Is 32 cm bigger than 315 mm

Rewrite the inner limit as

[tex]\displaystyle \lim_{n\to\infty} \prod_{k=1}^n \left(1 + \frac{(k+1)^p}{n^{p+1}}\right) \\\\ = \exp\left(\lim_{n\to\infty} \ln \prod_{k=1}^n \left(1 + \frac{(k+1)^p}{n^{p+1}}\right)\right) \\\\ = \exp\left(\lim_{n\to\infty} \sum_{k=1}^n \ln \left(1 + \frac{(k+1)^p}{n^{p+1}}\right)\right)[/tex]

For any x > 0, we have the useful bounds

[tex]x - x^2 \le \ln(1 + x) \le x[/tex]

so that

[tex]\displaystyle \sum_{k=1}^n \left(\frac{(k+1)^p}{n^{p+1}} - \frac{(k+1)^{2p}}{n^{2(p+1)}}\right) \le \sum_{k=1}^n \ln \left(1 + \frac{(k+1)^p}{n^{p+1}}\right) \le \sum_{k=1}^n \frac{(k+1)^p}{n^{p+1}}[/tex]

In the limit, we have

[tex]\displaystyle \lim_{n\to\infty} \sum_{k=1}^n \frac{(k+1)^p}{n^{p+1}} \\\\ = \lim_{n\to\infty} \frac1n \sum_{k=1}^n \left(\frac{k+1}n\right)^p \\\\ = \int_0^1 x^p \, dx = \frac1{p+1}[/tex]

and

[tex]\displaystyle \lim_{n\to\infty} \sum_{k=1}^n \frac{(k+1)^{2p}}{n^{2(p+1)}} \\\\ = \lim_{n\to\infty} \frac1n \times \frac1n \sum_{k=1}^n \left(\frac{k+1}n\right)^{2p} \\\\ = 0 \times \int_0^1 x^{2p} \, dx = 0[/tex]

Then by the squeeze theorem, the log sum converges to 1/(p + 1), so the infinite product converges to [tex]e^{\frac1{p+1}}[/tex], as suspected.

Finally,

[tex]\displaystyle \lim_{p\to\infty} \left(e^{\frac1{p+1}}\right)^{H_p} \\\\ = \exp\left(\lim_{p\to\infty} \frac{H_p}{p+1}\right) \\\\ = \exp\left(\lim_{p\to\infty} \frac{H_p-\ln(p) + \ln(p)}{p+1}\right) = e^0 = \boxed{1}[/tex]

since Hₙ - ln(n) converges to the Euler-Mascheroni constant γ.

Answer: D

Step-by-step explanation:  I am sure it is if it's not rata me a 1 if it is rata me a 5

Answer:

4 + 6 = 10

6 + 4 = 10

10 - 4 = 6

10 - 6 = 4

Step-by-step explanation:

Answer:

400000

Step-by-step explanation:

The first significant figure of a number is the first digit which is not zero.

The second significant figure of a number is the digit after the first significant figure.

Steps:

Step 1: 389528 (the original number has 6 sig figs)

Step 2: 400000 (rounded to 1 significant figures)

[RevyBreeze]

Answer:

12. √197

13. √89

14. 2√10

15.  (-3, 2)

16. (3/2, 0)

17. (2, -8)

18. 21

Step-by-step explanation:

12. Point 1: (-8, -2); Point 2: (6, -1)

d = √(x2 - x1)² + (y2 - y1)²

d = √(6 - (-8)² + (-1 - (-2)²

d = √(14)² + (1)²

d = √196 + 1

d = √197

13. Point 1: (-4, 5); Point 2: (4, 0)

d = √(x2 - x1)² + (y2 - y1)²

d = √(4 - (-4))² + (0 - 5)²

d = √(8)² + (-5)²

d= √64 + 25

d = √89

14. G: (-2, -3); H: (0, 3)

d = √(x2 - x1)² + (y2 - y1)²

d = √(0 - (-2))² + (3 - (-3))²

d = √(-2)² + (6)²

d = √4 + 36

d = √40

d = √4 x 10

d = 2√10

15. Point 1: (-1, -5); Point 2: (-5, 9)

Midpoint = ((x1 + x2))/2, ((y1 + y2))/2

Mid = (-1 + (-5)/2, (-5 + 9)/2

Mid = (-6)/2, (4)/2

Mid = (-3, 2)

16. Point 1: (7, -2); Point 2: (-4, 2)

Midpoint = ((x1 + x2))/2, ((y1 + y2))/2

Mid = (7 + (-4)/2, (-2 + 2)/2

Mid = (3)/2, (0)/2

Mid = (3/2, 0)

17. M:(-3, -1); Y:(-8, 6), X: (X, y)

Midpoint = ((x1 + x2))/2, ((y1 + y2))/2

X      = ((-8 + x2))            ,((6 + y2))

                ÷      = -3              ÷           = -1

                2                          2

To get rid of the 2 multiply the 2 by -3 for X and -1 for Y

X = ((-8 + x2))                      ,((6 + y2))

             ÷       = -3(2)                 ÷         = -1(2)

           2(2)                              2(2)

X = (-8 + x2) = -6, (6 + y2) = -2

           +8          +8,   -6             -6

X2 = 2, Y2 = -8

X: (2, -8)

18. QR = 8x - 51; RS = 3x - 6

8x - 51 = 3x - 6

-3x         -3x

5x - 51 = -6

     + 51   +51

5x = 45

÷5    ÷5

x = 9

QR = 8(9) - 51

QR = 72 - 51

QR = 21

RS = 3x - 6

RS = 3(9) - 6

RS = 21

(QR + RS)/2

(21 + 21)/2

42/2 = 21

QS = 21

I really hope this helps!

Answer:

You are correct.

Step-by-step explanation:

This is a semi circle. The central angle is 180 so the according to Thales Theorem, the angle that is opposite of the diameter is 90 degrees.

A triangle has at max 180 degrees So

[tex]180 - 90 - 60 = x[/tex]

[tex]30 = x[/tex]

So the angle is 30

Answer:

5n(2n^2-7n+5)

Step-by-step explanation:

Answer:

No they are not.

Step-by-step explanation:

Without the angels, imagine flipping over one of the triangles and overlapping them. They may be the same shape, but they are different sizes.

Answer:

Well a parallelogram has congruent opposite sides.
We need to find the value of a here.

A shape’s angle must add up to following this equation
180(n-2) = ?

Now solve for this equation right here with “n” as “sides.

THis shape has 4 sides so 180(4-2) = 360

You have each interior angle of the parrlelogram which is 360.
Let’s solve 112 and 4b +8 first.

We know they have to be equal since opposite angles of a parrlelogram has to be equal.

112 = 4b + 8

104 = 4b
26 = b

You have b as 26.

Now solving it we know that two angles “G” and “I” are both 112.

112 *2 = 224

Thats one side done.
Now the opposite…

With 224 already being taken away subtract 360 by 224 since we figured out 360 was the amount of all the interior angles in the shape add upo to. 360 - 224 = 136

136 is the other two angles ADDED UP.

Divide it by 2 since both has to be equal and be the same.

68

Now solve for a.

2a = 68.

= 34

Answer:

34

Step-by-step explanation:

Consecutive angles of a parallelogram are supplementary

2a + 112 = 180

2a = 68

a = 34

Answer:

[tex]g(x)=x^3-8x^2+9x+11[/tex]

Step-by-step explanation:

[tex]f(x)=-x^3-8x^2-9x+11[/tex]

When a function is reflected across the y-axis, negative x-values become positive, and positive x-values become negative.

Therefore, substitute -x in place of x in the function f(x):

[tex]g(x)=-(-x)^3-8(-x)^2-9(-x)+11[/tex]

We know that [tex](-x)^3=-(x^3)[/tex]

[tex]\implies -(-x)^3=--(x^3)=x^3[/tex]

We know that [tex](-x)^2=x^2[/tex]

[tex]\implies -8(-x)^2=-8(x)^2=-8x^2[/tex]

Also [tex]-9(-x)=+ \ 9x[/tex]

Therefore,

[tex]g(x)=x^3-8x^2+9x+11[/tex]

Step-by-step explanation:

15 long

12 wide

10 high

we need all for walls

hight times length two times ( these are the front and back walls )

hight times width two times ( These are the side walls )

the roof is

width times length (only once as only the ceiling)

same measurement as the floor

can you work it out with that

please mark brainiest

-4(v+1)

hope this works i looked it up and this is what i got

Answer:

-4( v+1)

Step-by-step explanation:

(-12v + 3) + (8v - 7)

-12v + 3 + 8v - 7

-4v - 4

-4 (v+1)

Answer: Option (a) x > 1/6 is the solution to the given expression -2(8x - 4) < 2x + 5.

The solution to the inequality is x > 1/6

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

-2(8x - 4) < 2x + 5

On simplifying , we get

-16x + 8 < 2x + 5

Subtracting 2x on both sides , we get

-18x + 8 < 5

Subtracting 8 on both sides , we get

-18x < -3

Multiply by -1 on both sides , we get

18x > 3

Divide by 18 on both sides , we get

x > 1/6

Hence , the solution is x > 1/6

To learn more about inequality equations click :

https://brainly.com/question/11897796

#SPJ7

Answer:

1.94 & -1.94

Step-by-step explanation:

I took the test! Hope this helps :)

Answer:

(x+3)^2 + (y-7)^2 = 2^2

Step-by-step explanation:

Follow the standard form of a circle, (x-h)^2 + (y-k)^2 = r^2, given that (-3,7) is (h,k) and 2 is r.

Answer:

y = 22

Step-by-step explanation:

Consecutive Angles of a parallelogram are supplementary

y + 4y -70 = 180

5y - 70 = 180

5y = 110

y = 22

Answer:

14.58 m3

Step-by-step explanation:

here, breadth (b) = 4cm

length (l) = 6cm

volume (v) = 350cm3

height (h) = ??

we know, volume of cuboid=

length × breath× height

or, v = L× B × H

or, 350 = 6 × 4 × H

or, 350 = 24 × H

or, 350/25 = H

or 14.58 = H

therefore, H = 14.58cm3

Answer:

7

Step-by-step explanation:

please give brainliest!!

Answer:

7 is the answer.

Answer:

x = 128

Step-by-step explanation:

49 + x + 3 = 180

52 + x =180

x + 52 = 180

x + 52 - 52 = 180 - 52

x = 128

Answer:

128

Step-by-step explanation:

49+(x+3)=180

49+x+3=180

52+x=180

x=180-52

x=128

Answer:

cos(x)

Step-by-step explanation:

[tex]Remember: sin(x) = \frac{1}{csc(x)}[/tex]

[tex]\frac{cos(x)}{sin(x) *csc(x)}[/tex]    OG Question

[tex]\frac{cos(x)}{\frac{1}{csc(x)} *\frac{csc(x)}{1} }[/tex]  Convert [tex]sin(x) = \frac{1}{csc(x)}[/tex]

[tex]\frac{cos(x)}{1 }[/tex]  Cross multiply and cancel out. Equals to one.

[tex]cos(x)[/tex] Anything divided by 1 is itself. You have your answer.

Hope this makes sense. Lmk if you need more help.

Answer:

-2

Step-by-step explanation:

Slope equals rise over run. The line goes forwards by two and down by 4 between the two charted points, so the slope would be -4/2 or -2.

Answer:  y = 2000(0.78)^t

This is the same as writing [tex]y = 2000(0.78)^t[/tex]

=====================================================

Explanation:

The answer above is in the form y = a*b^t

a = initial price = 2000 dollars

b = decay factor = 0.78

We have a decay factor because 0 < b < 1 and because the price decreases. The 0.78 is from the computation of 1 - 0.22 = 0.78

Meaning that if the price goes down 22%, then we keep the remaining 78%

So each year, the laptop keeps 78% of its previous price after losing 22%.

The given expression when written in standard form gives; 10.1 * 10⁴

A number written in standard form is usually as A * 10ⁿ

where;

A is a number bigger than or equal to 1 and less than 10

Now, we are given;

(6.3 * 10⁴) + 38000

⇒ (6.3 * 10⁴) + (3.8 * 10⁴)

Using distributive property of equality, we have it in standard form as;

(6.3 + 3.8) * 10⁴

⇒ 10.1 * 10⁴

Read more about standard form at; https://brainly.com/question/17939013

Answer:

Step-by-step explanation:

The sum of the polynomials (-x2 + 9) + (-3x2 - 11x + 4) is -4x2 - 11x - 5.

Answer:

-9 is rational

5/8 is rational

30/sqrt of 25 is rational

sqrt 70 is irrational

pi is irrational

Step-by-step explanation:

rational number: a number that can be expressed as an integer or the quotient of an integer divided by a nonzero integer.  A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero, whereas an irrational number cannot be expressed in the form of fractions. Rational numbers are terminating decimals, but irrational numbers are non-terminating. Irrational Numbers Definition An irrational number is a real number that cannot be expressed as a ratio of integers, for example, √ 2 is an irrational number. Again, the decimal expansion of an irrational number is neither terminating nor recurring.

Hope this helps mark brainliest please :)

Step-by-step explanation:

[tex] \frac{d}{dx} {e}^{x} \cos(x) = {e}^{x} cos(x) - {e}^{x} \sin(x) [/tex]

Answer:

mass production, application of the principles of specialization, division of labour, and standardization of parts to the manufacture of goods.

Answer:

  a = 1.5

Step-by-step explanation:

Assuming side 'a' is the short side of a right triangle with the given dimensions, we can find it using the Pythagorean theorem.

  c² = a² +b²

  a = √(c² -b²) = √(2.5² -2²) = √2.25

  a = 1.5

_____

The ratio of the given sides is 2.5 : 2 = 5 : 4. Only one right triangle has hypotenuse and long side in the ratio 5 : 4. That is the 3-4-5 triangle. This means the short side is 3/5 of the hypotenuse, or (3/5)(2.5) = 1.5

The length of side 'a' is 1.5 units.