Melody

Hi Manas, it is nice to hve your on the forum  

This is a great question :))     

the super spy james bond is riding on his super bike at a uniform speed of 60 kmph towards a rocket launcher in chinese territory.the road is straight and horizontal.when he reaches the point x on his way he look at the top of the rocket launcher and finds the angle of elevation to be 30 degree. after 1min. and 30 sec.he looks at the top of the rocket launcher again and finds the angle of elavation is now increased by 30 degree. he takes out a powerful bomb from his pocket and thinks how many sec. he has now,to reach the base of the rocket launcher

can you help him and tell him how many sec. he has?

He is travelling at  60mph

This converts to  1000m/s

When he starts thinking, which is instantaneous becsues he IS James Bond,  let him be y metres from his target.

Ther the height of the launcher be h

In 1 minute and 30 seconds he will have travelled  1.5*1000=1500 metres

so at point X he will be  1500+y  metres frpom the base of the launcer.

so

\(tan30=\frac{h}{y+1500} \qquad and \qquad tan60=\frac{h}{y}\\ \frac{1}{\sqrt3}=\frac{h}{y+1500} \qquad and \qquad \frac{\sqrt3}{1}=\frac{h}{y}\\ \frac{y+1500}{\sqrt3}=h \qquad and \qquad \sqrt3\;y=h\\ \frac{y+1500}{\sqrt3} =\sqrt3\;y\\ y+1500 =3\;y\\ 1500 =2\;y\\ y=750 metres\\ \)

\(750m\times\frac{1min}{1000m}=0.75 minutes = 45seconds\)

If conditions stay perfect he has 45 seconds to go.

If you have a problem understanding then let me know but make sure you draw the pic and try to work it out first.  :)

This is a great little question   

If 4^x=10^4, what would the value of 8^x be?

\(4^x=10^4\\ (2)^{2x}=10^4\\ (2^3)^{\frac{2x}{3}}=10^4\\ (8)^{\frac{2x}{3}}=10^4\\ [(8)^{\frac{2x}{3}}]^{\frac{3}{2}}=[10^4]^{\frac{3}{2}}\\ 8^x=10^6 \)

Hi Manas, it is nice to meet you.  :)

I got 7  

This is an OUTLINE of my logic.

I drew up the diagram. Let X be the centre of the cirlce.

Draw in each radii and draw in t he intervals between the centre ifthe circle and the vertices

The angle between a radius and a tangent is 90 degrees 

So you have now split your triangle up into 6 right angled triangles

cr=cp=8   tangents subtended from a point intersect the circle at equal distances.

br=bQ=6

ap=aq = ?

tan(< rbX)=tan(<Xbq)=4/6     so       < rbX = 33.69 degrees (2dp)  

tan(<rcX) = tan(<pcX) = 4/8      so      those angles each =26.56  degrees (2dp)

Now < pax= 29.75 degrees         Working involves angle sum of a triangle

so

tan 29.75 = 4/ap

ap=aq=6.99 = near enough to 7.

It may be exactly 7.  You would have to do the working without any rounding to find out :))

NOTE:  I have not checked my working it is quite possible that some of the numbers are incorrect.  

You need to check it!

If something doesn't make sense then ask about it.  :)

Yes they should be the same and I just checked. on the web2.0calc they ARE the same.

Perhaps your calc is NOT set on degrees ??

Hi Girl 573.15       

how do you graph this y=3/4x-1

There are a number of ways depending on what you have learned so far.

The most common way it to recognise that this is a line AND it is in gradient and y intercept form  (y=mx+b)

The y intercept is b and b=-1.     This is a point.  You can graph it straight away :))

The gradient or slope is m and m= \(\frac{3}{4}= \frac{rise}{run}\)

The slop is positive so the line has to head off towards the top right corner of the number plane.

Start at the y intercept.  Go up 3, go across 4  (in the right direction, which is right) put a little cross.

Join the points up and you have your line.

Now label you line with the equation and it is all done.  :))

Here is the graph :

https://www.desmos.com/calculator/26tumtcepp

59 cause I ate one!

Which bit don't you understand?

The instructions look pretty good.  Thanks answering guest :)

You are a guest and we did not invite any dinosaurs therefore you cannot be a dinosaur.

Tell me, is the logic of this statement valid ?

\(-1\frac{1}{3}\div2\frac{2}{3}\\ =\frac{-4}{3}\div\frac{8}{3}\\ =\frac{-4}{3}\times\frac{3}{8}\\ =-\frac{1}{2} \)

There isn't one.

There is a fraction mode but it does not work properly.