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3 years ago

On the set of axes below, Geoff drew rectangle ABCD. He will transform the rectangle by

Mathematics

1 answer:

Georgia [21]3 years ago

3 0

Answer:

C, exactly 28 square units

Step-by-step explanation:

This is because it's a translation, not a transformation. The size won't change, and therefore the area won't change. Just the position.

Since the area is 28 and it doesn't change, the answer is C.

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Numbers that are close in value to the actual numbers

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4 years ago

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Aleksandr [31]

Circumference of a circle - derivation

This page describes how to derive the formula for the circumference of a circle.

Recall that the definition of pi (π) is the circumference c of any circle divided by its diameter d. Put as an equation, pi is defined as

π

=

c

d

Rearranging this to solve for c we get

c

=

π

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The diameter of a circle is twice its radius, so substituting 2r for d

c

=

2

π

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If you know the area

Recall that the area of a circle is given by

area

=

π

r

2

Solving this for r

r

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=

a

π

So

r

=

√

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The circumference c of a circle is

c

=

2

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r

5 0

3 years ago

Read 2 more answers

Identify whether the series sigma notation infinity i=1 15(4)^i-1 is a convergent or divergent geometric series and find the sum

const2013 [10]

Answer: The correct option is

(d) This is a divergent geometric series. The sum cannot be found.

Step-by-step explanation: The given infinite geometric series is

$S=\sum_{i=1}^{\infty}15(4)^{i-1}.$

We are to identify whether the given geometric series is convergent or divergent. If convergent, we are to find the sum of the series.

We have the D' Alembert's ratio test, states as follows:

Let, $\sum_{i=1}^{\infty}a_i$ is an infinite series, with complex coefficients $a_i$ and we consider the following limit:

$L=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}.$

Then, the series will be convergent if L < 1 and divergent if L > 1.

For the given series, we have

$a_i=15(4)^{i-1},\\\\a_{i+1}=15(4)^i.$

So, the limit is given by

$L\\\\\\=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i-1}}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i}4^{-1}}\\\\\\=\dfrac{1}{4^{-1}}\\\\=4>1.$

Therefore, L >1, and so the given series is divergent and hence we cannot find the sum.

Thuds, (d) is the correct option.

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4 years ago

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Tamiku [17]

F(X)=(4)12+x6.50
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3 years ago