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Lubov Fominskaja [6]

1 year ago

8

If the greatest integer function is called the floor function because it rounds any number down to the nearest integer, what wou

ld you presume about the ceiling function?

2 answers:

makvit [3.9K]1 year ago

6 0

<h2>Answer with explanation:</h2>

The greatest integer function which is also known as a floor function rounds any number down to the nearest integer.

for example--

If -2 ≤x <-1 then value of function is -2

If -1 ≤x < 0 then value of function is -1

If 0 ≤x < 1 then value of function is 0

If 1 ≤x < 2 then value of function is 1

and so on.

Similarly the least integer function which is also known as a ceiling function rounds any number up to the nearest integer.

for example--

If -2 < x ≤ -1 then value of function is -1

If -1 < x ≤ 0 then value of function is 0

If 0 < x ≤ 1 then value of function is 1

If 1 < x ≤ 2 then value of function is 2

and so on.

Phantasy [73]1 year ago

5 0

Ceiling Function is the least integer that is greater than or equal to x.

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Use Euler's formula to derive the identity. (Note that if a, b, c, d are real numbers, a + bi = c + di means that a = c and b =

storchak [24]

Answer with Step-by-step explanation:

We have to prove that

$sin 2\theta=2sin\theta cos\theta$ by using Euler's formula

Euler's formula : $e^{i\theta}=cos\theta+isin\theta$

$e^{i(2\theta)}=(e^{i\theta})^2$

By using Euler's identity, we get

$cos2\theta+isin2\theta=(cos\theta+isin\theta)^2$

$cos2\theta+isin2\theta=(cos^2\theta-sin^2\theta+2isin\theta cos\theta)$

$(a+b)^2=a^2+b^2+2ab, i^2=-1$

$cos2\theta+isin2\theta=cos2\theta+i(2sin\theta cos\theta)$

$cos2\theta=cos^2\theta-sin^2\theta$

Comparing imaginary part on both sides

Then, we get

$sin2\theta=2sin\theta cos\theta$

Hence, proved.

8 0

2 years ago

Crop researchers plant 15 plots with a new variety of corn. The yields in bushels per acre are: 138.0 139.1 113.0 132.5 140.7 10

son4ous [18]

There is a relationship between confidence interval and standard deviation:
$\theta=\overline{x} \pm \frac{z\sigma}{\sqrt{n}}$
Where $\overline{x}$ is the mean, $\sigma$ is standard deviation, and n is number of data points.
Every confidence interval has associated z value. This can be found online.
We need to find the standard deviation first:
$\sigma=\sqrt{\frac{\sum(x-\overline{x})^2}{n}$
When we do all the calculations we find that:
$\overline{x}=123.8\\ \sigma=11.84$
Now we can find confidence intervals:
$($90\%,z=1.645): \theta=123.8 \pm \frac{1.645\cdot 11.84}{\sqrt{15}}=123.8 \pm5.0\\($95\%,z=1.960): \theta=123.8 \pm \frac{1.960\cdot 11.84}{\sqrt{15}}=123.8 \pm 5.99\\ ($99\%,z=2.576): \theta=123.8 \pm \frac{2.576\cdot 11.84}{\sqrt{15}}=123.8 \pm 7.87\\$
We can see that as confidence interval increases so does the error margin. Z values accociated with each confidence intreval also get bigger as confidence interval increases.
Here is the link to the spreadsheet with standard deviation calculation:
https://docs.google.com/spreadsheets/d/1pnsJIrM_lmQKAGRJvduiHzjg9mYvLgpsCqCoGYvR5Us/edit?usp=sharing

6 0

1 year ago

*NO 194 39% 13:08 Pilih jawaban yang paling tepat Segitiga PQR dan segitiga XYZ 5 poin merupakan dua segitiga yang kongruen. Bes

Illusion [34]

Answer:

Option d. PQ = YZ

Step-by-step explanation:

<u><em>The question in English is</em></u>

Choose the most appropriate answer. The PQR triangle and the XYZ triangle are two congruent triangles. The angle P = the angle Y and PR = YX. Side pairs of the same length are ... a. PQ = XZ b. QR = YZ c. QR = XY d. PQ = YZ

we know that

If two triangles are congruent, then its corresponding sides and its corresponding angles are congruent

Corresponding sides are named using pairs of letters in the same position on either side of the congruence statement

so

we have that

$m\angle P=m\angle Y$

$PR=YX$

so

Triangle PQR is congruent with Triangle YZX

That means

<em><u>Corresponding angles</u></em>

$m\angle P=m\angle Y$

$m\angle Q=m\angle Z$

$m\angle R=m\angle X$

<u><em>Corresponding sides</em></u>

$PQ=YZ\\QR=ZX\\PR=YX$

8 0

1 year ago

Students at a high school were polled to determine the type of music they preferred. There were 1940 students who

Reika [66]

Answer:

students preferred alternative music

= 461/1940 ×100%=23.7%

6 0

2 years ago

Evaluate. 58−(14)2=58-142= ________

nasty-shy [4]

For this case we have the following expression:

$58- (14) ^ 2$

The first step is to solve the quadratic term.

We have then:

$58- (14) ^ 2 = 58-196$

Then, the second step is to subtract both resulting numbers:

$58- (14) ^ 2 = -138$

We observe that the result obtained is a negative number.

Answer:

The result of the expression is given by:

$58- (14) ^ 2 = -138$

7 0

1 year ago