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2 years ago

NO LINKS PLEASE,

Mathematics

1 answer:

STALIN [3.7K]2 years ago

5 0

Answer:

Step-by-step explanation:

According to the divergence test, for an infinite series $\sum a_n$ , the series diverges if $\lim_{n \to \infty} a_n \neq 0$ .

Applying the divergence test here:

$\lim_{n \to \infty} \frac{3n^5}{6n^6+1}=0$

Therefore, the limit of the infinite series is 0.

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21 is less than or equal to -3(x-4) is less than 18

Maslowich

Answer:

-3 ≤ x <-2

Step-by-step explanation:

First, you should set up the equation to solve it, which is,

21 ≤ -3(x-4)<18

Then you should simplify the equation to,

21 ≤ -3x+12<18

Then subtract 12 from both sides.

9 ≤ -3x<6

Lastly, divide -3 from both sides.

-3 ≤ x<-2

8 0

3 years ago

What is the solution to this system of equations?

IRISSAK [1]

Hola cómo estás cómo te fue te conozco

8 0

3 years ago

Please Help NO LINKS

schepotkina [342]

$V = 864\pi$

Step-by-step explanation:

Since one of the boundaries is y = 0, we need to find the roots of the function $f(x)=-2x^2+6x+36$ . Using the quadratic equation, we get

$x = \dfrac{-6 \pm \sqrt{36 - (4)(-2)(36)}}{-4}= -3,\:6$

But since the region is also bounded by $x = 0$ , that means that our limits of integration are from $x=0$ (instead of -3) to $x=6$ .

Now let's find the volume using the cylindrical shells method. The volume of rotation of the region is given by

$\displaystyle V = \int f(x)2\pi xdx$

$\:\:\:\:\:\:\:= \displaystyle \int_0^6 (-2x^2+6x+36)(2 \pi x)dx$

$\:\:\:\:\:\:\:= \displaystyle 2\pi \int_0^6 (-2x^3+6x^2+36x)dx$

$\:\:\:\:\:\:\:= \displaystyle 2\pi \left(-\frac{1}{2}x^4+2x^3+18x^2 \right)_0^6$

$\:\:\:\:\:\:\:= 864\pi$

3 0

3 years ago

Solve for x. Round to the nearest tenth, if necessary.

serg [7]

Answer:

x = 8.8

Step-by-step explanation:

take 20 degree as reference angle .the,

hypotenuse = OQ = x (hypotenuse is always opposite of 90 degree)

perpendicular(opposite) = PQ 3 (opposite of reference angle is perpendicular or also called as opposite)

base(adjacent) = OP (side which lies on the same line where 90 degree and reference angle)

using sin rule

sin 20 = opposite / hypotenuse

0.34 = 3 / x

x = 3/0.34

x = 8.82

x = 8.8

4 0

3 years ago

Read 2 more answers

7 measured data points have a sample mean of 1403 and a standard deviation of 27. Determine the best estimate of the mean value

mina [271]

Answer:

Step-by-step explanation:

Hello!

You have sample of n=7 with mean X[bar]= 1403 and standard deviation S=27 and are required to estimate the mean with a 95%CI.

Asuming this sample comes from a normal population I'll use a stuent t to estimate the interval (a sample of 7 units is too small for the standard normal to be accurate for the estimation):

[X[bar]± $t_{n-1;1-\alpha /2}$ * $\frac{S}{\sqrt{n} }$ ]

$t_{n-1;1-\alpha /2} = t_{6;0.975}= 2.365$

[1403±2.365* $\frac{27}{\sqrt{7} }$ ]

[1378.87;1427.13]

The margin of error is the semiamplitude of the interval and you can calculate it as:

$d= \frac{Upbond-Lowbond}{2}= \frac{1427.13-1378.87}{2} = 24.13$

With a confidence level of 95% you'd expect that the real value of the mean is contained by the interval [1378.87;1427.13], the best estimate of the mean value is expected to be ± 24.13 of 1403.

I hope it helps!

4 0

3 years ago