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3 years ago

Which expression uses the correct comparison symbol?

Mathematics

1 answer:

jeka943 years ago

8 0

Answer:

Step-by-step explanation:

1 is greater than -1

Hope this helps :)

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Determine whether the series is convergent or divergent.

elixir [45]

Answer:

Step-by-step explanation:

Test for convergence or divergence of a series using Comparison test

Function.

Σ Sin(1/n). From n= 1 to n=∞

Comparison test states that

Let, 0 ≤ an ≤ bn

For all n

Then, if

Σbn converges then, Σan converge

Σan diverges then, Σbn diverge

I.e if the small series diverges, then, the big series diverges and if the big series converges then, the small series converges.

Let compare the given function to 1/n

1/n is greater than Sin(1/n)

0 ≤ Sin(1/n) ≤ 1/n

1/n is a positive number and it is always greater than 1.

We know that 1/n diverse from p series

P series says that,

Σ 1/n^p

If p≤1 then the series diverges

If p>1 the series converges

So when we compare this to 1/n, then p is equal to 1, therefore, the series diverges.

Now, comparing this to the comparison thereom

Since, the large series bn diverges, then the smaller series an diverges.

Then,

Σ 1 / n diverges implies that.

Σ Sin(1/n) diverges too

5 0

4 years ago

What is the greatest common factor of the polynomial expression 2x^3 - 4x^2 + 6x?

iren2701 [21]

Step-by-step explanation:

$2 {x}^{3} - 4 {x}^{2} + 6x \\ = 2x( {x}^{2} - 2x + 3) \\ \because \: 2x \: is \: common \: from \: all \: terms \\ \therefore \: greatest \: common \: factor = 2x$

5 0

3 years ago

Evaluate the function for h(1) <br><br> h(x) = |1 – 7x|

daser333 [38]

Answer:

We conclude that:

$h\left(1\right)=6$

Step-by-step explanation:

Given

The function is

$h\left(x\right)\:=\:|1\:-\:7x|$

To determine

h(1) = ?

Given the function

$h\left(x\right)\:=\:|1\:-\:7x|$

substitute x = 1 in the function

$h\left(1\right)=\left|1-7\left(1\right)\right|$

$h(1)=\left|1-7\right|$

$h(1)=\left|-6\right|$

Apply absolute rule: |-a| = a

$h\left(1\right)=6$

Therefore, we conclude that:

$h\left(1\right)=6$

6 0

3 years ago

Calculate an estimate of a square root of 119 + 120i

uysha [10]

Answer:

Step-by-step explanation:

Given

z=119+120 i

Let $\sqrt{119+120 i}=p+iq$

Squaring both sides

$119+120 i=p^2-q^2+2ipq$

Comparing real and imaginary part

Re(LHS)=Re(RHS)

$119=p^2-q^2$ -----------1

comparing Im(LHS)=Im(RHS)

120=2pq

$q=\frac{60}{p}$

Substitute q in 1

$119=p^2-(\frac{60}{p})^2$

$p^4-119p^2-(68)^2=0$

Let $x=p^2$

$x^2-119x-4624=0$

$x=frac{119\pm \sqrt{119^2+4\times 4624}}{2}$

$x=\frac{119\pm 180.71}{2}$

we take only Positive value because $p^2=x$

x=149.85

$p^2=149.85$

thus $p=\pm 12.24$

$q=\mp 4.90$

thus $\sqrt{119+120 i}=\pm (12.24+i 4.90)$

6 0

4 years ago

a construction crew is digging a hole. On the first day, they dug a hole 3 feet deep. On the second day, they dug 2 more feet. O

Tamiku [17]

(-3)+(-2)+(-4)= -9. The hole is 9 feet deep. It's related to the problem because it's the total depth of the hole.

3 0

4 years ago

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