Answer:
204 inches
Step-by-step explanation:
First, change the 5yd2ft to be just feet.
1 yard = 3 feet
5 yd × 3ft/yd = 15 ft
15 ft + 2ft = 17ft
Next, change to inches.
1 ft = 12 inches
17ft × 12in/ft = 204 in
5 yds 2 ft = 204 in
If we want to find when the population of species A will be equal to the population of species B, we need to see when the two equations for the population of each species are equal, ie. equate them and solve for t. Thus:
2000e^(0.05t) = 5000e^(0.02t)
(2/5)e^(0.05t) = e^(0.02t) (Divide each side by 5000)
2/5 = e^(0.02t) / e^(0.05t) (Divide each side by e^(0.05t))
2/5 = e^(-0.03t) (use: e^a / e^b = e^(a - b))
ln(2/5) = -0.03t (use: if b = a^c, then loga(b) = c )
t = ln(2/5) / -0.03 (Divide each side by -0.03)
= 30.54 (to two decimal places)
Therefor, the population of species A will be equal to the population of species B after 30.54 years.
I wasn't entirely sure about the rounding requirements so I've left it rounded to two decimal places.
Answer:
79
Step-by-step explanation:
the other side is also 79 and they are equal
Hello from MrBillDoesMath!
Answer:
- 8064 x^5 y^5
Discussion:
The binomial theorem gives us the expansion of (a + b) ^n :
(a + b ) ^n
= a^n + na^(n-1)b + (n(n-1)/ 2!) a^(n-2)b^2 +....
In our case, taking the 6th term above, setting a = 2x, b = -y, and n = 10 gives
( (10*9*8*7*6)/ (5 *4*3*2*1) ) * (2x)^5 (-y)^5r
= - 8064 x^5 y^5
Thank you,
MrB
