The measure of the angle is 165 degrees.
Answer:
X= 2 and y = 3
Step-by-step explanation:
![D)u=\mleft_{}](https://tex.z-dn.net/?f=D%29u%3D%5Cmleft%3C-4%2C-7%5Cmright%3E_%7B%7D)
1) We can find the magnitude of a vector(a.k.a. the norm) of a vector and the direction, by making use of the following formulas:
![\begin{gathered} \mleft\|v\mright\|=\sqrt[]{a^2+b^2} \\ \tan (\theta)=\frac{b}{a} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cmleft%5C%7Cv%5Cmright%5C%7C%3D%5Csqrt%5B%5D%7Ba%5E2%2Bb%5E2%7D%20%5C%5C%20%5Ctan%20%28%5Ctheta%29%3D%5Cfrac%7Bb%7D%7Ba%7D%20%5Cend%7Bgathered%7D)
2) In this question, the magnitude and the direction of that vector have been given to us. So, let's do the other way around to identify which one has this magnitude and direction.
![\begin{gathered} \mleft\|u\mright\|=\sqrt[]{(-4)^2+(-7)^2}=\sqrt[]{16+49}=\sqrt[]{65} \\ \tan (\theta)=\frac{-4}{-7} \\ (\theta)=\tan ^{-1}(\frac{-4}{-7}) \\ D=\tan ^{-1}(\frac{-4}{-7})-180 \\ D=-119.74+360 \\ D=240.2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cmleft%5C%7Cu%5Cmright%5C%7C%3D%5Csqrt%5B%5D%7B%28-4%29%5E2%2B%28-7%29%5E2%7D%3D%5Csqrt%5B%5D%7B16%2B49%7D%3D%5Csqrt%5B%5D%7B65%7D%20%5C%5C%20%5Ctan%20%28%5Ctheta%29%3D%5Cfrac%7B-4%7D%7B-7%7D%20%5C%5C%20%28%5Ctheta%29%3D%5Ctan%20%5E%7B-1%7D%28%5Cfrac%7B-4%7D%7B-7%7D%29%20%5C%5C%20D%3D%5Ctan%20%5E%7B-1%7D%28%5Cfrac%7B-4%7D%7B-7%7D%29-180%20%5C%5C%20D%3D-119.74%2B360%20%5C%5C%20D%3D240.2%20%5Cend%7Bgathered%7D)
Note that since we want a positive value, we need to add 360 degrees.
Answer:
A
Step-by-step explanation:
clearly, the equation has to allow t=0, and for that point we need to get 100% (of carbon-14) as result.
and so we also see, that the function calculates the % of the remaining carbon-14.
so, we need the desired outcome 60(%),
because 60 = 100 - 40.
and again, we need a function that shows t=0.
the only answer option fulfilling both criteria is A.
B divides in the exponent by t, so t=0 is not in the domain of the function.
and C and D aim for the wrong remaining percentage.
Answer:
C. xy²
Step-by-step explanation:
You have to add the exponents:
(xy) exponent is 1
(x) exponent is 1
Combine the (x):
xy²