Wednesday, August 1, 2018

Youtube daily report Aug 1 2018

LIVERPOOL captain Jordan Henderson is no longer guaranteed a starting spot following Jurgen

Klopp's spending spree, a report claims.

Henderson was one of the club's unsung heroes last term en route to the Champions League

final while the Reds' front three of Mohamed Salah, Roberto Firmino and Sadio Mane grabbed

the headlines.

Henderson made 41 appearances last season before going on the play a key part in helping

England reach the semi-finals of the World Cup in Russia.

Klopp has strengthened heavily this summer splashing out more than £170million to bring

in Naby Keita, Xherdan Shaqiri and Brazil duo Fabinho and Alisson.

And according to the Liverpool Echo, Henderson's place in the starting line-up is no longer

guaranteed despite being the club captain.

The report suggests that the 28-year-old will more likely be used in a squad rotation system

with new boys Fabinho and Keita.

It is also said the trio could occasionally start together but that option would be preferred

for bigger games.

Meanwhile, Klopp insists his side do not need to fill the void left by Philippe Countinho's

departure to Barcelona.

"I don't want to put one of my players in the position where people will now say constantly

'he's the Phil replacement'," said the Reds boss.

"We don't need to replace Phil.

We need to make a squad for the next year.

"Out there on the market, there isn't a Phil Coutinho light.

It's not there.

"But there are a lot of good players and we have brought a few of them in."

For more infomation >> Will Liverpool 's Jordan Henderson be forced out of the side by Fabinho & Keita ? ● News Now ● #LFC - Duration: 2:01.

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Těžký osud herečky Aleny Vránové: Pyšná princezna bojovala s despotickým manželem - Duration: 5:43.

For more infomation >> Těžký osud herečky Aleny Vránové: Pyšná princezna bojovala s despotickým manželem - Duration: 5:43.

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"M*A*S*H"-Serienheld Alan Alda ist an Parkinson erkrankt - Duration: 2:41.

For more infomation >> "M*A*S*H"-Serienheld Alan Alda ist an Parkinson erkrankt - Duration: 2:41.

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Rarities 0.5ctw Black Diamond Sterling Silver Negative S... - Duration: 11:52.

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Rarities 0.5ctw Black Diamond Sterling Silver Negative S... - Duration: 1:54.

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Audi A7 Sportback 50 TDI 286pk tiptronic quattro Pro Line S - Duration: 1:10.

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Mazda 6 2.0 S-VT Bns Plus - Duration: 1:05.

For more infomation >> Mazda 6 2.0 S-VT Bns Plus - Duration: 1:05.

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汪小菲看见"昂贵"水果,赶紧递给大S,旁边蒋勤勤的表情亮了 - Duration: 1:37.

For more infomation >> 汪小菲看见"昂贵"水果,赶紧递给大S,旁边蒋勤勤的表情亮了 - Duration: 1:37.

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2018 PBS Online Film Festival Winners - Duration: 0:31.

- Sometimes the universe just says here you go.

It's our time to shine, man.

- [Child] Cool.

- [Woman] It's about connection--

- Yeah. - and it's about life.

(crowd cheering)

(upbeat, joyful music)

(train whistle blaring)

It's like watching magic.

It's pretty cool.

For more infomation >> 2018 PBS Online Film Festival Winners - Duration: 0:31.

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Tumbler Chase Scene | Batman Begins (2005) Movie Clip - Duration: 4:59.

I've gotta get me one of those.

- He is in a vehicle. - Make and color?

It's a black...

...tank.

Stay calm.

You've been poisoned.

I'm on him.

Breathe slowly.

Hold on.

- What are you doing? - Shortcut.

Air One to ground, block that ramp.

He's got no way off that roof.

Turn off your engine. Step away from the car.

- Trust me. - Weapons system activated.

Who is this guy?

- Where's he going? - He's on the roof.

- What street is he taking? - He's not on a street.

He's flying on rooftops.

At least tell me what it looks like.

Never mind.

Got him.

Coming right up on his butt.

We're tracking suspect vehicle heading west on l- 17.

- Air One to ground. - I lost him.

We've lost visual. Exit 9 is blocked.

We'll loop back to check the frontage road.

Stealth mode activated.

Stay with me.

What...? There he is.

Just hold on.

Rachel!

For more infomation >> Tumbler Chase Scene | Batman Begins (2005) Movie Clip - Duration: 4:59.

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Zoom U-44 Overview - Duration: 3:40.

Hi everyone, this is John from Zoom and I'm here to introduce you to the U-44 Handy Audio Interface.

The U-44 is a compact, 4-in/4-out audio interface that enables you to record and perform wherever you are.

Small enough to fit in the palm of your hand,

the U-44 comes equipped with the features you need to record 24-bit/96 kHz audio anywhere.

Use the U-44 with your PC, Mac, or iPhone/iPad via USB.

Or as a standalone converter and mic preamp.

Inspired by our Zoom H-series recorders, the U-44 is equipped with high-performance, low-noise mic preamps

that enable recording and playback at resolutions up to 24-bit/96 kHz.

Plus compatibility with Zoom's Interchangeable Input Capsules.

The U-44 features a full array of inputs and outputs

so you'll always be prepared for any recording or live performance.

Two combo inputs with independent gain knobs and multi-color level indicators

provide flexibility for connecting mics, keyboards, and mixers.

48V phantom power can be supplied to inputs 1 and 2,

and input 1 supports hi impedance input for connecting passive guitars, basses, or other instruments.

MIDI I/O jacks enable synchronization with devices like electronic keyboards,

controllers, and synthesizer or sampler modules.

Thanks to its 10-pin connector, the U-44 is compatible with all of our interchangeable input capsules,

representing a powerful field recording setup.

Choose from six capsules—X/Y, Shock Mount X/Y, Mid-Side, Shotgun, Stereo Shotgun, and

Dual XLR/TRS Combo Input—each with its own unique applications.

Wherever you want to record, the bus-powered U-44 forms the perfect centerpiece of your mobile studio.

Connect instruments, monitors, and other devices when you're recording at home.

Or hook it up to your iPhone or iPad to make music on the go.

If bus power isn't available, the U-44 can run on just two AA batteries, allowing you to record anywhere.

With advanced monitoring options, the U-44 lets you dial in your ideal mix.

Create a balanced headphone mix between your click track and main out signals during live performances.

Or balance the cue and main out signals when you're DJ'ing.

The outputs of channels A and B can be muted, providing even more control.

Plus, direct monitoring enables you to hear the live signal you're recording without latency.

Multiple output options—including 1/4", RCA, and S/PDIF,

allow you to connect DJ mixers, speakers, and more.

Monitoring your mixes is easy thanks to a studio quality headphone output with independent volume control.

The direct monitor knob makes it possible to blend your headphone mix between the input and playback signals.

Perfect for live electronic music performance and DJ'ing.

When you're transferring audio, high-quality AD/DA conversion is critical.

The U-44 functions in standalone mode as a high-quality mic preamp and AD/DA converter

to ensure complete transparency when converting audio formats.

Combine the U-44 with Pro Tools First, Ableton Live 9 Lite, and Steinberg Cubasis LE, all included with the U-44

so you will have everything the modern music creator needs.

For more information about Zoom products, please visit zoom-na.com

For more infomation >> Zoom U-44 Overview - Duration: 3:40.

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Audi A5 Cabriolet 2.0 TFSI 252pk quattro s-tronic Sport Pro Line S - Duration: 1:13.

For more infomation >> Audi A5 Cabriolet 2.0 TFSI 252pk quattro s-tronic Sport Pro Line S - Duration: 1:13.

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Esl Learn English Alien Dance Music Video - Learning Color Dan Kids Show | Musically Compilation - Duration: 1:40.

Learn Colors Alien Dance Musically 2018 education give me your little song

For more infomation >> Esl Learn English Alien Dance Music Video - Learning Color Dan Kids Show | Musically Compilation - Duration: 1:40.

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5 recettes à l'eau de rose pour embellir votre visage - Duration: 10:15.

For more infomation >> 5 recettes à l'eau de rose pour embellir votre visage - Duration: 10:15.

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Po půl roce u Gacíkových - Duration: 2:07.

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Audi A4 Avant 1.4 TFSI 150pk s-tronic S Line Black Edition - Duration: 1:09.

For more infomation >> Audi A4 Avant 1.4 TFSI 150pk s-tronic S Line Black Edition - Duration: 1:09.

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Toyota RAV4 2.0 VVTi Comfort 2WD - Duration: 1:06.

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Why Trump may want to rethink a government shutdown - Duration: 6:43.

For more infomation >> Why Trump may want to rethink a government shutdown - Duration: 6:43.

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Toyota ProAce Worker 2.0 D-4D Professional 122PK EX BTW - Duration: 0:53.

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Toyota Hilux Xtra Cab 2.4 D-4D 4WD Prof excl BTW - Duration: 1:06.

For more infomation >> Toyota Hilux Xtra Cab 2.4 D-4D 4WD Prof excl BTW - Duration: 1:06.

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Toyota Hilux Xtra Cab 2.4 D-4D 4WD Prof excl BTW - Duration: 1:06.

For more infomation >> Toyota Hilux Xtra Cab 2.4 D-4D 4WD Prof excl BTW - Duration: 1:06.

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Toyota Hilux Xtra Cab 2.4 D-4D 4WD Prof excl BTW - Duration: 1:06.

For more infomation >> Toyota Hilux Xtra Cab 2.4 D-4D 4WD Prof excl BTW - Duration: 1:06.

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Helping You To Sleep ASMR RolePlay - Duration: 20:27.

Hi there how are you?

I'm fine, thanks for ask

Yes, I will tell you, this center is for help people to fall asleep

That's the point of this, it's for people who's having sleep problems

Many times it's for stress or anxiety

And what we do in this center is help people through visual and auditive stimuli

So the person can get some relaxation and sleep

We use here a technique call "ASMR" you probably hear about it

Yes, the ASMR is when you feel a tingly sensation

with help of some triggers

those "triggers" are the main thing that gives you ASMR

You can feel ASMR through different triggers

There's some people how don't the tingles feel it at all

But even when they don't feel the tingles they get relaxed and sleepy

For example

There's people that react to certain kind of triggers

For example, hear this with your eyes closed

Yes. This sound is a classic "crinkle sound" trigger

There's people who loves this trigger and they feel the tingles

But there are other who doesn't, but if the sound is low they get relaxed

It's like put some white noise

For example a little bit of rain sound

Let's put some rain sound now

and so, let's make the rain hear a little bit

The rain sounds tends to help a lot of people

It's a perfect background noise

Yes, exactly if you let yourself go the sound will relax you

Yes, and it's better because your hear from ear to ear

The most important thing about all this is always be in a quiet place

Be calm to hear all this kind of sounds

That's right, because if you are trying to relax and sleep, with your headphones on

With some music or videos, in a low volume

It's all think so you can relax, without extra noises

So, if your are trying to get sleep and in the other room there is someone with a hammer

You probably cannot sleep

that's why when you use this kind of videos or this sounds, you must be in a quiet place

Better if it's at night

so you can take the most of it

making sure that there's no extra noise

should I leave the rain sound on?

I will leave it on but lets down a little bit

So the technique that we gonna use today is a Guided relaxation

but at the same time I will be doing some triggers

To see if you feel something, please let me know if you feel the tingles

You be calm, I want you to lay down

Yes, perfect

Try to stay in the most confortable position

please close your eyes

Don't be afraid of sleep, the only thing that I will ask you is that let me know if you feel any tingles

So I can know that to some triggers you feel ASMR

How are the tingles? You will feel some kind of shaking chills

In the back of your neck

It's a very nice sensation, you will no laugh haha

It's the kind of tingle that relaxed you, you will notice if it happen

So let's star with the triggers

I will start with this sponge

Keep your eyes close, relax and don't thing about anything

hear the rain sound, and if it relaxed you, hear my voice

the sounds will travel through your ears.

imagine that you are in your favorite place

in a place where you feel fine

it's important that you let yourself go through the sounds

the sounds must fill all your head

so you can relax

That you free your head of stress

So you can think in absolutely nothing

the rain sound and my voice

to the point that all disappears

a simple company to your travel to the dreams

where you will fall asleep

without anything or anyone who bother you

I will be changing triggers to follow your dreams

Feels fine get out of all the problems for a couple of hours

taking off all the stress, the anxiety

and take a break and let yourself go

it's very important that you can rest, so tomorrow you can deal with everything more calm

That's why here and know, in the place that you choose to relax, you will be calm as posible

we leave all the problems behind for a while

So you can relax your mind

For more infomation >> Helping You To Sleep ASMR RolePlay - Duration: 20:27.

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Shuffle Review - Unlimited Phone Number App for Your iPhone! - Duration: 6:24.

For more infomation >> Shuffle Review - Unlimited Phone Number App for Your iPhone! - Duration: 6:24.

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5 recettes à l'eau de rose pour embellir votre visage - Duration: 10:15.

For more infomation >> 5 recettes à l'eau de rose pour embellir votre visage - Duration: 10:15.

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CRASH BANDICOOT N. SANE TRILOGY (PC) | Part #12 - GETTING THE BOXES!! - Duration: 21:17.

hi guys and welcome back to crash bandicoot the insane trilogy now it's

actually been quite a while since I played there's been a couple of weeks

because obviously I recorded quite a few things in advance and obviously last

time we finally got the gem cuz I had to cut it cuz I got very angry it took me

an hour and a half so I thought what we should do today let me just switch to

call call and we are going to go back and complete the levels get the crates

because we now obviously we've got the green gem it unlocks and different

sections of the other one so we're gonna try and we're gonna go back and do these

so I'm going to be recording for quite a lot for quite a lot of time today

because I'm trying to get ahead for you guys whilst I go on holiday which is not

good so we're going for jungle rollers with coca so we're gonna do all these

extra go back and thingy levels with Coco because I think that I think that's

quite fitting I don't know yep so this weekend I've just I've just got back

from camping the weather was horrible despite the fact the UK being sunny

everywhere else and yeah it was not not at all so we're

gonna do we're gonna go and get back all these and then we're gonna carry on with

heavy machinery which is the level we have got to oh no okay pop pop drive so

we're going back to get all the boxes that's the that's the idea of this

wasn't this some thanks I like it kick it's pretty cool but yeah so um let me

think there was like her or just gonna say there was there's a few of the state

all the gems we're gonna get and if I don't know whether the challenge is are

different to get each gem why we see that one way we couldn't done

yeah I was just you know just I was just giving you an example you know I was

like yeah yeah that's that shit oh my god about 31 that's right yeah

we got tons of lives from the level yeah so because you can't die that made it so

tough you know you I think I would get almost the end of

the level and if he died you have to do the complete thing all over again

and the annoying thing was you have to you have to completely reload so it

wasn't like a quick sort of crash restart the level kind of thing it was a

proper like I had to reload everything that's go back out to go back to the

level so how I kept my cool I was a lot calmer than I thought I was gonna be oh

yeah so yeah so we're gonna be redoing a few levels I need to pay attention it's

been a while okay okay it's been it's been at least a week in a bit since I've

played this so give me give me strength so yeah so I'll be going on holiday look

here we go look here's the gym it's the here's the new platform so yeah

so by the end next this time next week although well the timer the time it

recording not when you're going to get this I am going to be ogre nice I'll be

on holiday enjoying the Sun and I'm going to be taking Crash Bandicoot with

me on my with me on holiday so I will be playing it up see I won't be able to

record it well it's not that it's not the problem I probably could record it

on my laptop however it's not blade in it and you

don't I did we don't get you think it good see we're doing a good Wi-Fi where

we are okay forget it to the same place this is like our 15th year in a row

Yeah right so hopefully that's all the crates at this level now we've got this

thing was it three I have no idea how many we had left whoa wait for the

skunk's yeah I'm gonna be trying the could be like I'm trying to get as much

record as I can today there's gone I'm trying to get a bit of northern Springs

done a bit of yeah I've got my n I've got my ocular set up as well now so I'll

get and going to hopefully I'm gonna might get a bit of VR for you guys one

holiday say though the facility I want to do a year I want to do a proper

update but um I think I'm going to be uploading like one Episode a day just so

although it's not gonna be you know you're not gonna be getting 30-second

mods and stuff at least it'll give you something once a day that's that's

that's what I'm trying to so any like 1414 stuff so I'm thinking if I can get

like roughly three hours of this she'll give you 9 episodes and then I'll get

the other episodes of northern Springs that's a massive model oh no we didn't

get them all oh for God's sake God's sake me talking at me talking to you

guys yeah I can get the boxes again it was just the germ I'm used to I'm used

to having to quit the level after last time

after doing about 50 times before

me not paying attention I need to get these boxes goddamnit

well we'll do the tough I'm not quite sure on the time trial thing is this I

don't know I don't know how I feel about doing the trial trials ghosts like to

get the Platinum of it if I remember correctly you have to do you have to

beat the time but you've also gotta get all the boxes as well just to add insult

to injury let's try and not lose any acuities this time yes that would be bad

so China I'm trying to blast these Oh God trying to blast these Devils as

quick as I can yeah so I've just finished doing a video on the fallout 76

beta because we finally be given information and of course yeah that's

the information out to come out when I was away on a camping trip so that's

really frustrating always happens I want to be like one of the first to get the

information to you guys but obviously other things happen nope thank you no no

need that like one client Thanks

I see this is not life anymore

so we've got to get them you've got to get the bonus okay we've got the life

back right I was over said I think it was on said I missed two on the bonus

that she's weird

hmm oh did I read the wrong thing there's literally five boxes I kind of I

can't have possibly missed them I don't know

oh right sorry I I just recited that lower for no reason didn't I Oh kidding

me here the two boxes and we have unlocked the Joe can you see it

got all the boxes yi oh god he died give me the jam yay okay that's one Jam folks

I'll try not to restart another level perfect thank you oh we got a key

oh no that's just telling me I've got one key cool thanks Kay Kay good oh my

god you should have seen I think it was in the other day some of the idols that

Koga has is safe when she starts getting it like it a failure now I'm doing like

some selfies it's very funny very funny the great great

I can't remember well from its now some of me my not able to do because like

some of them require the different gems

will be to go oh I've got it but I'm pom-pom but I'm I haven't had

many of these actually I don't know many super will be diggers and there we go

bonus time time to get the boxes

okay pong buying buying got it two more we'll take those lives nicely

done Evan out of it alert maybe on the platform thank you eight boxes to go oh

no this is not one of the green gem ones okay that looks like yellow so we can't

get that one yet oh I need to run it should really say like what one it is

because I don't want to have to play through everyone Bogdan that one up

stream see I think I think this might like require like both gems so what I'm

thinking I love those I love the sound of hope for those issues so funny

was this the one we had to go back for before I'm pretty sure it was

mr. Go Go Go Go Fish oh my god really James really you got attacked by

the gobble-gobble fish it's that technical night that's why I'm

calling this for no one no gobble gobble fish no oak another

gobble gobble fish mister gobbles Oh No yeah well I don't know can't do this one

I'm not dead yep thank you we don't need to carry on with this one

I wonder if I press pause neither it tells me alright

no that's good can I do that

Rolling Stones let me see if I pause it see if it'll tell me like maybe as an

outline of the color would be helpful if it was it doesn't say which is a bit

unfortunate

I didn't know we could blast them through them we just check I've

forgotten I have a funny thing this was one where

it had it had a a box we couldn't see

like here or something there we go oh I did not know there was a and here

abrió on this one release oh Jesus do you know give me give me me one pose

simple mistakes steer this money in them so we got to look out for the Brio stuff

cuz I I have you already got it I've

checkpoint right oh I did not see naked bounce on them tears China I'm sorry I'm

just getting paranoid the missing boxes

the rest are just I don't need them

ah hang on Oh God I thought this turtle might be

here for a reason maybe not no no no no no no no it's not that I need another

one I need a Brio nope maybe it's just I'm gonna get we're gonna get to a path

aren't we that we go on we're just gonna end up getting to a path we can't go on

isn't it that's what's gonna happen now look so there must be one here it must

be the most yeah

okay none no extras oh no right we got the bonuses anyway let's get the out

first

Wow definitely other Sundays no I love the life life's lives right so collects

limes also here nightly that's that's what else for doing for the harder

levels when we need like 12 million lives we've got 50 lives it's pretty

good innit we should be okay for when we get to the see that blue one god damn it

which means you don't get those lines either

no I've done that one hog wild native fortress and then we run to the second

island of the creek by native fortress

let's see if this one's a green one I almost hope it doesn't cause this

one's way they were fastest level is showing it's a bit difficult bit our

guts let's try again eat me thanks mister plant Oh

Oh that was an achievement yeah completely that was that was completely

intentional ladies and gents completely well and truly hey no food for you

sucker so is that challenges I need to actually

I need to get killed by certain enemies didn't realize that sure we can I'm sure

I can make that happen pretty easily no time on this one okay jobs the good news

there was one where we missed like it said we missed Windsor boxes and I think

I'm over this one

fire fires nice show good

doo-doo-doo-doo-doo-doo no nope nope nope

big ol knope's to you nope nope nope nope nope nope nope okay got you sucka

Oh God Oh God do-do-do-do-do that was the key okay

I would rather voice it up than be completely murdered to be honest all

right fairness nice um Oh any Firefox's Hey

name up nope better be two bucks whose coin coin take the lives nicely done see

you know this is what I was saying about the game is like it's a massive like

skill change between like you have the first island and then suddenly whack

they hit you with this next next level oh you know difficulty change see cuz

some some of these levels could be could have invisible things but are they okay

good job we got that checkpoint

For more infomation >> CRASH BANDICOOT N. SANE TRILOGY (PC) | Part #12 - GETTING THE BOXES!! - Duration: 21:17.

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Fenerbahçe 2-1 Cagliari Maç Özeti | 1 Ağustos 2018 - Duration: 2:59.

For more infomation >> Fenerbahçe 2-1 Cagliari Maç Özeti | 1 Ağustos 2018 - Duration: 2:59.

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F.1F.T.Y SH4DES FR33D 2018 - Duration: 1:25:52.

For more infomation >> F.1F.T.Y SH4DES FR33D 2018 - Duration: 1:25:52.

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Lexus GS 450h F Sport Line - Duration: 1:08.

For more infomation >> Lexus GS 450h F Sport Line - Duration: 1:08.

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Lexus GS 450h F Sport Line - Duration: 1:08.

For more infomation >> Lexus GS 450h F Sport Line - Duration: 1:08.

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Will Liverpool 's Jordan Henderson be forced out of the side by Fabinho & Keita ? ● News Now ● #LFC - Duration: 2:01.

LIVERPOOL captain Jordan Henderson is no longer guaranteed a starting spot following Jurgen

Klopp's spending spree, a report claims.

Henderson was one of the club's unsung heroes last term en route to the Champions League

final while the Reds' front three of Mohamed Salah, Roberto Firmino and Sadio Mane grabbed

the headlines.

Henderson made 41 appearances last season before going on the play a key part in helping

England reach the semi-finals of the World Cup in Russia.

Klopp has strengthened heavily this summer splashing out more than £170million to bring

in Naby Keita, Xherdan Shaqiri and Brazil duo Fabinho and Alisson.

And according to the Liverpool Echo, Henderson's place in the starting line-up is no longer

guaranteed despite being the club captain.

The report suggests that the 28-year-old will more likely be used in a squad rotation system

with new boys Fabinho and Keita.

It is also said the trio could occasionally start together but that option would be preferred

for bigger games.

Meanwhile, Klopp insists his side do not need to fill the void left by Philippe Countinho's

departure to Barcelona.

"I don't want to put one of my players in the position where people will now say constantly

'he's the Phil replacement'," said the Reds boss.

"We don't need to replace Phil.

We need to make a squad for the next year.

"Out there on the market, there isn't a Phil Coutinho light.

It's not there.

"But there are a lot of good players and we have brought a few of them in."

For more infomation >> Will Liverpool 's Jordan Henderson be forced out of the side by Fabinho & Keita ? ● News Now ● #LFC - Duration: 2:01.

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Прогноз руны дня на сегодня 2 августа 2018 года от Наталии Рунной #рунныймаг - Duration: 2:43.

For more infomation >> Прогноз руны дня на сегодня 2 августа 2018 года от Наталии Рунной #рунныймаг - Duration: 2:43.

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4.7 - Video 2 - Inverse Trigonometric Functions - Duration: 3:25.

We will apply the concepts of inverse functions to the sine, cosine, and tangent functions.

Here is the extended chart of values for these functions.

We have put it into a chart instead of an arrow diagram to save space, but the information

is still the same.

Let's take a moment to focus on the sine chart.

Remember that the inverse asks the question, "Given an output value, what input value

could it have come from?"

We'll focus on a specific value.

If sin(theta) = sqrt(3)/2, what can we know about theta?

By looking at the chart, we can see that pi/3 and 2 pi/3 are both possible values of theta.

But because of the periodicity of the sine function, we know that if we add or subtract

multiples of 2 pi to these, we will get even more values.

This means that the inverse isn't going to be a function unless we restrict the range.

In this case, it turns out that the interval [-pi/2, pi/2] is the natural choice.

So when we ask what arcsin(sqrt(3)/2) is, the answer will be pi/3.

We can look at the cosine and tangent charts in the same way.

If we look at the cosine chart, the interval [0,pi] turns out to be the most natural range to

pick.

For the tangent function, we restrict ourselves to (-pi/2, pi/2).

We have grayed out a couple values because the tangent function isn't actually defined

there at +-pi/2, but those endpoints are important values to know.

To get the inverse functions, we simply swap the rows in our restricted charts.

We could also rearrange the rows to put the x values in increasing order, but we'll

leave it in this form for now.

Let's look at this graphically.

Here is the graph of the sine function.

Recall that the graph of the inverse is the graph we get when we reflect this across the

line y=x.

This will result in a curve that vibrates left and right as it goes up the y-axis.

Notice that this fails the vertical line test, so it's not a function.

But by restricting the range to the interval [-pi/2, pi/2], we will get a graph that does

represent a function.

This is the same effect as restricting the chart of values from earlier.

Looking at the cosine function, we see that the inverse has the same back and forth behavior

as the sine function, so we would also need to restrict the range.

From the picture, it makes a little more intuitive sense why we pick the range as we do.

It has to do with finding a piece of the graph that can pass the vertical line test.

There are other pieces that we could have picked, but notice how those values end up

being further away from the origin or negative.

So the choice of the range of the inverse cosine is in this sense the natural choice.

The inverse tangent function is different because it extends from negative to positive

infinity.

We still have the problem of repeated values, so we will restrict the inverse to just the

connected piece that passes through the origin.

The important idea to get out of this video is that all of these steps are really

trying to define a function that can answer the question, "Given an output value, what

input value could it have come from?"

If you keep focused on this question, you will find the inverse functions to be less

confusing.

In the next video, we're going to take a look at a geometric interpretation of the

inverse trigonometric functions.

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