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Jlenok [28]
3 years ago
11

Find the greatest common factor of the following monomials: 20a3 and 8a2

Mathematics
1 answer:
dimulka [17.4K]3 years ago
5 0

GCF of given monomials are 4a^2

<em><u>Solution:</u></em>

<em><u>Given that we have to find the greatest common factor</u></em>

Given monomials are:

20a^3 \text{ and } 8a^2

When we find all the factors of two or more numbers, and some factors are the same, then the largest of those common factors is the Greatest Common Factor

Let us first find the GCF of 20 and 8 and then find GCF of variables and then multiply them together

<em><u>GCF of 20 and 8:</u></em>

The factors of 8 are: 1, 2, 4, 8

The factors of 20 are: 1, 2, 4, 5, 10, 20

Then the greatest common factor is 4

GCF\ of\ a^3 \text{ and } a^2\\\\a^3 = a^2 \times a\\\\a^2 = a^2

Thus GCF is a^2

<em><u>Therefore GCF of monomials are:</u></em>

\text{GCF of } 20a^3 \text{ and } 8a^2 = 4 \times a^2 = 4a^2

Thus GCF of given monomials are 4a^2

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For f(x)=4sin(x2) between x=0 and x=3, find the coordinates of all intercepts, critical points, and inflection points to two dec
telo118 [61]

Answer:

Intercepts:

x = 0, y = 0

x = 1.77, y = 0

x = 2.51, y = 0

Critical points:

x = 1.25, y = 4

x = 2.17 , y = -4

x = 2.8, y = 4

Inflection points:

x = 0.81, y = 2.44

x = 1.81, y = -0.54

x = 2.52, y = 0.27

Step-by-step explanation:

We can find the intercept by setting f(x) = 0

4sin(x^2) = 0

sin(x^2) = 0

x^2 = n\pi where n = 0, 1, 2,3, 4, 5,...

x = \sqrt(n\pi)

Since we are restricting x between 0 and 3 we can stop at n = 2

So the function f(x) intercepts at y = 0 and x:

x = 0

x = 1.77

x = 2.51

The critical points occur at the first derivative = 0

f^{'}(x) = 4cos(x^2)2x = 8xcos(x^2) = 0

xcos(x^2) = 0

x = 0 or

cos(x^2) = 0

x^2 = \frac{\pi}{2} + n\pi where n = 0, 1, 2, 3

x = \sqrt{\pi(n+1/2)}

Since we are restricting x between 0 and 3 we can stop at n =  2

So our critical points are at

x = 1.25, y = f(1.25) = 4sin(1.25^2) = 4

x = 2.17 , y = f(2.17) = 4sin(2.17^2) = -4

x = 2.8, y = f(2.8) = 4sin(2.8^2) = 4

For the inflection point, we can take the 2nd derivative and set it to 0

f^[''}(x) = 8(cos(x^2) - xsin(x^2)2x) = 8cos(x^2) - 16x^2sin(x^2) = 0

cos(x^2) = 2x^2sin(x^2)

tan(x^2) = \frac{1}{2x^2}

We can solve this numerically to get the inflection points are at

x = 0.81, y = f(0.81) = 4sin(0.81^2) = 2.44

x = 1.81, y = f(1.81) = 4sin(1.81^2) = -0.54

x = 2.52, y = f(2.52) = 4sin(2.52^2) = 0.27

3 0
3 years ago
If x represents an even number, which expression represents an odd number?
Sauron [17]
Test the choices !
Pick an even number, and see what each choice does to it.

Let's start with, say,  6 .
We'll try each choice, and see which one produces an odd number:

a).  6 to the 2nd power. . . . . .  6 x 6 = 36.  That's not an odd number.

b).  6 + 3  =  9  This could be it.  9 is odd. We'll save this one.

c).  3·6 = 18.  That's not an odd number.

d).  6/3 = 2.  That's not an odd number.

The only one that gave us an odd number is (b).


3 0
3 years ago
Which of the following is equivalent to 0.000001?
Sergio039 [100]
You didn’t post the options but that is also equal to 1.0 x 10^-6
7 0
2 years ago
Number 3 plz I don't get when they say dimensions
STatiana [176]
Well 1 cm = 2ft, so it might be asking the scale?
7 0
3 years ago
Read 2 more answers
A farmer sells 7.8 kilograms of pears and apples at the farmer's market. 3/4 of this weight is pears, and the rest is apples. Ho
tangare [24]

Answer:

He sold 1.95 kilograms of apples.

Step-by-step explanation:

First we find out what 3/4 of 7.8 is.

3/4 of 7.8 = 5.85

Next we subtract 7.8 by 5.85

7.8 - 5.85 = 1.95

So, the answer is 1.95

Hope this helps! :)

4 0
2 years ago
Read 2 more answers
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