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Nina [5.8K]
2 years ago
7

When writing expressions for complex numbers, what does i represent?

Mathematics
1 answer:
lubasha [3.4K]2 years ago
3 0

Answer: See below

Step-by-step explanation:

i is an imaginary number.

i=\sqrt{-1}

i^2=-1

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What is the cheapest way to go to a ball game if the admissions options are as shown? A) $10 for a single B) $15 for a couple C)
vivado [14]

Answer: C

Step-by-step explanation: A = 10 for one person. B = 7.5 for one person. C = 6.67 for one person. D = 8.75 for one person. E = 10 for one person.

Out of all of these, C is the cheapest.

5 0
2 years ago
Use the quadratic formula to solve the equation.–x2 + 5x = 3
Karo-lina-s [1.5K]

Given the equation - x² + 5x = 3, which can be rewritten as:

- x² + 5x - 3 = 0

where a = -1, b = 5 and c = -3.

Quadratic formula:

\frac{-b\text{ }\pm\text{ }\sqrt[]{b^2\text{ - 4ac}}}{2a}

Now, we just replace the values of a, b and c on the equation above.

\frac{-5\text{ }\pm\text{ }\sqrt[]{5^2\text{ - 4(-1)(3)}}}{2(-1)}

=

\frac{5}{2}\text{ }\pm\text{ }\frac{\sqrt[]{13}}{2}

4 0
1 year ago
Exhibit B: A restaurant has tracked the number of meals served at lunch over the last four weeks. The data shows little in terms
Mekhanik [1.2K]

Answer:

Option E is correct.

The expected number of meals expected to be served on Wednesday in week 5 = 74.2

Step-by-step Explanation:

We will use the data from the four weeks to obtain the fraction of total days that number of meals served at lunch on a Wednesday take and then subsequently check the expected number of meals served at lunch the next Wednesday.

Week

Day 1 2 3 4 | Total

Sunday 40 35 39 43 | 157

Monday 54 55 51 59 | 219

Tuesday 61 60 65 64 | 250

Wednesday 72 77 78 69 | 296

Thursday 89 80 81 79 | 329

Friday 91 90 99 95 | 375

Saturday 80 82 81 83 | 326

Total number of meals served at lunch over the 4 weeks = (157+219+250+296+329+375+326) = 1952

Total number of meals served at lunch on Wednesdays over the 4 weeks = 296

Fraction of total number of meals served at lunch over four weeks that were served on Wednesdays = (296/1952) = 0.1516393443

Total number of meals expected to be served in week 5 = 490

Number of meals expected to be served on Wednesday in week 5 = 0.1516393443 × 490 = 74.3

Checking the options,

74.3 ≈ 74.2

Hence, the expected number of meals expected to be served on Wednesday in week 5 = 74.2

Hope this Helps!!!

8 0
2 years ago
Hiiii.. please help me with this limit question ​
Alenkasestr [34]

Answer:

π

Step-by-step explanation:

Solving without L'Hopital's rule:

lim(x→0) sin(π cos²x) / x²

Use Pythagorean identity:

lim(x→0) sin(π (1 − sin²x)) / x²

lim(x→0) sin(π − π sin²x) / x²

Use angle difference formula:

lim(x→0) [ sin(π) cos(-π sin²x) − cos(π) sin(-π sin²x) ] / x²

lim(x→0) -sin(-π sin²x) / x²

Use angle reflection formula:

lim(x→0) sin(π sin²x) / x²

Now we multiply by π sin²x / π sin²x.

lim(x→0) [ sin(π sin²x) / x² ] (π sin²x / π sin²x)

lim(x→0) [ sin(π sin²x) / π sin²x] (π sin²x / x²)

lim(x→0) [ sin(π sin²x) / π sin²x] lim(x→0) (π sin²x / x²)

π lim(x→0) [ sin(π sin²x) / π sin²x] [lim(x→0) (sin x / x)]²

Use identity lim(u→0) (sin u / u) = 1.

π (1) (1)²

π

Solving with L'Hopital's rule:

If we plug in x = 0, the limit evaluates to 0/0.  So using L'Hopital's rule:

lim(x→0) [ cos(π cos²x) (-2π cos x sin x) ] / 2x

lim(x→0) [ -π cos(π cos²x) sin(2x) ] / 2x

-π/2 lim(x→0) [ cos(π cos²x) sin(2x) ] / x

Again, the limit evaluates to 0/0.  So using L'Hopital's rule one more time:

-π/2 lim(x→0) [ cos(π cos²x) (2 cos(2x)) + (-sin(π cos²x) (-2π cos x sin x)) sin(2x) ] / 1

-π/2 lim(x→0) [ 2 cos(π cos²x) cos(2x) + π sin(π cos²x) sin²(2x) ]

-π/2 (-2)

π

8 0
2 years ago
A Spruce tree was measured three years after sprouting at a height of 3.87 feet. After its sixth year, the tree reached a height
bonufazy [111]
(3,3.87),(6,7.74)
slope = (7.74 - 3.87) / (6 - 3) = 3.87 / 3 = 1.29

An additional year is associated with an additional 1.29 feet of growth 
5 0
3 years ago
Read 2 more answers
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