The factors of 50a³ are 1, 2, 5, 10, 25, 50,
and their products with a, a² and a³ .
The factors of 10a² are 1, 2, 5, 10,
and their products with 'a' and a² .
Their common factors are 1, 2, 5, 10,
and their products with 'a' and a².
Their greatest common factor is 10a² .
(Another way to spot it, easily, is to remember this helpful factoid:
If the smaller number is a factor of the larger number,
then the smaller number is their greatest common factor.
Using the greatest common factor, then . . .
50a³ + 10a² = 10a²(5a + 1) .
Answer:
1 mile
----------
5280 feet
Step-by-step explanation:
There are 5,280 feet in one mile, so to convert it, multiply by ^
Composite functions is a way of substituting one function into another. The value of the composite function f(g(1)) is 1
<h3>Composite functions</h3>
Composite functions is a way of substituting one function into another.
Given the function expressed as:
y = 3√x + 1
g(1) from the mapping is 0
Substitute g(1) = 0 into the given function to have:
f(g(1)) = 3√0 .+ 1
f(g(1)) =0 + 1
f(g(1)) = 1
Hence the value of the composite function f(g(1)) is 1
Learn more on composite function here: brainly.com/question/10687170
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Given that we know the initial mass of Iodine and its half-life, we want to see how much will remain after 40 days.
After 40 days, 244.17 grams of Iodine will remain.
<h3 /><h3>The half-life of materials and how to use it:</h3>
The half-life of a material is the time it takes for that amount of material to reduce to its half.
We can model the amount of Iodine as:
A(t) = A*e^{k*t}
- Where A is the initial amount, in this case, 7800g.
- k is a constant that depends on the half-life.
- t is the time in days.
Replacing what we know, we get:
A(t) = 7800g*e^{k*t}
Now we use the fact that the half-life is 8 days, this means that:
e^{k*8} = 1/2
ln(e^{k*8}) = ln(1/2)
k*8 = ln(1/2)
k = ln(1/2)/8 = -0.0866
Then the function is:
A(t) = 7800g*e^{-0.0866*t}
So now we just need to evaluate this in t = 40.
A(40) = 7800g*e^{-0.0866*40} = 244.17g
So, after 40 days, 244.17 grams of Iodine will remain.
If you want to learn more about half-life and decays, you can read:
brainly.com/question/11152793
Answer:
76017.69 mm²
631000 mm³
295045.04 mm³
Step-by-step explanation:
Surface area = bh + 2ls + lb
Since the sides of the triangular prism are equal (equilateral triangle) = 60 mm each
Height = 405 mm
The surface area of triangular = 76017.69 mm
The volume of triangular prism :
1/2 * base * height * length
Volume = 631000 mm³
If amount of chocolate inside = 335954.96 mm3
Empty space =
Volume of triangular prism - amount of chocolate inside
631000 - 335954.96
= 295045.04 mm³
