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4 years ago

Evaluate the series 4+2+1+1/2+1/4 to s10

Mathematics

2 answers:

stiks02 [169]4 years ago

8 0

Answer:

<u>The correct answer is 13.75</u>

Step-by-step explanation:

4+2= 6

6+1=7

6+7= 13

13+1/2= 13.5

13.5+1/4= 13.75

Alja [10]4 years ago

3 0

Answer:

$s_10=\frac{1023}{128}$

Step-by-step explanation:

4+2+1+1/2+1/4.....

WE need to find out the sum s10

first term is 4 and second term is 2

2/4 = 1/2

1/2= 1/2

1/2 / 1= 1/2

so common ratio is 1/2

The given series is geometric series

we use the sum formula for the geometric series

$s_n= a\frac{(1-r^n)}{1-r}$

Where 'r' is the common ratio and 'a' is the first term

a= 4 and r= 1/2

Plug in the values in the sum formula'

$s_n= 4\frac{(1-(\frac{1}{2})^n)}{1-(\frac{1}{2})}$

Given n=10

$s_10= 4\frac{(1-(\frac{1}{2})^{10})}{1-(\frac{1}{2})}=\frac{1023}{128}$

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babymother [125]

Answer:

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Step-by-step explanation:

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3 years ago

Let R be a ring with identity and let S be a subring of R containing the identity. Prove that if m is a unit in S then u is a un

kumpel [21]

Explanation:

Since m is a unit in S, then, there exists b ∈ S such that m*b = 1, where 1 is the identity. Since S is a subring of R we have that m ∈ R, and therefore b is also the multiplicative inverse of m in R. The converse isnt true.

The set of real numbers is a Ring with the standard sum and multiplication. Every real number different from 0 has a multiplicative inverse. For example, the inverse of 2 is 1/2. However, 2 is not a unit on the subring of Integers Z.

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3 years ago

Which is a correct expansion of (4x + 1)(2x - 2)?

bekas [8.4K]

Answer:

8x^2 -6x-2

Step-by-step explanation:

formula= ab^2(- or +)b-ab

3 0

3 years ago

(1 point) Find the length traced out along the parametric curve x=cos(cos(4t))x=cos⁡(cos⁡(4t)), y=sin(cos(4t))y=sin⁡(cos⁡(4t)) a

Mazyrski [523]

The length of a curve $C$ given parametrically by $(x(t),y(t))$ over some domain $t\in[a,b]$ is

$\displaystyle\int_C\mathrm ds=\int_a^b\sqrt{\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt$

In this case,

$x(t)=\cos(\cos4t)\implies\dfrac{\mathrm dx}{\mathrm dt}=-\sin(\cos4t)(-\sin4t)(4)=4\sin4t\sin(\cos4t)$

$y(t)=\sin(\cos4t)\implies\dfrac{\mathrm dy}{\mathrm dt}=\cos(\cos4t)(-\sin4t)(4)=-4\sin4t\cos(\cos4t)$

So we have

$\displaystyle\left(\frac{\mathrm dx}{\mathrm dt}\right)^2+\left(\frac{\mathrm dy}{\mathrm dt}\right)^2=16\sin^24t\sin^2(\cos4t)+16\sin^24t\cos^2(\cos4t)=16\sin^24t$

and the arc length is

$\displaystyle\int_0^1\sqrt{16\sin^24t}\,\mathrm dt=4\int_0^1|\sin4t|\,\mathrm dt$

We have

$\sin(4t)=0\implies4t=n\pi\implies t=\dfrac{n\pi}4$

where $n$ is any integer; this tells us $\sin(4t)\ge0$ on the interval $\left[0,\frac\pi4\right]$ and $\sin(4t)$ on $\left[\frac\pi4,1\right]$ . So the arc length is

$=\displaystyle4\left(\int_0^{\pi/4}\sin4t\,\mathrm dt-\int_{\pi/4}^1\sin4t\,\mathrm dt\right)$

$=-\cos(4t)\bigg_0^{\pi/4}-\left(-\cos(4t)\bigg_{\pi/4}^1\right)$

$=(\cos0-\cos\pi)+(\cos4-\cos\pi)=\boxed{3+\cos4}$

7 0

3 years ago

Sammy usually takes a 18 minute shower in the morning. If a 4 minute shower uses an average of 20-40 gallons of water, what is t

Luda [366]

Answer:

Step-by-step explanation:

This can be set up like an inequality. Chances are just as likely that you are in ratios and proportions, but since I'm not sure, I'm going with the easier way for this particular situation. The inequality, before reducing, is:

20 < 4x < 40,

which states that a 4 minute shower uses less than 40 gallons but greater than 20 gallons, where x is the number of gallons of water. Therefore,

5 < x < 10 results when you simplify. This puts things in terms of 1 minute now. This states that a 1 minute shower uses less than 10 gallons of water but more than 5 gallons. We got this by dividing everything by 4.

Now that things are in terms of a single minute, all you have to do is multiply the greatest number of gallons by 18 and the least number of gallons by 18 (and the x as well) to get the number of gallons used in an 18 minute shower as a range:

90 < 18x < 180

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3 years ago