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4 years ago

In the diagram, point O is the center of the circle and AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E. If m∠AOB = 90° and

Mathematics

1 answer:

Romashka [77]4 years ago

7 0

m∠CED = 1/2(m∠AOB + m∠COD) = 1/2(90° + 16°) = 1/2(106°) = 53°

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What is the greatest common factor you can use to divide the numerator and denominator of the fraction 28/32?

Anastaziya [24]

The greatest common factor is 4.

28/32 / 4 = 7/8

7 0

3 years ago

Can someone help me with this work please

tangare [24]

Answer:

-See below

Step-by.step explanation:

In the first column, on the left of the vertical line, you place the first digit of the number , then on the second row on you place the second digit.

So on the second row you have the entries:

1 | 2 2 4 representing 12, 12 and 14.

On the first row the 2 0ne digit numbers 3 and 8 are represented by

0 | 3 8.

Similarly the last 2 rows are:

2 | 0 1 3 6

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3 years ago

Which expression has a value of 15 when n = 7? 43 minus 5 n 3 n minus 5 6 n minus 28 19 minus StartFraction 28 Over n EndFractio

andrey2020 [161]

Answer:

$19-\dfrac{28}{n}$ is the expression with value of 15 when n = 7.

Step-by-step explanation:

To find the expression whose value is 15, substitute the value of n = 7 in each given expression.

Expression 1:

$43-5n$

Substituting the value of n,

$43-5\left(7\right)$

Simplifying,

$43-35=8$

Since the value of the expression is 8 which is not equal 15.

Hence expression $43-5n$ does not have value of 15 when n = 7.

Expression 2:

$3n-5$

Substituting the value of n,

$3\left(7\right)-5$

Simplifying,

$21-5=16$

Since the value of the expression is 16 which is not equal 15.

Hence expression $3n-5$ does not have value of 15 when n = 7.

Expression 3:

$6n-28$

Substituting the value of n,

$6\left(7\right)-28$

Simplifying,

$42-28=14$

Since the value of the expression is 14 which is not equal 15.

Hence expression $6n-28$ does not have value of 15 when n = 7.

Expression 4:

$19-\dfrac{28}{n}$

Substituting the value of n,

$19-\dfrac{28}{7}$

Simplifying,

$19-4=15$

Since the value of the expression is 15 which is equal 15.

Hence expression $19-\dfrac{28}{n}$ has the value of 15 when n = 7.

4 0

3 years ago

Read 2 more answers

Determine whether the sequences converge.

Alik [6]

$a_n=\sqrt{\dfrac{(2n-1)!}{(2n+1)!}}$

Notice that

$\dfrac{(2n-1)!}{(2n+1)!}=\dfrac{(2n-1)!}{(2n+1)(2n)(2n-1)!}=\dfrac1{2n(2n+1)}$

So as $n\to\infty$ you have $a_n\to0$ . Clearly $a_n$ must converge.

The second sequence requires a bit more work.

$\begin{cases}a_1=\sqrt2\\a_n=\sqrt{2a_{n-1}}&\text{for }n\ge2\end{cases}$

The monotone convergence theorem will help here; if we can show that the sequence is monotonic and bounded, then $a_n$ will converge.

Monotonicity is often easier to establish IMO. You can do so by induction. When $n=2$ , you have

$a_2=\sqrt{2a_1}=\sqrt{2\sqrt2}=2^{3/4}>2^{1/2}=a_1$

Assume $a_k\ge a_{k-1}$ , i.e. that $a_k=\sqrt{2a_{k-1}}\ge a_{k-1}$ . Then for $n=k+1$ , you have

$a_{k+1}=\sqrt{2a_k}=\sqrt{2\sqrt{2a_{k-1}}\ge\sqrt{2a_{k-1}}=a_k$

which suggests that for all $n$ , you have $a_n\ge a_{n-1}$ , so the sequence is increasing monotonically.

Next, based on the fact that both $a_1=\sqrt2=2^{1/2}$ and $a_2=2^{3/4}$ , a reasonable guess for an upper bound may be 2. Let's convince ourselves that this is the case first by example, then by proof.

We have

$a_3=\sqrt{2\times2^{3/4}}=\sqrt{2^{7/4}}=2^{7/8}$
$a_4=\sqrt{2\times2^{7/8}}=\sqrt{2^{15/8}}=2^{15/16}$

and so on. We're getting an inkling that the explicit closed form for the sequence may be $a_n=2^{(2^n-1)/2^n}$ , but that's not what's asked for here. At any rate, it appears reasonable that the exponent will steadily approach 1. Let's prove this.

Clearly, $a_1=2^{1/2}$ . Let's assume this is the case for $n=k$ , i.e. that $a_k$ . Now for $n=k+1$ , we have

$a_{k+1}=\sqrt{2a_k}$

and so by induction, it follows that $a_n$ for all $n\ge1$ .

Therefore the second sequence must also converge (to 2).

4 0

3 years ago

15 less than 2 times a number is represented by the algebraic expression of 2h - 15. True or false

Advocard [28]

False here are extra words tho make 20 words

8 0

3 years ago