Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement.

Express 1/10 cm as a fraction of 3 metres

Liula [17]

Answer:

1/3000

Step-by-step explanation:

3 meters to centimeters:

3 × 100 = 300

= 1/10 ÷ 300

= 1/10/300

= 1/(10×300)

= 1/3000

7 0

2 years ago

Use any of the methods to determine whether the series converges or diverges. Give reasons for your answer.

Aleks [24]

Answer:

It means $\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$ also converges.

Step-by-step explanation:

The actual Series is::

$\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$

The method we are going to use is comparison method:

According to comparison method, we have:

$\sum_{n=1}^{inf}a_n\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n$

If series one converges, the second converges and if second diverges series, one diverges

Now Simplify the given series:

Taking"n^2"common from numerator and "n^6"from denominator.

$=\frac{n^2[7-\frac{4}{n}+\frac{3}{n^2}]}{n^6[\frac{12}{n^6}+2]} \\\\=\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{n^4[\frac{12}{n^6}+2]}$

$\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\ \ \ \ \ \ \ \ \sum_{n=1}^{inf}b_n=\sum_{n=1}^{inf} \frac{1}{n^4}$

Now:

$\sum_{n=1}^{inf}a_n=\sum_{n=1}^{inf}\frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\ \\\lim_{n \to \infty} a_n = \lim_{n \to \infty} \frac{[7-\frac{4}{n}+\frac{3}{n^2}]}{[\frac{12}{n^6}+2]}\\=\frac{7-\frac{4}{inf}+\frac{3}{inf}}{\frac{12}{inf}+2}\\\\=\frac{7}{2}$

So a_n is finite, so it converges.

Similarly b_n converges according to p-test.

P-test:

General form:

$\sum_{n=1}^{inf}\frac{1}{n^p}$

if p>1 then series converges. In oue case we have:

$\sum_{n=1}^{inf}b_n=\frac{1}{n^4}$

p=4 >1, so b_n also converges.

According to comparison test if both series converges, the final series also converges.

It means $\sum_{n=1}^\inf} = \frac{7n^2-4n+3}{12+2n^6}$ also converges.

5 0

3 years ago

How much greater is the area of a square with a side length of 9 inches than the area of a circle with a radius of 3 inches?

fredd [130]

The area of the square is 81 sq in, and the area of the circule is (3.14)(3 in)^2, or approx 3.14(9) sq in, or approx 28.27 sq in.

Subtract: 81 sq in - 28.27 sq in = approx. 52.73 sq in.

The difference is 52.73 sq in; the square is larger, the circle smaller.

7 0

2 years ago

PLS HELP ME GUYS ITS MY LAST QUESTION IN GEOMETRY

aliina [53]

Answer:

Example = ( 12, 1 )

Step-by-step explanation:

There are many possible solutions to this equation, and all you would have to do to determine the ordered pair, is satisfy the following criteria -

$x - 6y = 6,\\- 6y = - x + 6,\\y = 1 / 6x - 1$

Take a look at a graph of the line y = 1 / 6x - 1. Any ordered pair that lies on this line is a solution to the equation. The " criteria " is that the ordered pair must lie on this line. Let me give you an example, ( 12, 1 ).

Hope that helps!

7 0

2 years ago

Which expression shows how to find the quotient of 4.8÷2?

xenn [34]

Answer:

[A] (4 ÷ 2)+(0.8 ÷ 2)

Step-by-step explanation:

Divide the 2 into each digit, which must be in the same spot it was before:

Knowing that 8 in 4.8 ⇒ 0.8

Thus, you can infer that [B] is wrong

You also infer that [D] and [C] is wrong because 4 is a whole number.

Thus, that left us with [A] 4 ÷ 2+0.8 ÷ 2 which shows the quotient of 4.8 ÷ 2

Hence, [A] 4 ÷ 2+0.8 ÷ 2 is the answer.

~Learn with Lenvy~

5 0

2 years ago

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