Answer:
74 feet and 6 feet
Step-by-step explanation:
Mentioned that
The Length of the dog park is = (8x + 2)............(i)
And,
The Width of the park is = (2x -12)..................(ii)
Perimeter = 160 feet
Now here we use the perimeter formula which is
Perimeter is
= 2 (length + width)
160 = 2 (8x + 2 + 2x - 12)
160 = 2 (10x - 10)
160 = 20x - 20
180 = 20x
x = 9
Now put the x value into the equation 1 and equaton 2
For the equaton 1, the length us
= 8x + 2
= 8(9) + 2
= 74 feet
And, the width is
= 2x - 12
= 2(9) - 12
= 18 - 12
= 6 feet
Answer:
a. C(t)=205*(1-0.08)^t
b. t=log_0.92(C(t)/205)=(log_10(C(t)/205))/(log_10(0.92))
c. 16.92 hours
Step-by-step explanation:
Let's say that C(t) is the expression of the amount of caffeine remaining in Darrin's system after t time, hours in this particular case.
a. Then for the first hour the expression would be:
C(t)=205*(1-0.08)
For the second hour:
C(t)=205*(1-0.08)-205*(1-0.08)*(1-0.08)
For the third
C(t)=205*(1-0.08)-205*(1-0.08)*(1-0.08)-205*(1-0.08)*(1-0.08)*(1-0.08)
And so on, for that reason the best way to fit the expression is:
C(t)=205*(1-0.08)^t
2. To find the correct expression for time, we must solve for t the equation recently written above:
Considering that log_b(a)=c and log_b(a)=log_c(a)/log_c(b), then:
t=log_0.92(C(t)/205)
t= (log_10(C(t)/205))/(log_10(0.92))
3. Finally we replace the given value of C(t) into the equation for t:
t= (log_10(50/205))/(log_10(0.92))=16.92
t= 16.92 hours
Now, to change a decimal to fraction, we use "as many zeros on the denominator as there are decimals, and lose the dot", so let's do so.
-83.2 has only 1 decimal, so we'll use one zero,
![\bf -83.\underline{2}\implies \cfrac{-832}{1\underline{0}}\implies \stackrel{simplified}{\cfrac{-416}{5}}](https://tex.z-dn.net/?f=%5Cbf%20-83.%5Cunderline%7B2%7D%5Cimplies%20%5Ccfrac%7B-832%7D%7B1%5Cunderline%7B0%7D%7D%5Cimplies%20%5Cstackrel%7Bsimplified%7D%7B%5Ccfrac%7B-416%7D%7B5%7D%7D)
now if we divide 416 by 5, we end up with a quotient of 83, and a remainder of 1,
The answer would be 15/21