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3 years ago

The difference of the squares of twenty and thirteen

Mathematics

1 answer:

sineoko [7]3 years ago

5 0

20 squared = 400
13 squared = 169
400
-139

(231)

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(x^2-1)(4x^3-3x^2+5)

emmainna [20.7K]

Anwser: 4x^5-3x^4-4x^3+8x^2-5

Step-by-step explanation:

yes

6 0

2 years ago

How many ml of a 20% acid mixture and a 80% acid mixture should be mixed to get 120ml of a 35% acid mixture?

shutvik [7]

Answer:

Volume of Mixture A =90 ml

Volume of Mixture B =30 ml

Step-by-step explanation:

Let say, Mixture A + Mixture B = Mixture C

Volume of Mixture A is x

Volume of Mixture B is y

So, Volume of Mixture C is x+y = 120 ml

Now, Acid contain in Mixture A is 20% =0.2x

Acid contain in Mixture B is 80% =0.8y

Also, Acid contain in Mixture C is 35% =(0.35)(x+y) = 0.35×120=42

Now, we know that,

Acid contain of Mixture A + Acid contain of Mixture B=Acid contain of Mixture C

∴ 0.2x+0.8y=42

∴ 2x+8y=420

We get two linear equations

2x+8y=420 and x+y = 120

Solving above equation...

∴ x=120-y

Replacing x value in 2x+8y=420

∴ 2(120-y)+8y=420

∴ 240-2y+8y=420

∴ 6y=180

∴ y=30

Replacing y value in any equation

∴ x=120-y=120-30=90

∴ x=90

Thus,

Volume of Mixture A is x=90 ml

Volume of Mixture B is y=30 ml

3 0

4 years ago

What is the exact circumference of the circle?

fredd [130]

Data:

Formula: diameter = 2*radius

Formula: (Circle length)
 $C = 2* \pi *r$

Solving: Using the data
diameter = 2*radius
20 = 2*r
2r = 20
$r = \frac{20}{2}$
$\boxed{r = 10\:ft}$

Now, replace in the circumference length formula
 $C = 2 \pi *r$
$C = 2 \pi *10$
$\boxed{\boxed{C = 20 \pi \:ft}}\end{array}}\qquad\quad\checkmark$

Answer:
The exact circumference of the circle is $20 \pi \:ft$

7 0

3 years ago

. Evaluate the series 1 + 0.1 + 0.01 + . . .

EastWind [94]

We can employ a simple repeated decimal trick:

$x=1.111\ldots$

$0.1x=0.111\ldots$

$\implies x-0.1x=1\implies0.9x=1\implies x=\dfrac1{0.9}=\dfrac{10}9$

###

Alternatively, we can compute the partial sum of the series.

$\displaystyle S_n=\sum_{k=0}^n\dfrac1{10^k}$

$S_n=1+0.1+0.01+\cdots+\dfrac1{10^n}$

$0.1S_n=0.1+0.01+0.001+\cdots+\dfrac1{10^{n+1}}$

$\implies S_n-0.1S_n=0.9S_n=1-\dfrac1{10^{n+1}}$

$\implies S_n=\dfrac{10}9-\dfrac9{10^n}$

As $n\to\infty$ , the second term vanishes and we're left with $\dfrac{10}9$ . Notice that this is really just a more formal version of the earlier trick.

6 0

3 years ago

Read 2 more answers

Which function is most likely graphed on the coordinate plane below?

Ber [7]

Answer:

2nd one

Step-by-step explanation:

6 0

3 years ago