We find the value of N₀ since we are provided with initial conditions.
The condition is that, at time t = 0, the amount of substance contains originally 10 grams.
We substitute:
10 = N₀ (e^(-0.1356)*0)
10 = N₀ (e^0)
N₀ = 10
When the substance is in half-life (meaning, the half of the original amount), it contains 5 grams. We solve t in this case.
5 = 10 e^(-0.1356*t)
0.5 = e^(-0.1356*t)
Multiply natural logarithms on both sides to bring down t.
ln(0.5) = -0.1356*t
Hence,
t = -(ln(0.5))/0.1356
t ≈ 5.11 days (ANSWER)
Step-by-step explanation:
I'll do one for you.
Using the formula for turning exponents into radicals
![(b) {}^{ \frac{x}{y} } = \sqrt[y]{b} {}^{x}](https://tex.z-dn.net/?f=%28b%29%20%7B%7D%5E%7B%20%5Cfrac%7Bx%7D%7By%7D%20%7D%20%20%3D%20%20%20%20%5Csqrt%5By%5D%7Bb%7D%20%7B%7D%5E%7Bx%7D%20%20)
where b is the base
This means that the numerator in the exponet form becomes the power under the radical in radical form and
the denominator in exponet form becomes the nth root in radical form.
For example 5,
That becomes in radical form
![\sqrt[5]{5 {}^{ - 3} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7B5%20%7B%7D%5E%7B%20-%203%7D%20%7D%20)
or if you want to write it using positive exponents
![\frac{1}{ \sqrt[5]{5 {}^{3} } }](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B%20%5Csqrt%5B5%5D%7B5%20%7B%7D%5E%7B3%7D%20%7D%20%7D%20)
I'll do one more for you
For example 6,
That becomes in radical form
![\sqrt[3]{11 {}^{4} }](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B11%20%7B%7D%5E%7B4%7D%20%7D%20)
Answer:
-15/16 or -0.9375
Step-by-step explanation:
3/5x=6 +7x
3x=30+35x
3x-35x=30
-32x=30
x= -15/16
Answer: For first page only.
1. 3
2. 1/2
3. -5
Step-by-step explanation:
Let
x = the number of tapers (each coss $1)
y = the number of pillars (each costs $4)
z = the number of jars (each costs $6)
There are 8 candles in each basket, therefore
x + y + z = 8 (1)
The cost per basket is $24, therefore
x + 4y + 6z = 24 (2)
The number of tapers equals the sum of pillars and jars, therefore
x = y + z (3)
Substitute (3) into (1) and into (2).
y + z + y + z = 8
2y + 2z = 8
y + z = 4 (4)
y + z + 4y + 6z = 24
5y + 7z = 24 (5)
From (4), y = 4 -z. Substitute into (5).
5(4 - z) + 7z = 24
2z + 20 = 24
2z = 4
z = 2
y = 4 - z = 4 - 2 = 2
x = y + z = 2 + 2 = 4
Answer: 4 tapers, 2 pillars, 2 jars.
