Answer:
about 5.84 mg
Step-by-step explanation:
The amount remaining after t days can be written as ...
remaining = initialAmount · (1/2)^(t/(halfLife))
Filling in the given numbers, you have
remaining = (40 mg)·(1/2)^(180/64.84) ≈ 5.84 mg
About 5.84 mg would be left after 180 days.
Check the picture below.
so let's use the law of sines then
![\textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1.9}{sin(Z)}~~ = ~~\cfrac{XZ}{sin(Y)}\implies \cfrac{1.9}{sin(89^o)}~~ = ~~\cfrac{XZ}{sin(70^o)}\implies \cfrac{1.9\cdot sin(70^o)}{sin(89^o)}=XZ \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Ctextit%7BLaw%20of%20sines%7D%20%5C%5C%5C%5C%20%5Ccfrac%7Bsin%28%5Cmeasuredangle%20A%29%7D%7Ba%7D%3D%5Ccfrac%7Bsin%28%5Cmeasuredangle%20B%29%7D%7Bb%7D%3D%5Ccfrac%7Bsin%28%5Cmeasuredangle%20C%29%7D%7Bc%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ccfrac%7B1.9%7D%7Bsin%28Z%29%7D~~%20%3D%20~~%5Ccfrac%7BXZ%7D%7Bsin%28Y%29%7D%5Cimplies%20%5Ccfrac%7B1.9%7D%7Bsin%2889%5Eo%29%7D~~%20%3D%20~~%5Ccfrac%7BXZ%7D%7Bsin%2870%5Eo%29%7D%5Cimplies%20%5Ccfrac%7B1.9%5Ccdot%20sin%2870%5Eo%29%7D%7Bsin%2889%5Eo%29%7D%3DXZ%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
quick observation, the picture of the triangle is very misleading, since those angles as drawn are not good representers of the angles values.
16<2(3x-1)<28 divide all terms by 2
8<3x-1<14 add 1 to all terms
9<3x<15 divide all terms by 3
3<x<5
x=(3,5) in interval notation
On a number line, it would be a line segment from 3 to 5 with open circles at 3 and 5.
On a coordinate system graph, it would be an infinitely high shaded plane between the vertical lines x=3 and x=5
Answer:
x =42
Step-by-step explanation:
x and 138 are same side interior angles. Same side interior angles are supplementary when the lines are parallel
x+138 = 180
x = 180-138
x =42
