♪♪ ♪ WHEN WE’RE TOGETHER THESE
ARE THE HAPPIEST TIMES FOR ME ♪ ♪ LAUGHING AND PLAYING
HAVING FUN WITH MY FAMILY ♪ ♪ MY CHILD, ME AND BABYFIRSTTV ♪ ♪ MY CHILD, ME AND BABYFIRSTTV ♪ ♪ MY CHILD AND ME ♪ ♪ WHEN WE’RE TOGETHER ♪ ♪ SHOWING YOU ALL
THAT THERE IS TO SEE ♪ ♪ SHARING AND LEARNING ♪ ♪ JUST HOW WONDERFUL
THE WORLD CAN BE ♪ ♪ MY CHILD, ME AND BABYFIRSTTV ♪ ♪ MY CHILD, ME AND BABYFIRSTTV ♪ ♪ MY CHILD AND ME ♪ ♪♪ ♪♪ ♪ MY CHILD, ME AND BABYFIRSTTV ♪ ♪ MY CHILD, ME AND BABYFIRSTTV ♪ ♪ MY CHILD AND ME ♪ ♪ WHEN WE’RE TOGETHER ♪ ♪ WATCHING YOU GROW
SO BEAUTIFULLY ♪ ♪ SMILING AND DREAMING ♪ ♪ ABOUT ALL THE JOYS
THE NEXT DAY WILL BRING ♪ ♪ MY CHILD, ME AND BABYFIRSTTV ♪ ♪ MY CHILD, ME AND BABYFIRSTTV ♪ ♪ MY CHILD, ME
AND BABYFIRSTTV ♪♪
Olly look at my Cheeky Chompers neckerchew, it’s right here for me to dribble and chew on and I can’t drop it on the floor. Oh my mummy bought me that muuuunths ago … And my Cheeky Chompers Comfortchew to cuddle and chew I’ve had THAT for weeks … Here’s Chewy, my Hippo teether Hippo? What Hippo ?! And my attached Cheeky Blanket with cosy hand pouch and fun tags Blanket? Fun tags? Mummyyyyy! To keep your baby happy, visit cheekychompers.com Developed by mums who make great stuff that helps.
Who’s that swinging up and down?
LA—RRY Join him as he has some fun
LA—RRY! Look at Larry he’s so bright
LA—RRY Learns new words and gets them right Vocabu-Larry, Vocabu-Larry Say that word out loud Vocabu-Larry, Vocabu-Larry That’s what it’s about Vocabu-Larry, Vocabu-Larry That’s what it’s about Hello Larry. Hello! Larry, look! It’s ok Larry. Do you know what it is? This is an apple. Apple? Yes, apple. Apple. Apple! Apple! Apple! Apple! Apple! Right Larry, many apples. Many apples! Many apples! Time to go home now. Goodbye Larry! Goodbye! Goodbye!
>>This is Your Math Gal, Julie Harland. Please visit my website at YourMathGal.com, where all my videos are organized by topic. We’re going to solve this multiple angle trig equation, and we’re going to be using a calculator, so make sure you have a scientific or graphing calculator with you. Find all values of x in degrees that satisfy this equation. Round degrees to the nearest tenth of a degree. And then we’re also going to state the values in degrees in this interval 0 to 360 degrees. Alright. So it’s solve for tangent, right? But this isn’t a special value, this negative 3.2, so we’re going to have to use the inverse tangent. So remember what that means. If the tangent of this angle equals negative 3.2, then the angle, alright, which is 4x… is the inverse tangent of 3.2. Remember, this is an angle, so if you put this in your calculator in degree mode, it will come out to an angle in degrees. But since it’s negative, it’ll be between negative 90 degrees and 90 degrees, because that is the range for the inverse tangent function. But we have to remember the tangent is, has a period of pi, or 180 degrees; so to get all the possibilities, we would have to add 180 degrees times k. Now, this will give us all the solutions once we solve for x, which we’re going to do. But then remember, we’re going to look for which solutions are in between 0 and 360. Okay, so what do I do from here? I need to divide everything by 4 to solve for x. Keep in mind, again, this tangent inverse of 3.2, that is just something in degrees. Once you plug it in your calculator, it’s going to come up to something in terms of degrees. It is an angle. Okay, now, we’ve got to be really careful when you use your calculator when you do this calculation here, this inverse tangent of 3.2. You might first want to just put the inverse tangent of 3.2, enter it, and then divide it by 4. Otherwise make sure you’re using your parentheses carefully, because we don’t want to do 3.2 divided by 4. We want to first do the inverse tangent and then divide by 4. And then we’re going to round that to the nearest tenth of a degree. So I have, when I plug that in, negative 18.2 degrees, and this isn’t exactly equal because I rounded to the nearest tenth; plus, what’s 180 degrees divided by 4? That’s 45 degrees k. So keep in mind this first angle, negative 18.2 degrees, is not in between 0 and 360. But this is a perfectly okay answer. This will give you all the possible answers where k is an integer. Sometimes people like this first number to be positive. So to get the first positive number, you could just go over here and do, well, what is negative 18.2 plus 45? Okay. So you do that, and you could also just do that on your calculator if you add 45. And you’re going to get 26.8. So another way you might write this is 26.8 degrees plus 45 degrees k. So either of these really do give you all the solutions to this problem. Tangent of 4x equals negative 3.2. But now the question is, what are the values in degrees between 0 and 360? Okay, well, the first one would be 26.8, remember? Because if I subtract 45, I’d be at this negative angle. And so once you have that, once you have 26.8, then you just add 45 to get another one, and that would be 71.8 degrees. It’s still less than 360. And then you would just add 45 again to get the next one, which is 116.8 degrees. Then you would just add 45 again until finally you can’t get anything — once you get up to 360, you’re done. So in other words, just keep doing this: add 45, add 45, and get them all so we’re at 206.8 degrees. I’m doing this in real time. I’m adding 45 on my calculator over and over. 25… 251.8 degrees and I think I — what happens if I add 45 again? Whoop — running out of space. Let’s see, make this a little bit smaller so I can get all the values in on one line. Alright. So 296.8 degrees. Add 45 again, 341.8. I think that’s it. I think if you add any more, you’re going to be too high up. So let’s see. It’s the last one, and hopefully you can see that. So I ended up with one, two, three, four, five, six, seven, eight; there’s eight solutions between 0 and 360 degrees. This is Your Math Gal, Julie Harland. Please visit my website at YourMathGal.com where all of my videos are organized by topic.
[MUSIC PLAYING] She was out cold
when we first found her. She needed our help. We needed her help too. Since the fractures… …things…changed. The animals are different… …angry. The Sparklite that once gave life, now corrupts and pollutes. The Baron wants all the Sparklite for himself. And the evil mining corporation
will stop at nothing to get it for him. We depend on Ada now. She won’t watch a world suffer. She won’t let the Baron win. She may fall… …but she will get up and fight again. And we will help.
– GUESS WHAT.
– WHAT? – YOU KNOW WHAT I DID
IN MY HOTEL ROOM? – TELL ME.
– I JUMPED BED TO BED. THERE WAS, LIKE, THIS ONE GUY
WHO FILMED ME… – YEAH? – IN SLOW-MOTION
JUMPING ONTO THE OTHER BED, DOING A BARREL ROLL. – YEAH.
– BARREL ROLL! – YEAH. – AND THEY FILMED ME
JUMPING ON THE BED, JUST SLAMMING DOWN
ON THE BED. – WOW.
YOU JUST REALLY LOVE– YOU JUST LOVE LIFE,
DON’T YOU? – YEAH, AND BY THE WAY,
I LOVE HOW YOU GET TO JUMP ONTO BEDS. – YEAH. WELL, THAT’S WHAT YOU DO
IN HOTEL ROOMS. I THINK EVERYBODY HERE
GETS IN A HOTEL ROOM, AND YOU JUMP ON BEDS,
DON’T YOU? [cheers and applause] EVERYBODY DOES. – YEAH, BUT MY GRANDPA,
HE DOESN’T LIKE ME JUMPING FROM BED TO BED. THIS IS WHY I WOULD JUMP
FROM THIS BED TO THE OTHER BED. – THAT’S PRETTY FAR.
– YEAH, BUT I MADE IT. I CAN MAKE IT.
I FALL. – WOW.
– I GO LIKE… [shouting] – WOW. – AND THEN I FALL, LIKE–
– YEAH. SO WHEN YOU’RE DOING THIS, IS YOUR GRANDPA
OPENING THE MINI BAR, OR WHAT’S HAPPENING? – IT’S MY MOM’S BOYFRIEND.
HE OPENED– [laughter and applause] THIS GUY, GRANDPA,
RIGHT HERE… [speaking indistinctly] – YEAH. NOW WE’RE GETTING
TO THE GOOD STUFF. – I DON’T KNOW
IF YOU HAVE TO PAY. I DON’T KNOW YOU HAVE TO PAY
TO GET INTO THE BAR, BUT IT’S KIND OF A BAR. SO YOU HAVE TO PAY
FOR A DRINK. – YUP.
– I MEAN– I MEAN, THERE’S SO MANY–
I HAVE–HE HAS SO MANY. – YEAH, HEY, I HAVE A QUESTION
ABOUT DINOSAURS. I HEARD YOU LIKE DINOSAURS
A LOT, RIGHT? – YEAH, I DO.
– OKAY. WHAT KIND OF DINOSAURS
DO YOU LIKE? – CROCODON.
– I NEVER HEARD OF THAT ONE. – WELL, HE–
HE WASN’T ACTUALLY JUST THIS NORMAL
MEAT-EATING DINOSAUR. – NOW, THAT’S YOU. – NO, I’M NOT
THE CROCODON. – NO?
– CROCODON IS RED. HE HAS GREEN EYES, AND HE CAMOUFLAGED THEM
TO THE SIGHT OF BLOOD EYES. – OH, OH. WHAT IF I TOLD YOU
WE HAD A DINOSAUR HERE TODAY? – THAT’S ME. – NO.
NO, IT’S NOT YOU. IT’S A DINOSAUR
THAT CAME TO SAY HELLO TO YOU. DO YOU WANT TO MEET IT?
– YUP. – ALL RIGHT, LET’S–
IS THE DINOSAUR HERE? IT’S A FRIENDLY DINOSAUR TOO.
I THINK YOU’RE GONNA LIKE IT. LOOK. – WHOA! WHOA! [cheers and applause] WHOA! [dinosaur squeaking] [howls] [chitters] – OKAY. – I’M PRETTY SURE
THAT’S A GUY IN A COSTUME. [laughter and applause] [dinosaur howls] – OH, IS THAT A FURRY T REX? YOU KNOW,
WITH THE TWO CLAWS. – RIGHT.
– AND THE SHORT ARMS. – RIGHT, YEAH. HE’S ANGRY.
NOW YOU’VE MADE HIM MAD. LISTEN, GUESS WHAT
YOU’RE GONNA DO. YOU’RE GONNA GET TO GO SEE
“WALKING WITH DINOSAURS, THE ARENA SPECTACULAR.” YOU’RE GONNA GET
VIP TICKETS AND GO SEE
ALL THE DINOSAURS. – OH, YEAH! [cheers and applause] – AND BECAUSE YOUR GRANDPA
LIKES TO WATCH THE NEWS FOR THE POWERBALL, EVERYONE IN THE AUDIENCE
AND YOUR GRANDPA IS GOING HOME
WITH POWERBALL TICKETS. [cheers and applause] – [speaking indistinctly] – NO, IT’S A REAL DINOSAUR. WE’LL BE RIGHT BACK–
– I CAN SEE HIM! I CAN SEE– [cheers and applause]