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3 years ago

Write the next 3 numbers in this pattern. Then describe the rule for this pattern in an nth expression.

Mathematics

1 answer:

hram777 [196]3 years ago

8 0

Answer:

An=10^n + 1 is the expression for the nth term.

Next three terms:

100001

1000001

10000001

Step-by-step explanation:

The number ot 0's imcrease between the two 1's starting at no zeros, 1 zero, two zeros, and so on...

So the next terms are 100001, 1000001, 10000001 and that's without finding the formula.

Now let's find the formula:

A1=11=10+1

A2=101=100+1

A3=1001=1000+1

Notice we have increasing powers of 10 and then just adding 1.

A1=10^1 +1

A2=10^2 +1

A3=10^3 +1

....

An=10^n +1

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Solve the following equation |2x+3|+|x-2|=6x

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Answer:

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3 years ago

What is the surface area of a cylinder that is 5 centimeters high and has a diameter of 1.5 centimeters?

olchik [2.2K]

The surface area of cylinder is 8.625 $\pi$ $cm^{2}$ , if the cylinder has 5 centimeters high and 1.5 cm of diameter.

Step-by-step explanation:

The given is,

Cylinder has a 5 centimeters height

Diameter of the cylinder is 1.5 centimeters

Step:1

Formula for the surface area of cylinder is,

$A=2\pi r h + 2\pi r^{2}$ ......................................(1)

Where,

h - Height of cylinder

r - Radius of cylinder

From the values of h and r,

$r=\frac{d}{2}$

= $\frac{1.5}{2}$

r = 0.75 cm

From the formula,

= ( 2 × $\pi$ × 0.75 × 5 ) + ( 2 × $\pi$ × $0.75^{2}$ )

= ( 7.5 $\pi$ ) + ( 1.125 $\pi$ )

A = 8.625 $\pi$ $cm^{2}$

Result:

The surface area of cylinder is 8.625 $\pi$ $cm^{2}$ , if the cylinder has 5 centimeters high and 1.5 cm of diameter.

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4 years ago

Simplify..............

Neporo4naja [7]

(2x² + 7x + 10) - (x² + 2x - 9) =
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3 years ago

Read 2 more answers

Which expression is equivalent to (16 x Superscript 8 Baseline y Superscript negative 12 Baseline) Superscript one-half?.

loris [4]

To solve the problem we must know the Basic Rules of Exponentiation.

<h2>Basic Rules of Exponentiation</h2>

$x^ax^b = x^{(a+b)}$
$\dfrac{x^a}{x^b} = x^{(a-b)}$
$(a^a)^b =x^{(a\times b)}$
$(xy)^a = x^ay^a$

$x^{\frac{3}{4}} = \sqrt[4]{x^3}= (\sqrt[3]{x})^4$

The solution of the expression is $\dfrac{4x^4}{y^6}$ .

<h2>Explanation</h2>

Given to us

$(16x^8y^{12})^{\frac{1}{2}}$

Solution

We know that 16 can be reduced to $2^4$ ,

$=(2^4x^8y^{12})^{\frac{1}{2}}$

Using identity $(xy)^a = x^ay^a$ ,

$=(2^4)^{\frac{1}{2}}(x^8)^{\frac{1}{2}}(y^{12})^{\frac{1}{2}}$

Using identity $(a^a)^b =x^{(a\times b)}$ ,

$=(2^{4\times \frac{1}{2}})\ (x^{8\times\frac{1}{2}})\ (y^{12\times{\frac{1}{2}}})$

Solving further

$=2^2x^4y^{-6}$

Using identity $\dfrac{x^a}{x^b} = x^{(a-b)}$ ,

$=\dfrac{2^2x^4}{y^6}$

$=\dfrac{4x^4}{y^6}$

Hence, the solution of the expression is $\dfrac{4x^4}{y^6}$ .

Learn more about Exponentiation:

brainly.com/question/2193820

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2 years ago

The sum of two numbers a and b is equal to c. The number line below shows the values of a and c. Shat is the value of b?

Volgvan

Answer:

HIS SGSEIJGR

Step-by-step explanation:

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3 years ago