When we look at this thing for the first time, it looks like it's going to be a dog of a bear to solve, because 'q' is buried inside a squared term and a cubed term.
But this is why it's so important to learn that in math, you DON't immediately ignite your hair and go running around in circles as soon as you see the problem. The first thing you have to do <u>every</u> time is sit still, look at the problem, breathe air, and switch your brain into the 'ON' position.
Look at that big ugly fraction in the equation. Can it be simplified ? You betcha it can ! The quantity (q+r) is a factor of the numerator and denominator, so we can do some canceling.
Divide the top and the bottom of the fraction by (q+r)², and then the problem says . . .
<em>p = (q+r)/12 + 4r</em>
which is MUCH easier to unravel and solve for 'q' . Let's do this !
p = (q+r)/12 + 4r
Subtract (q+r)/12 from each side . . . p - (q+r)/12 = 4r
Subtract 'p' from each side . . . -(q+r)/12 = 4r - p
Multiply each side by -1 . . . (q+r)/12 = p - 4r
Multiply each side by 12 . . . (q+r) = 12p - 48r
Subtract 'r' from each side . . . <em>q = 12p - 49r</em>
240(v+2.5)=1300-240v
240v+600=1300-240v
480v=1900
v=95/24
v-2.5=v-5/2
95/24-60/24=35/24
So the faster group travels at 95/24 mph (≈3.96 mph) and the slower group travels at 35/24 mph (≈1.46mph)
check...
240(95/24)=950 miles from the origin...
1300-240(35/24)=950 miles from the origin...
Answser:
72 bars
Step-by-step explanation:
Thy are .25 each
.25 divided by 18.00 = 72
Hello there! A half-life is basically a decay of 50%. We will find the amount left after one day by exponential decay. The formula for exponential decay is A(1 - r)^t, where A = initial amount, r = rate (in decimal form), and t = time (or in this case, amount of half lives). The half-life is 6 hours and 24 goes into 6 four times. That's 4 half lives. Let's start by subtract 50% (0.5) from 1. 1 - 0.5 is 0.5. Now, we will use 0.5 and raise it to the 4th power, because the 4th power represents 4 half lives. 0.5^4 is 0.0625. Leave this number on the calculator. Do not round. Multiply that number by 448 to find the amount left. When you do, you get 28. There. 28 grams will be left after 24 hours.
Step-by-step explanation:
option C is the answer.
hope it helps
