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seropon [69]
3 years ago
14

Write answer as an inequality solved for c ​

Mathematics
1 answer:
g100num [7]3 years ago
5 0
He will spend at least $27. He has already spent $16

27-16=11

So, Henry will spend at least 11 more dollars

C ≥ 11
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A particle begins at point (1, 2) and is moving along the line segment joining (1, 2) to (3, 4). Initially, what is the rate of
Bumek [7]

Answer:

Initially, that is, at (1,2), the rate of increase of the function in the direction given = 0

Hence the function is neither increasing nor decreasing initially in the given direction.

Step-by-step explanation:

f(x,y) = 2x² - y²

Rate of Change of the function = ∇f = (fₓ, fᵧ)

And we're told to find the rate of change in a particular direction = ∇f.û

We first obtain the unit vector in that direction, û

Direction = (3,4) - (1,2) = (2,2)

Uni vector = vector/magnitude

Vector = 2î + 2j

magnitude = √(2² + 2²) = √8 = 2 √2

(2î + 2j)/(2√2) = (1/√2)î + (1/√2)j = û

Unit vector in the direction = (1/√2, 1/√2)

f = 2x² - y²

At (1,2)

fₓ = ∂f/∂x = 4x = 4

fᵧ = ∂f/∂y = -2y = -4

∇f = (4,-4)

∇f.û = (4î - 4j).((1/√2)î + (1/√2)j) = (4/√2) - (4/√2) = 0

If it was positive, then the function is increasing, if it was negative, the function is decreasing. Zero means neither of them.

Hence the function is neither increasing nor decreasing initially in the given direction.

7 0
3 years ago
DJ Titus is making a playlist for a radio show; he is trying to decide what 10 songs to play and in what order they should be pl
Dominik [7]

Answer:

Different playlists possible = 18287141644800

Step-by-step explanation:

Given - DJ Titus is making a playlist for a radio show; he is trying to

            decide what 10 songs to play and in what order they should be

            played.

            Step 1 of 2 : If he has his choices narrowed down to 7 blues,

                                 7 disco, 5 pop, and 7 reggae songs.

To find - He wants to play no more than 4 reggae songs.

              How many different playlists are possible ?

Proof -

Given that he wants to play no more that 4 reggae songs.

So the possibility of choice of reggae song is 0, 1, 2, 3, 4

Now,

Case I -

If 0 reggae song is selected

⇒All 10 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₁₀ ₓ ⁷C₀ = 92,378

Case II -

If 1 reggae song is selected

⇒All 9 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₉ ₓ ⁷C₁ = 646,646

Case III -

If 2 reggae song is selected

⇒All 8 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₈ ₓ ⁷C₂ = 1,587,222

Case IV -

If 3 reggae song is selected

⇒All 7 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₇ ₓ ⁷C₃ = 1,763,580

Case V -

If 4 reggae song is selected

⇒All 6 songs selected from 7 blue, 7 disco, 5 pop,

Number of ways = ¹⁹C₆ ₓ ⁷C₄ = 949,620

So,

Total possible ways = 92,378+ 646,646+ 1,587,222+ 1,763,580+ 949,620

                               = 5,039,446

⇒Total possible ways = 5,039,446

Now,

Also the 10 songs selected can arranged themselves in 10! ways. ( because order of song played does not matter )

∴ we get

Different playlists possible = 10! × 5,039,446

                                          = 18287141644800

⇒Different playlists possible = 18287141644800

6 0
3 years ago
Select the values that make the inequality - 4z > - 28 true. Then write an
Olenka [21]

Answer:

vyxkgxgjxufxruzfjzfjzf

gxiggxifxifx

  1. xkzufxurzt
  2. izifxur
7 0
3 years ago
Find m angle Y
LiRa [457]
I think it is A 54 because I did it already and I got a 100
6 0
3 years ago
The work of a student to solve a set of equations is shown:
butalik [34]
Step 2! The reason for that is the student didnt multiplied (15-2z) with -2. But she should have!
8 0
3 years ago
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