45° angle?
<h3>
According to the
question,</h3>
Coterminal angles are those angles that share the terminal side of an angle occupying the standard position.
The standard position means that one side of the angle is fixed along the positive x-axis, and the vertex is located at the origin.
<h3>A
coterminal with 45°
is
45°+k°360° with
k as an
integer.</h3>
Then,
The coterminal angle with 45°,
When k = 0
Then,
![\rm = 45+(0)360\\\\= 45+0\\\\= 45 \ degree](https://tex.z-dn.net/?f=%5Crm%20%3D%2045%2B%280%29360%5C%5C%5C%5C%3D%2045%2B0%5C%5C%5C%5C%3D%2045%20%5C%20degree)
When k = 1
Then,
![\rm = 45+(1)360\\\\= 45+360\\\\= 405 \ degree](https://tex.z-dn.net/?f=%5Crm%20%3D%2045%2B%281%29360%5C%5C%5C%5C%3D%2045%2B360%5C%5C%5C%5C%3D%20405%20%5C%20degree)
When k = -1
Then,
![\rm = 45+(-1)360\\\\= 45-360\\\\= -315 \ degree](https://tex.z-dn.net/?f=%5Crm%20%3D%2045%2B%28-1%29360%5C%5C%5C%5C%3D%2045-360%5C%5C%5C%5C%3D%20-315%20%5C%20degree)
Hence, The measure of an angle that is coterminal with a 45A°+360A°.
For more details about the Coterminal angle refer to the link given below.
brainly.com/question/12378421
Answer:
n+k=k+n=
n= k+n
n=k+n
Is that what your looking for? if it wrong I'm very sorry, and hav a great weekend
The model is p(x) = 75,000 ∛(x - 1940)
Now use p(x) = 245,000 and solve for x
245,000 = 75,000 ∛(x - 1940) =
245,000 / 75,000 = ∛(x - 1940)
49/15 = ∛(x - 1940)
x - 1940 = [49/15]^3 = 34.86
x = 1940 + 34.86 = 1974.85
Then, the answer is 1975 (option b)
The population in 20 years is 719 people.
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
According to the question
where P is population at any time
solving equation,
![\int](https://tex.z-dn.net/?f=%5Cint)
![\int kP](https://tex.z-dn.net/?f=%5Cint%20kP)
-(1)
Applying the conditions,
at t=0, P = 500
-(2)
at t=10, P= 600
putting it in equation gives
![ln(600) = k(10)+ln(500)](https://tex.z-dn.net/?f=ln%28600%29%20%3D%20k%2810%29%2Bln%28500%29)
ln(6/5) = k(10)
![k = \frac{ln(6/5)}{10}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7Bln%286%2F5%29%7D%7B10%7D)
at t=20 , P= ?
![lnP=(\frac{ln(6/5)}{10})20 + ln500](https://tex.z-dn.net/?f=lnP%3D%28%5Cfrac%7Bln%286%2F5%29%7D%7B10%7D%2920%20%2B%20ln500)
![lnP=({ln(6/5)}{2 + ln500](https://tex.z-dn.net/?f=lnP%3D%28%7Bln%286%2F5%29%7D%7B2%20%2B%20ln500)
On putting the values of ln(6/5) , ln(500)
![lnP=0.182(2) + 6.214](https://tex.z-dn.net/?f=lnP%3D0.182%282%29%20%2B%206.214)
![P = e^{6.578}](https://tex.z-dn.net/?f=P%20%3D%20e%5E%7B6.578%7D)
P = 719.099
On rounding off
P ≈ 719 people
Thus the population in 20 years is 719 people.
Learn more about differential equations here :
brainly.com/question/1584190
#SPJ4