I think its 32 because I times all of the equation an then add
Answer:
![\displaystyle \sec(\theta)=\frac{9\sqrt{17}}{17}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csec%28%5Ctheta%29%3D%5Cfrac%7B9%5Csqrt%7B17%7D%7D%7B17%7D)
Step-by-step explanation:
We are given that:
![\displaystyle \sin(\theta)=\frac{8}{9}\text{ and } \tan(\theta)>0](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csin%28%5Ctheta%29%3D%5Cfrac%7B8%7D%7B9%7D%5Ctext%7B%20and%20%7D%20%5Ctan%28%5Ctheta%29%3E0)
And we want to find sec(θ).
First, note that both sine and tangent are positive. The only quadrant in which this can occur is QI. Hence, all trig ratios will be positive.
Also, recall that sine is the ratio of the opposite side to the hypotenuse. Using this information and the Pythagorean Theorem, we can determine the adjacent side:
![a=\sqrt{9^2-8^2}=\sqrt{17}](https://tex.z-dn.net/?f=a%3D%5Csqrt%7B9%5E2-8%5E2%7D%3D%5Csqrt%7B17%7D)
So, with respect to θ, the adjacent side is √(17), the opposite side is 8, and the hypotenuse is 9.
Secant is the ratio of the hypotenuse to the adjacent. Hence:
![\displaystyle \sec(\theta)=\frac{9}{\sqrt{17}}=\frac{9\sqrt{17}}{17}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csec%28%5Ctheta%29%3D%5Cfrac%7B9%7D%7B%5Csqrt%7B17%7D%7D%3D%5Cfrac%7B9%5Csqrt%7B17%7D%7D%7B17%7D)
Again, since θ is in QI, all trig ratios are positive.
Answer:
x = 1/12
Step-by-step explanation:
2/3x + 1/4 = (8x+3) /12 (create equivalent fractions with a denominator of 12)
23/3x - 1/3 = (23x - 1) /3 *(46/6x = 23/3x)
<u>8x + 3</u> = <u>23x - 1</u>
12 3
now cross-multiply:
3(8x + 3) = 12(23x - 1)
24x + 9 = 273x - 12
9 = 252x - 12
21 = 252x
x = 21/252 which reduces to 1/12
Answer: Hello there!
We know that the culture has 2000 bacteria initially (at t = 0 min), and it doubles when t = 40min, again at t = 80 min, and so on
And the rate of grouth is proportional to the population, then we can obtain an expression of the form:
P(t) = 2000*k(t) where k(t) is the factor that defines the growth of the population:
we know that:
p(0) = 2000*k(0) = 2000
p(40) = 2000*k(40) = 2000*2 = 4000
p(80) = 2000*k(80) = 2000*2*2 = 8000
etc
then we can see that k(t) = 2^(t/40)
where k(0) = 1, k(40) = 2, k(80) = 2*2, etc
then the function that models the population of the culture is:
p(t) = 2000*2^(t/40)
where t is in minutes.
Answer:
1.) 1
2.) 3600
3.) 242
Step-by-step explanation:
1- 523 / 523 = 1
2- 12 x 300 = 3600
3- 144 + 98 = 242