MATHEMATICS HIGH SCHOOL

Is this correct? The answer I picked was the only one that had no limit. If I did it correctly the other choices limit was zero.

Answers

Answer 1

Answer:

Step-by-step explanation:

These are all examples of p-series:

∑(1 / nᵖ), where p>0.

If p > 1, the series converges. If 0 < p ≤ 1, the series diverges.

First option:

∑(1/n⁵)

Here, p = 5. Since 5 > 1, the series converges.

Second option:

∑((√n+3)/n³)

∑((√n)/n³) + ∑(3/n³)

∑(1/n^2.5) + 3 ∑(1/n³)

In the first sum, p = 2.5. In the second sum, p = 3. Both are greater than 1, so the series converges.

Third option:

∑((n−4)/(n⁴√n))

∑(1/(n³√n)) − ∑(4/(n⁴√n))

∑(1/n^3.5) − 4 ∑(1/n^4.5)

In the first sum, p = 3.5. In the second sum, p = 4.5. Both are greater than 1, so the series converges.

Fourth option:

∑(1/∛n)

∑(1/n^⅓)

Here, p = ⅓. This is less than 1, so the series diverges.

Note: if a series is converging, then the limit is 0.

However, if the limit of a series is 0, it does not necessarily mean that series is converging.

Here, the limit of all 4 options is 0. However, the fourth option is a diverging series.

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Sam created a porch that was part wooden and part concrete, as shown in the figure below.Note: Figure not drawn to scale If a = 18 ft, b = 24 ft, and c = 30 ft, what is the total area of the porch? Assume that the wooden part is a right triangle and the concrete part is a square. A. 186 ft2 B. 102 ft2 C. 1,260 ft2 D. 1,116 ft2
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Compare and contrast the absolute value of a real number to that of a complex number.

$3z - 2 = 4 \n z =$
what does z equal

Answers

The answer that I found was z=2

What is the maximum number of turning points the function f(x)=7x^5+6x^3-4x^2+1 , can have

Answers

The maximum number of turning points of the polynomial is the degree of the polynomial minus 1. In this case the degree is 5, so the maximum number of turning points is 5-1=4.

you have 10 black marbles, 10 white marbles, and 2 buckets. i am going to pick one of the two buckets at random and select one marble from it at random. how would you fill the two buckets with marbles to maximize the odds that i select a white marble?

Answers

To maximize the odds of selecting a white marble, you can fill one bucket with all the white marbles and the other bucket with all the black marbles.

Luis distributes 49 roses equally among seven friends then three of his friends combined the roses they received to make a bouquet how many roses are in this bouquet there are blank roses in this bouquet

Answers

Answer:

The are 21 roses in the bouquet

Step-by-step explanation:

Since the 49 roses are distributed evenly amongst the 7, then what each of the seven will get would be 49/7 = 7 roses

So 3 of the friends combine every of theirs to make a bouquet

The number of roses in the bouquet will be 7 + 7 + 7 = 21 roses

Complete the pairs of corresponding parts if △ RST ≅ △ TXY. ∠ R =
∠ XYT
∠ XTY
∠ TXY

Answers

Solution:

Given: △ RST ≅ △ TXY

We are given ΔRST and ΔTXY are congruent to each other.

If two triangles are congruent to each other then their corresponding parts are equal.

Please see the attachment of two triangles.

∠R is corresponding to ∠T

∵ ∠R=∠T By CPCT

∠XYT is corresponding to ∠STR

∵ ∠XYT=∠STR By CPCT

∠XTY is corresponding to ∠SRT.

∵ ∠XTY=∠SRT By CPCT

∠TXY is corresponding to ∠RST

∵ ∠TXY=∠RST By CPCT

CPCT: Congruent part of congruence triangle.

So, two triangles are similar. Ordering of letters matters when you are writing this down. So, RST~TXY, then ∠R = ∠T, or ∠TRS = ∠YTX = ∠XTY

(HELP!!!!!!)the diagram shows the dimensions of the pool cover for a hotel pool

Answers

Step-by-step explanation:

16.5 add all then divide