Answer: Lines of latitude (parallels) run east-west around the globe and are used to measure distances NORTH and SOUTH of the equator.
Step-by-step explanation:
Answer: B) (-4,5)
Step-by-step explanation:
Begin the problem by solving for y with the second equation. Add -4x to both sides of the equation so it reads y=4x+21. Then, substitute y into the first equation and solve. -2x-3(4x+21)=-7 turns into -14x-63=-7, which becomes -14x=56. Divide 56/-14 to get -4 for x. Since only one answer has -4 as an option for x, that's the correct answer.
Answer:
x = 90°
Step-by-step explanation:
Using the identity
cos²x = 1 - sin²x
Given
cos²x - sin x + 1 = 0
1 - sin²x - sin x + 1 = 0
- sin²x - sin x + 2 = 0 ← quadratic equation in sin x ( multiply through by - 1 )
sin²x + sin x - 2 = 0 ← in standard form
(sinx + 2)(sinx - 1) = 0 ← in factored form
Equate each factor to zero and solve for x
sinx + 2 = 0 ⇒ sinx = - 2 ← has no solution as - 1 ≤ x ≤ 1
sinx - 1 = 0 ⇒ sinx = 1 ⇒ x = 90°
solution is x = 90°
11) 2i
12) 7
13) -16-3i
14)4
15) -3-3i
That’s all I got for you
Answer:
Therefore the age of paint is 8915.78 years.
Step-by-step explanation:
Given that, the paint contain 34 % of the original carbon-14.
The exponential decay model for carbon-14 is
![A=A_0e^{-0.000121t}](https://tex.z-dn.net/?f=A%3DA_0e%5E%7B-0.000121t%7D)
A= Remaining amount of carbon.
= initial amount of carbon.
Here A= 34% of
![=\frac{34}{100}A_0](https://tex.z-dn.net/?f=%3D%5Cfrac%7B34%7D%7B100%7DA_0)
![\therefore \frac{34}{100}A_0=A_0e^{-0.000121t}](https://tex.z-dn.net/?f=%5Ctherefore%20%5Cfrac%7B34%7D%7B100%7DA_0%3DA_0e%5E%7B-0.000121t%7D)
![\Rightarrow \frac{34}{100}=e^{-0.000121t}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B34%7D%7B100%7D%3De%5E%7B-0.000121t%7D)
Taking ln both sides
![\Rightarrow ln|\frac{34}{100}|=ln|e^{-0.000121t}|](https://tex.z-dn.net/?f=%5CRightarrow%20ln%7C%5Cfrac%7B34%7D%7B100%7D%7C%3Dln%7Ce%5E%7B-0.000121t%7D%7C)
![\Rightarrow ln|\frac{34}{100}|={-0.000121t](https://tex.z-dn.net/?f=%5CRightarrow%20ln%7C%5Cfrac%7B34%7D%7B100%7D%7C%3D%7B-0.000121t)
![\Rightarrow t=\frac{ln|\frac{34}{100}|}{-0.000121}](https://tex.z-dn.net/?f=%5CRightarrow%20t%3D%5Cfrac%7Bln%7C%5Cfrac%7B34%7D%7B100%7D%7C%7D%7B-0.000121%7D)
![\Rightarrow t= 8915.78](https://tex.z-dn.net/?f=%5CRightarrow%20t%3D%208915.78)
Therefore the age of paint is 8915.78 years.