Ֆիզիկա 11.09.24. Առաջադրանքներ

a² + b² = c²
AB² + BC² = AC² 
2² + (√5)² = AC² 
4 + 5 = AC²
AC² = 9
AC = √9 = 3 մ

Պատ․ 3 մ


x = 6 մ
y = 8 մ

a² + b² = c²
x² + y² = AC²

6² + 8² = AC²
36 + 64 = AC²
100 = AC²
AC = 10 մ

Պատ․ 10 մ


V = 36 կմ/ժ
s = 500 մ = 0,5 կգ
t – ?

t = s/V
t = (0,5 կգ)/(36 կմ/ժ) = 1/72 ժ = 3600/72 վ = 50 վ

Պատ․ 50 վ


s = 18 կմ = 1800 մ
V1 = 15 մ/վ
V2 = 10 մ/վ
V = V1 + V2
t – ?

V = V1 + V2 = 15 մ/վ + 10 մ/վ = 25 մ/վ
t = s/V
t = (1800 մ)/(25 մ/վ) = 72 վ

Պատ․ 72 վ


s = 600 մ
t1 = 25 վ
t2 = 15 վ
V2 – V1 – ?

V1 = s/t1
V1 = (600 մ)/(25 վ) = 24 մ/վ

V2 = s/t2
V2 = (600 մ)/(15 վ) = 40 մ/վ

V2 – V1 = 40 մ/վ – 24 մ/վ = 16 մ/վ

Պատ․ 16 մ/վ-ով


s1 = 600 մ
s2 = 300 մ
s = s1 + s2
V = 36 կմ/ժ
t – ?

s = s1 + s2 = 600 + 300 = 900 մ = 0,9 կմ
t = (0,9 կմ)/(36 կմ/ժ) = 1/40 ժ = 1,5 ր

Պատ․ 1,5 ր


V1 = 15 մ/վ
V2 = 10 մ/վ
s1 = 3/4s
s2 = 1/4s
t1/t2 – ?

t1 = s1/V1
t1 = (3/4s)/(15 մ/վ) = (1/20)s վ
t2 = s2/V2
t2 = (1/4s)/(10 մ/վ) = (1/40)s վ

t1/t2 = ((1/20)s վ)/((1/40)s վ) = 2

Պատ․ 2 անգամ


V1 = 15 մ/վ
V2 = 10 մ/վ
V = V1 + V2
t = 30 վ
s – ?

V = V1 + V2
V = 15 մ/վ + 10 մ/վ = 25 մ/վ

s = t * V
s = 30 վ * 25 մ/վ = 750 մ

Պատ․ 750 մ


x = -3 + 5t
y = 7 – 12t
|V| – ?

Vx = 5 մ/վ
Vy = 12 մ/վ

a² + b² = c²
Vx² + Vy² = V²
5² + 12² = V²
25 + 144 = V²
169 = V²
V² = √169
V = 13 մ/վ
|V| = 13 մ/վ


Vհյուսիս = Vհ =16 մ/վ
Vարևելյան = Vա = 12 մ/վ
V – ?

a² + b² = c²
Vհ² + Vա² = V²
16² + 12² = V²
256 + 144 = V²
400 = V²
V² = √400
V = 20 մ/վ

Պատ․ 20 մ/վ


|AB→| = 3
|BC→| = 6
<ACB – ?

tan <ACB = |AB→|/|BC→|
tan <ACB = 3/6 = 0,5
<ACB = 30°

Պատ․ 30°


V1 = 12 մ/վ
V2 = 9 մ/վ
V1 – V2 – ?

V1 – V2 = 12 մ/վ – 9 մ/վ = 3 մ/վ

Պատ․ 3 մ/վ


V1 = 6 մ/վ
V2 = 8 մ/վ
V1 + V2 – ?

V1 + V2 = 6 մ/վ + 8 մ/վ = 14 մ/վ

Պատ․ 14 մ/վ


Vնավ = Vն
Vգետ = Vգ
Vն = 2 * Vգ
Vհակ/Vուղղ – ?

Vհակ = Vն – Vգ = 2 * Vգ – Vգ = Vգ
Vուղղ = Vն + Vգ = 2 * Vգ + Vգ = 3 * Vգ
Vհակ/Vուղղ = Vգ/3*Vգ = 1/3

Պատ․ 1/3


t1 = 6 վ
t2 = 10 վ
t3 = 4 վ
s1 = 30 մ
s2 = 110 մ
s3 = 20 մ
Vմիջին – ?

t = t1 + t2 + t3 = 6 + 10 + 4 = 20 վ
s = s1 + s2 + s3 = 30 + 110 + 20 = 150 մ
Vմիջին = s/t = 150/20 = 7,5 մ/վ

Պատ․ 7,5 մ/վ


V1 = 5 մ/վ
V2 = 7,5 մ/վ
s1 = s2 = 0,5s
Vմիջին – ?

t1 = s1/V1 = 0,5s/5 = 0,1s վ
t2 = s2/V2 = 0,5s/7,5 = (0,2s/3) վ
t = t1 + t2 = 0,1s + 0,2s/3 = 0,5s/3
Vմիջին = (t1 * V1 + t2 * V2)/t
Vմիջին = (0,1s * 5 + 0,2s/3 * 7,5)/(0,5s/3) = (0,5s + 0,5s) * (3/0,5s) = 3s/0,5s = 6 մ/վ

Պատ․ 6 մ/վ

Մաթեմատիկա 11.09.24

1. (x + 1)/(x – 3) > 0

    (x + 1)(x – 3) = 
    ⌈x + 1 = 0 ⇒ x = -1

    ⌊x – 3 = 0 ⇒ x = 3

    (x + 1)(x – 3) > 0
    x ∈ (-∞; -1) ∪ (3; +∞)

    x – 3 ≠ 0 ⇒ x ≠ 3

    Պատ․ x ∈ (-∞; -1) ∪ (3; +∞)


    2. (2x – 6)/(x + 4) ≤ 0

    (2x – 6)(x + 4) = 0
    ⌈2x – 6 = 0 ⇒ x = 3
    ⌊x + 4 = 0 ⇒ x = -4

    (2x – 6)(x + 4) ≤ 0
    x ∈ [-4; 3]

    x + 4 ≠ 0 ⇒ x ≠ -4

    Պատ․ x ∈ (-4; 3]


    3. ((x + 4)(3x – 6))/(2x + 10) > 0

    (x + 4)(3x – 6)(2x + 10) = 0
    ⌈x + 4 = 0 ⇒ x = -4
    |3x – 6 = 0 ⇒ x = 2
    ⌊2x + 10 = 0 ⇒ x = -5

    (x + 4)(3x – 6)(2x + 10) > 0
    x ∈ (-5; -4) ∪ (2; +∞)

    2x + 10 ≠ 0 ⇒ x ≠ -5

    Պատ․ x ∈ (-5; -4) ∪ (2; +∞)


    4. (x – 3)/((2x – 4)(x + 5)) ≥ 0

    (x – 3)(2x – 4)(x + 5) = 0
    ⌈x – 3 = 0 ⇒ x = 3
    |2x – 4 = 0 ⇒ x = 2
    ⌊x + 5 = 0 ⇒ x = -5

    (x – 3)(2x – 4)(x + 5) ≥ 0
    x ∈ [-5; 2] ∪ [3; +∞)

    2x – 4 ≠ 0 ⇒ x ≠ 2
    x + 5 ≠ 0 ⇒ x ≠ -5

    Պատ․ x ∈ (-5; 2) ∪ [3; +∞)


    5.(x(x + 5))/((2x + 6)(x – 7)) ≥ 0

    x(x + 5)(2x + 6)(x – 7) = 0
    ⌈x = 0
    |x + 5 = 0 ⇒ x = -5
    |2x + 6 = 0 ⇒ x = -3
    ⌊x – 7 = 0 ⇒ x = 7

    x(x + 5)(2x + 6)(x – 7) ≥ 0
    x ∈ (-∞; -5] ∪ [-3; 0] ∪ [7; +∞)

    ⌈2x + 6 ≠ 0 ⇒ x ≠ -3
    ⌊x – 7 ≠ 0 ⇒ x ≠ 7

    Պատ․ x ∈ (-∞; -5] ∪ (-3; 0] ∪ (7; +∞)

    Մաթեմ 10.09.24

    a-ի տեղը y եմ օգտագործել որպեսզի չխառնվի։

    5․ (y² – 9)x² – (2y + 6)x + 1 = 0

    D < 0
    a = (y² – 9)
    b = -(2y + 6)
    c = 1

    D = b² – 4ac = (-(2y + 6))² – 4 · (y² – 9) = 4y² + 24y + 36 – 4y² + 36 = 24y + 72
    D = 0
    24y + 72 = 0
    24y = -72
    y = -3

    D < 0
    y < -3

    Պատ․ y ∈ (-∞; -3)


    6. (y + 2)²x² – (y + 2)x² – 1 = 0

    D < 0
    a = (y + 2)²
    b = -(y + 2)
    c = -1

    D = b² – 4ac = (-(y + 2))² – 4 · (y + 2)² · -1 = (y + 2)² + 4(y + 2)² = 5(y + 2)²
    D = 0
    5(y + 2)² = 0
    5(y + 2) = 0
    y + 2 = 0
    y = -2

    D < 0
    y < -2

    Պատ․ y ∈ (-∞; -2)


    8. (y – 1)x² – x(y – 1) + 1 = 0

    D ≥ 0
    a = y – 1
    b = -(y – 1)
    c = 1

    D = b² – 4ac = (-(y – 1))² – 4 · (y – 1) = y² – 2y + 1 – 4y + 4 = y² – 6y + 5

    D = 0
    y² – 6y + 5 = 0

    y1y2 = c/a = 5
    y1 + y2 = -b/a = 6
    y1 = 1
    y2 = 5

    D ≥ 0
    y² – 6y + 5 ≥ 0
    a > 0
    y ∈ (-∞; 1] ∪ [5; +∞)

    a ≠ 0
    y – 1 ≠ 0
    y ≠ 1

    Պատ․ y ∈ (-∞; 1) ∪ [5; +∞)


    9. (y² – 4)x² + (y + 2)x + 2 = 0

    D ≥ 0
    a = y² – 4
    b = y + 2
    c = 2

    D = b² – 4ac = (y + 2)² – 4 · (y² – 4) · 2  = (y + 2)² – 8(y – 2)(y + 2) = (y + 2)(y + 2 – 8y + 16 = (y + 2)(18 – 7y)
    D = 0
    (y + 2)(18 – 7y) = 0
    ⌈y + 2 = 0 ⇒ y = -2
    ⌊18 – 7y = 0 ⇒ y = 18/7

    D ≥ 0 
    (y + 2)(18 – 7y) ≥ 0
    a < 0
    y ∈ [-2; 18/7]
    a ≠ 0
    y² – 4 ≠ 0
    y² ≠ 4
    y ≠ ±2

    Պատ․ y ∈ (-2; 18/7] \ 2


    12. yx² – 2(y – 1)x + y + 1 = 0

    D > 0
    a = y
    b = -2(y – 1)
    c = y + 1

    D = b² – 4ac = (-2(y – 1))² – 4 · y · (y + 1) = (-2y + 2)² – 4y² + 4y = 4y² – 8y + 4 – 4y² + 4y = 4 – 4y
    D = 0
    4 – 4y = 0
    4y = 4
    y = 1

    D > 0
    y > 1

    a ≠ 0
    y ≠ 0

    Պատ․ y ∈ (1; +∞)


    16. x² + 2(y – 1)x + y² – y – 2

    D > 0 
    c/a > 0

    a = 1
    b = 2(y – 1)
    c = y² – y – 2

    D = b² – 4ac = (2(y – 1))² – 4(y² – y – 2) = 4(y² – 2y + 1) – 4(y² – y – 2) = 4(y² – 2y + 1 – y² + y + 2) = 4(3 – y) = 12 – 4y

    D = 0
    12 – 4y = 0
    12 = 4y
    y = 3
    D > 0
    y > 3

    c/a = 0
    y² – y – 2 = 0
    a = 1, b = -1, c = -2
    x1 + x2 = -b/a = 1
    x1x2 = c/a = -2

    x1 = -2
    x2 = 1

    a > 0
    y² – y – 2 > 0
    y ∈ (-∞; -2) ∪ (1; +∞)
    y ∈ ((-∞; -2) ∪ (1; +∞)) ∩ (3; +∞)

    Պատ․ y > 3

    The impact of technology on young people

    While the internet has given us more interesting stuff to see, I feel like it has ruined the real world a little, as the internet tends to show the highlights of everything, when life is actually much more complicated. It has also likely ruined many people’s ability to socialize, as the anonymity on the internet gives people much more time to think than they would normally have and doesn’t provide the same feelings as face to face communication.

    English 09.09.24. David Schwimmer interview.

    1. David Schwimmer was born in New York and grew up in Los Angeles. He appeared as Ross Geller in the popular TV show, Friends. He’s also a stage actor and a film director.

    Once a journalist took an interview from him. He was asked 10 unexpected questions, and he gave unexpected answers to them.

    How would you answer to the same questions?  

    When were you happiest?

    David’s answer – Before I realized my parents, my sister and I were all mortal.

    Your answer – When I thought school/life was gonna get easier with each passing year.

    What is your greatest fear?

    David’s answer – Besides death? Standing on stage in front of thousands of people, forgetting what happens next, but knowing I’m supposed to be doing it. Also, being in the ocean alone and feeling something large brush against my leg.

    Your answer – A house fire.

    What is your earliest memory?

    David’s answer – Diving off a piece of furniture and onto my parents’ bed.

    Your answer – My fourth birthday.

    What or who is the greatest love of your life?

    David’s answer – The theatre.

    Your answer – My sisters.

    Is it better to give or receive?

    David’s answer – I am always happier giving, rather than receiving, a gift – and happiest when I give anonymously.

    Your answer – When I do either one disproportionately more than the other, it becomes boring. I don’t really prefer either.

    Where would you like to live?

    David’s answer – Near the ocean, one day.

    Your answer – In a spacious apartment.

    What is your guiltiest pleasure?

    David’s answer – Pizza and television, hopefully together.

    Your answer – Doing nothing and watching youtube.

    Who would you invite to your dream dinner party?

    David’s answer – Dostoevsky, Sophia Loren, Mahatma Gandhi, Gene Kelly, Martin Luther King Jr, Leonardo da Vinci, Charlie Chaplin, Cole Porter, Sade, my family, my friends, my lady and a translator.

    Your answer – Probably just my family and extended family (cousins, aunts, grandparents).

    When did you last cry and why?

    David’s answer – Three days ago, when I saw the film, La Vie en Rose. It reminded me how brief our time is here, and how wonderful it is to fall in love.

    Your answer – I usually tear up when I get really angry, I don’t remember the last time.

    What song would you like played at your wedding party?

    David’s answer – Don’t Stop ‘Ti/ You Get Enough by Michael Jackson.

    Your answer – I can’t really speak for what I’ll want in the future, but probably something classical.

    1. Do you know that before the 1950s they used to form special questions with prepositions in the front position? For example:

    In what issues are you interested?

    About what do you like to talk?

    Now the prepositions are put at the end.

    What issues are you interested in?

    What do you like to talk about?

    Translate these questions into English paying attention to the position of the prepositions.

    Here is some help for you: rely on – հույսը դնել մի բանի կամ մեկի վրա, confide in smb – վստահել մեկին, refer to – վկայակոչել մի բանին կամ մեկին, insist on – պնդել մի բանի վրա, consist of – բաղկացած լինել,

    Ինչի՞ համար ես սովորում անգլերեն:

    Why are you learning English?

    Ո՞ր ուսումնական առարկաներից ես լավ:

    Which subjects are you good at?

    Ի՞նչ իրերի վրա ես ամենաշատը փող ծախսում:

    What items do you spend the most money on?

    Ինչի՞ կամ ու՞մ մասին ես անհանգստանում:

    What or who do you worry the most for?

    Ու՞մ հետ ես սիրում անցկացնել քո ազատ ժամանակը:

    Who do you like spending your free time with?

    Ինչի՞ վրա ես հույսդ դնում:

    What do you rely on?

    Ինչ բաղադրիչներից (components) է բաղկացած նախագիծը:

    What components does the project consist of?

    Ո՞րն է քո տեսակետը: Ինչի՞ վրա ես պնդում:

    What is your view? What do you insist on?

    Որքա՞ն հաճախ են վկայակոչում նրա տեսակետը:

    How often do they refer to their view?

    Ու՞մ ես վստահում: Ո՞վ է քո ամենամոտ ընկերը:

    Who do you confide in? Who is your closest friend?

    1. Some people are of the opinion that technology has made young people happier because it has made their life more interesting. Others think that technology has made young people’s life more stressed in physical environment because they feel at ease in virtual environment.

    What is your opinion?

    While the internet has given us more interesting stuff to see, I feel like it has ruined the real world a little, as the internet tends to show the highlights of everything, when life is actually much more complicated. It has also likely ruined some people’s ability to socialize, as the anonymity on the internet gives people much more time to think than they would normally have and doesn’t provide the same feelings as face to face communication.

    Should guns be sold to people?

    Whether people should be able to buy guns is a very controversial topic, with gun laws varying greatly around the world. Personally, I believe guns should be sold, as if they are completely unavailable for purchase, criminals with experience will still be able to get their hands on guns. However, guns shouldn’t be available to anyone.

    For cars, you need to have a driving license, for which you need to take a test. I believe guns should have something similar. While gun licenses do already exist, I feel as though obtaining one should be harder. It should require mandatory lessons and a test, as a shockingly large amount of gun accidents happen from people not knowing basic gun safety. It should also require a background check and psych evaluation to ensure there are no bad intentions.