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3 years ago

What is the two closest integer to 105

Mathematics

2 answers:

Aloiza [94]3 years ago

6 0

Answer:

104 and 106

Step-by-step explanation:

The closest to 105 (previous and next integer)

vlabodo [156]3 years ago

4 0

I believe it is 53 and 52.

Hope this helps! :D

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The following series are geometric series or a sum of two geometric series. Determine whether each series converges or not. For

Sergeeva-Olga [200]

Answer:

Required solution gives series (a) divergent, (b) convergent, (c) divergent.

Step-by-step explanation:

(a) Given,

$\sum_{n\to 0}^{\infty}\frac{2^n}{9^{2n}+1}$

To applying limit comparison test, let $a_n=\frac{2^n}{9^{2n}+1}$ and $b_n=\frac{9^{2n}}{2^n}$ . Then,

$\lim_{n\to\infty} \frac{a_n}{b_n}=\lim_{n\to\infty}(1+\frac{1}{9^{2n}})=1>0$

Because of the existance of limit and the series $\frac{9^{2n}}{2^n}$ is divergent since $\frac{9^{2n}}{2^n}=(\frac{9^2}{2})^n$ where $\frac{81}{2}>1$ , given series is divergent.

(b) Given,

$\sum_{n\to 1}^{\infty}(\frac{7^n}{7^n+4})$

Again to apply limit comparison test let $a_n=\frac{7^n}{7^n+4}$ and $b_n=\frac{1}{7^n}$ we get,

$\lim_{n\to \infty}\frac{a_n}{b_n}=\frac{1}{7^n+4}=0$

Since $\lim_{n\to \infty} \frac{1}{7^n}=0$ is convergent, by comparison test, given series is convergent.

$\sum_{n\to 1}^{\infty}\frac{5^n+2^n}{6^n}= \sum_{n\to 1}^{\infty}(\frac{5}{6})^n+\sum_{n\to 1}^{\infty}(\frac{1}{3})^n$ . Now applying Cauchy Root test on last two series, we will get,

\lim_{n\to \infty}|(\frac{5}{6})^n|^{\frac{1}{n}}=\frac{5}{6}=L_1
\lim_{n\to \infty}|(\frac{1}{3})^n|^{\frac{1}{n}}=\frac{1}{3}=L_2

Therefore,

$\lim_{n\to \infty}\frac{5^n+2^n}{6^n}=L_1+L_2=1.16>1$

Hence by Cauchy root test given series is divergent.

5 0

4 years ago

In circle A shown below, the measure of ∠BAD is 148°: Circle A with angle BAD measuring 148 degrees; points B, C, D lie on Circl

german

Answer:

52°

Step-by-step explanation:

In the figure attached, Circle A is shown. There we can see that:

∠BC + ∠CD = ∠BAD

We know that Arc BC measures 96° and arc BAD measures 148°. Replacing this data into the equation and solving for Arc CD, we get:

96° + ∠CD = 148°

∠CD = 148° - 96°

∠CD = 52°

5 0

3 years ago

Solve the inequality - 3 ( x - 5/3 ) <26

matrenka [14]

Answer:

x < 21

Step-by-step explanation:

to solve this - 3 ( x - 5/3 ) <26 inequality

- 3 ( x - 5/3 ) <26

- ( x - 5) = 26

x + 5 = 26

x = 26 - 5

x = 21

therefore x < 21

6 0

3 years ago

40 ➗ [24 - 4 x (2 + 3) ]<br><br> What is the value of this expression?

Natalija [7]

Answer: this is your answer

_____

6-5x

4 0

4 years ago

Read 2 more answers

Pls help I’m timed thanks

alexgriva [62]

Answer:

Picture 1: b

Picture 2: d

Picture 3: c

Step-by-step explanation:

Hi there,

For Picture 1, to solve for an inverse function, just simply solve for x. Since the closest you can get is arccos(πx)=2y+6, you just

solve for cosine as a function: cos(2y+6)=πx and solving for x:

x= (1/π)cos(2y+6) but since variable choice is arbitrary, you can now redefine y and x:

y= (1/π)cos(2x+6)

For Picture 2, tanx is equivalent to sinx/cosx and cscx is just the reciprocal of sinx. So, it becomes:

$\frac{sinx}{cosx} *\frac{1}{sinx} =\frac{1}{cosx} =cscx$

We have already been giving the cosine value of 2, and its inverse is thus 1/2.

For Picture 3, I would recommend revisiting polar coordinates.

Polar coordinates are in the form (r, θ).

$r = \sqrt{x^{2} +y^{2} } }$ and θ $=arctan(\frac{y}{x})$ . Recognize there are two possible radii, depending on what side of the circle you start from!

thanks,

3 0

3 years ago