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iVinArrow [24]
3 years ago
8

How to compare 2 5/9 and 21/3

Mathematics
2 answers:
max2010maxim [7]3 years ago
5 0

Answer:

2 5/9 is less than 21/3;  2 5/9 < 21/3

Step-by-step explanation:

<u>Step 1:  Convert 2 5/9 into an improper fraction</u>

2 5/9 = 2 * 9/9 + 5/9 = 18/9 + 5/9 = 23/9

<u>Step 2:  Convert 21/3 so the denominator is 9</u>

21*3 / 3*3 = 63/9

<u>Step 3:  Compare</u>

<em>23/9 < 63/9</em>

<em />

Answer:  2 5/9 is less than 21/3;  2 5/9 < 21/3

Troyanec [42]3 years ago
4 0

Answer:

21/3 > 2 5/9

Step-by-step explanation:

2 × 9 = 18

18 + 5 = 23 which makes the fraction 23/9

23/9 × 3 = 69/27

21/3 × 9 = 189/27

189/27 > 69/27 or 21/3 > 2 5/9

Or Simpler:

21/3 = 7

7 > 2 5/9

So, 21/3 > 2 5/9

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3 years ago
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Answer:

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Step-by-step explanation:

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3 years ago
What is the antiderivative of sin^2(x)cos^2(x)?
marin [14]

Answer:

\frac{x}{8}-\frac{\sin(4x)}{32}+C

Step-by-step explanation:

[Most of the work here comes from manipulating the trig to make the term (integrand) integrable.]

Recall that we can express the squared trig functions in terms of cos(2x). That is,

\cos(2x)=2\cos^2x-1 \\ \cos(2x)=1 - 2\sin^2x.

And so inverting these,

\cos^2x=\frac{1}{2} (1+\cos2x) \\ \sin^2x=\frac{1}{2} (1-\cos2x).

Multiply them together to obtain an equivalent expression for sin^2(x)cos^2(x) in terms of cos(2x).

\sin^2x \cdot \cos^2x =\frac{1}{2} (1-\cos2x) \cdot \frac{1}{2} (1+\cos2x) = \frac{1}{4}(1-\cos^2(2x)).

Notice we have cos^2(2x) in the integrand now. We've made it worse! Let's try plugging back in to the first identity for cos^2(2x).

\cos(2x)=2\cos^2x-1 \Rightarrow \cos(4x)=2\cos^2(2x)-1 \Rightarrow \cos^2(2x) = \frac{1}{2}(1+\cos(4x))

So then,

\sin^2x \cdot \cos^2x = \frac{1}{4}(1-\cos^2(2x)) = \frac{1}{4}(1-\frac{1}{2}(1+\cos(4x))) = \frac{1}{4}(1-\frac{1}{2}-\frac{1}{2}\cos(4x))=\frac{1}{8}(1-\cos(4x)).

This is now integrable (phew),

\int \sin^2x\cos^2x \ dx = \int \frac{1}{8}(1-\cos(4x)) \ dx = \frac{1}{8} \int (1-\cos(4x)) \ dx = \frac{1}{8}(x-\frac{1}{4}\sin(4x))+C.

7 0
3 years ago
Help please tap the picture above
Wewaii [24]

Answer:

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Step-by-step explanation:

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To find your percentage, look into the parenthesis to see the decimal. We see that it's 0.15, but that's not a percentage yet, so you have to multiply it by 100. Or, moving your decimal two times to the right. Therefore, r=15%.

Now to find what the function will equal when t=3, simply plug 3 for t. I've always used a calculator for this so I'm not going to write it out (sorry). Your result should be 4.9 (this is already rounded to the nearest tenth for you).

7 0
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Monica [59]

Answer:

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Step-by-step explanation:

The formula is A = P( 1 + r/2)^2n so we have:

50,000 = P(1 + 0.07/2)^(6*2)

50000 = P * 1.035^12

P = 50000/ 1.035^12

= $33,090 to the nearest dollar.

4 0
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