4 1/2 = 9/2
8 1/4 = 33/4
1/3 x 9/2 = 3/2
1/3 x 33/4 = 33/12
Answer:
a. attached graph; zero real: 2
b. p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)
c. the solutions are 2, -3-3i and -3+3i
Step-by-step explanation:
p(x) = x³ + 4x² + 6x - 36
a. Through the graph, we can see that 2 is a real zero of the polynomial p. We can also use the Rational Roots Test.
p(2) = 2³ + 4.2² + 6.2 - 36 = 8 + 16 + 12 - 36 = 0
b. Now, we can use Briott-Ruffini to find the other roots and write p as a product of linear factors.
2 | 1 4 6 -36
1 6 18 0
x² + 6x + 18 = 0
Δ = 6² - 4.1.18 = 36 - 72 = -36 = 36i²
√Δ = 6i
x = -6±6i/2 = 2(-3±3i)/2
x' = -3-3i
x" = -3+3i
p(x) = (x - 2)(x + 3 + 3i)(x + 3 - 3i)
c. the solutions are 2, -3-3i and -3+3i
The question is incomplete, here is the complete question:
Recall that m(t) = m.(1/2)^t/h for radioactive decay, where h is the half-life. Suppose that a 500 g sample of phosphorus-32 decays to 356 g over 7 days. Calculate the half life of the sample.
<u>Answer:</u> The half life of the sample of phosphorus-32 is 
<u>Step-by-step explanation:</u>
The equation used to calculate the half life of the sample is given as:

where,
m(t) = amount of sample after time 't' = 356 g
= initial amount of the sample = 500 g
t = time period = 7 days
h = half life of the sample = ?
Putting values in above equation, we get:

Hence, the half life of the sample of phosphorus-32 is 
Answer:
Step-by-step explanation:
1 12
2 19
3 10
4 28
5 2
Answer:
By comparison of the sides.
Step-by-step explanation:
If triangles are similar, that means their angles are equal and sides are proportional.
If you already have a proportion of two corresponding sides between triangles, then use that proportion and set it equal to a side you already know the measurement to. Hopefully that side is corresponding to your missing measurement, and you can then solve it.