Answer:
-8x-4 is the answer using distributive property.
The angle between two vectors is:
CosФ = u - v / Magnitude(u) x magnitude(v)
Magnitude of u = SQRT(7^2 + -2^2) = SQRT(49 +4) = SQRT(53)
Magnitude of v = SQRT(-1^2 +2^2) = SQRT(1 +4) = SQRT(5)
u x v = (7 x -1) + (-2 x 2) = -7 + -4 = -11
cosФ = -11 / sqrt(53) x sqrt(5)
cosФ = -11sqrt265) / 265
Ф =cos^-1(-11sqrt265) / 265)
Ф=132.51 degrees.
Answer: 60% decrease
Step-by-step explanation:
Look at the attachment
Answer:
The correct answer is:
Between 600 and 700 years (B)
Step-by-step explanation:
At a constant decay rate, the half-life of a radioactive substance is the time taken for the substance to decay to half of its original mass. The formula for radioactive exponential decay is given by:
![A(t) = A_0 e^{(kt)}\\where:\\A(t) = Amount\ left\ at\ time\ (t) = 75\ grams\\A_0 = initial\ amount = 1000\ grams\\k = decay\ constant\\t = time\ of\ decay = 2500\ years](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A_0%20e%5E%7B%28kt%29%7D%5C%5Cwhere%3A%5C%5CA%28t%29%20%3D%20Amount%5C%20left%5C%20at%5C%20time%5C%20%28t%29%20%3D%2075%5C%20grams%5C%5CA_0%20%3D%20initial%5C%20amount%20%3D%201000%5C%20grams%5C%5Ck%20%3D%20decay%5C%20constant%5C%5Ct%20%3D%20time%5C%20of%5C%20decay%20%3D%202500%5C%20years)
First, let us calculate the decay constant (k)
![75 = 1000 e^{(k2500)}\\dividing\ both\ sides\ by\ 1000\\0.075 = e^{(2500k)}\\taking\ natural\ logarithm\ of\ both\ sides\\In 0.075 = In (e^{2500k})\\In 0.075 = 2500k\\k = \frac{In0.075}{2500}\\ k = \frac{-2.5903}{2500} \\k = - 0.001036](https://tex.z-dn.net/?f=75%20%3D%201000%20e%5E%7B%28k2500%29%7D%5C%5Cdividing%5C%20both%5C%20sides%5C%20by%5C%201000%5C%5C0.075%20%3D%20e%5E%7B%282500k%29%7D%5C%5Ctaking%5C%20natural%5C%20logarithm%5C%20of%5C%20both%5C%20sides%5C%5CIn%200.075%20%3D%20In%20%28e%5E%7B2500k%7D%29%5C%5CIn%200.075%20%3D%202500k%5C%5Ck%20%3D%20%5Cfrac%7BIn0.075%7D%7B2500%7D%5C%5C%20k%20%3D%20%5Cfrac%7B-2.5903%7D%7B2500%7D%20%5C%5Ck%20%3D%20-%200.001036)
Next, let us calculate the half-life as follows:
![\frac{1}{2} A_0 = A_0 e^{(-0.001036t)}\\Dividing\ both\ sides\ by\ A_0\\ \frac{1}{2} = e^{-0.001036t}\\taking\ natural\ logarithm\ of\ both\ sides\\In(0.5) = In (e^{-0.001036t})\\-0.6931 = -0.001036t\\t = \frac{-0.6931}{-0.001036} \\t = 669.02 years\\\therefore t\frac{1}{2} \approx 669\ years](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20A_0%20%3D%20A_0%20e%5E%7B%28-0.001036t%29%7D%5C%5CDividing%5C%20both%5C%20sides%5C%20by%5C%20A_0%5C%5C%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20e%5E%7B-0.001036t%7D%5C%5Ctaking%5C%20natural%5C%20logarithm%5C%20of%5C%20both%5C%20sides%5C%5CIn%280.5%29%20%3D%20In%20%28e%5E%7B-0.001036t%7D%29%5C%5C-0.6931%20%3D%20-0.001036t%5C%5Ct%20%3D%20%5Cfrac%7B-0.6931%7D%7B-0.001036%7D%20%5C%5Ct%20%3D%20669.02%20years%5C%5C%5Ctherefore%20t%5Cfrac%7B1%7D%7B2%7D%20%20%5Capprox%20669%5C%20years)
Therefore the half-life is between 600 and 700 years
For the rectangle you add 12 plus 9 to get 21 then multiply by 24 to get 288. then. you multiply 15 times 9 to get 135 then divide by 2 to get 67.5 for the top triangle. you then add 12 and 9 together to get 21 and multiply that by 15 to find the middle rectangle then you get 315. you then add all of the final values together to get 670.5 square units