First step, write down the expression on one line, using necessary parentheses.
(2^8*5^(-5)*19^0)^(-2) * (5^(-2)/2^3)^4 *2^28
The apply the PEMDAS rule to simplify according to priority:
1. Parentheses
2. Exponentiation
3. Multiplication and Division (left to right)
4. Addition and Subtraction (left to right)
For exponentiation, it is convenient to convert all negative exponents to positive by taking the reciprocal, for example,
a^(-2)= 1/(a^2)
So
(2^8*5^(-5)*19^0)^(-2) * (5^(-2)/2^3)^4 *2^28
=1/[(2^8*5^(-5)*19^0)^(2)] * (1/[5^2*2^3])^4 *2^28
=5^5/[(2^8*19^0)^(2)] * (1/[5^2*2^3])^4 *2^28
Remember positive numbers raised to power zero equals 1, e.g.
a^0=a for any number a.
so 19^0=1
=5^10/[(2^8)^(2)] * (1/[5^2*2^3])^4 *2^28
Now, powers raised to a power equals the product of the powers, e.g.
(2^8)^2=2^16, (5^2)^4=5^8, (2^3)^4=2^12...
continuing,
=5^10/[2^16] * 1/[5^8*2^12] *2^28
When we have exponents to the same base in the denominator and numerator, we subtract exponents, e.g.
5^5/5^8=5^(5-8)=5^(-3), 2^28/[2^16*2^12]=2^(28-16-12)=2^0=1
so we get rid of many terms this way
continuing
=5^(10-8)*2^(28-16-12)
=5^2*2^0
=25*1
=25
Answer
-9/64
Step-by-step explanation:
Exponential decay is a very common process especially when we are talking about radioactive materials. So, there is already a common formula for this type of behavior which is written below:
A = Pe^-rt
where
A is the amount left after time t
P is the initial amount at t=0
r is the rate
Substituting the values,
A = (780 g)(e^-0.163*16)
A = 57.5 g
Answer:
C
Step-by-step explanation:
A models an exponentially increasing function.
B models an exponentially decreasing function.
C models a "bell" curve, similar to the one shown.
D models a "logistic" function, an s-shaped curve that smoothly transitions between two horizontal asymptotes.
Answer:
Let the speed of the train be x km/h.
Case 1:
Distance = 288 km
Speed = x km/h
Time = Distance/Speed
= 288/x h
Case 2:
Distance = 288 km
Speed = (x+4) km/h
Time = 288/x + 4 h
Since 288/x > 288/x + 4
288/x - 288/x+4 = 1
288[1/x - 1/x+4 ] = 1
[ x + 4 - x / x(x + 4) ] = 1/288
[4 / x^2 + 4x ] = 1/288
x^2 + 4x = 1152
x^2 + 4x - 1152 = 0
x^2 + 36x - 32x - 1152 = 0
x(x + 36) - 32(x + 36) = 0
(x + 36)(x - 32) = 0
x + 36 = 0 , x - 32 = 0
x = -36 , x = 32
x = -36 , rejected since speed cannot be negative.
Therefore , speed of the train = 32 km/h
