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I believe that the Guest has used the incorrect formula here......we need the formula for the surface area of a sphere.....so we have...

Sa  = 4 pi*r^2

271.6  = 4 pi* r^2     divise both sides by 4pi

[271.6 / (4pi)] = r^2    take the square root of both sides

r = about 4.649 in

So the diameter is twice this = about 9.298 in  = 9 in  [ to the nearest inch]

THANK YOU!

Orange!

If the design width doubles, then I'm assuming that the surface area of the balloon doubles when the balloon is inflated a second time.  And the balloon can be considered as a sphere.

Let's let the original radius = r

Then, the original surface area of the balloon =  4pi *r^2

Then, for the suface area to double, the radius must increase by a factor of  √2

Proof :   4pi (√2 r)^2  = 4pi (2)r^2  = 8pi*r^2  = twice the original surface area

So...let's find the original radius using the volume for a sphere

71  =(4/3)pi*r^3     divide both sides by (4/3)pi

71/ [ (4/3)pi] = r^3       take the cube root of both sides

cube root ( 71/ [ (4/3)pi] ) = r   = about 2.5687cm^3

So......if the original radius increases by a factor of √2, the new volume is :

V = (4/3)pi (2.5687√2)^3  = about 200.8 cm^3

V=4/3.Pi.r^3

271.6=4/3. 3.141592.r^3  divide both sides by 4/3. 3.141592

64.84=r^3 take the cubic root of sides

r=4.02 inches-this is the radius of the ball

4.02 x 2 =8.04 inches-the diameter of the ball.

Now, I hate hot dogs, love corn dogs..

BUT!

I would rather eat the hot dog with ghost pepper hot sauce and NO guac. 

~Guest

A terminating decimal is a decimal that eventually ends.Example- .32457566422571 or .2 

A non terminating decimal is a decimal that does not end.Example- .333333333333...

The dots symbolize the repeated threes that contiue without end.

~Songoflight

green/black!

One final note on this one.....apparently.....there isn't exactly a consensus of opinion about what the correct answer may be. As Melody stated, I have assumed that each person started at the same time and that D**k runs at a slower pace than Rick.....

One problem???   The statement that D**k is "30 minutes" behind Rick.....but.....from whose point of view does the "30 minutes" refer???  If it's from Rick's frame of reference, he would be farther ahead than if it was from D**k's frame of reference, given my assumption that Rick runs faster than D**k.......

Whatever.........this actually might be a very good problem if there were a little more info included.

no, its -9

Thank you, thank you, thank you!

This might be a little above your level, CarpeDiem....but.......we can find the angle opposite the longest side and determine what the correct answer is........this is done with the Law of Cosines.......we have.....   10,15,7

15^2  = 10^2 + 7^2 - 2(10)(7)cosA       where A is the angle opposite the longest side.......rearrange as:

cosA  = [15^2 - 10^2 - 7^2] / [-2(10)(7)]

And using the cosine inverse [ the arccos], we have

arccos ( [15^2 - 10^2 - 7^2] / [-2(10)(7)] )  = A  = about  122.9°

So.....this triangle is obtuse

BTW.....here's a handy-dandy resource that will let you calculate triangles yourself...

http://www.mathwarehouse.com/triangle-calculator/online.php

Lol

yes please

tanA + secA = e^x

tanA  = e^x - secA     square both sides

tan^2A  = e^[2x] - 2secA*[e^x] + sec^2A

tan^2A  = e^[2x] - 2secA*[e^x] + tan^2A + 1

0 = e^[2x] - 2secAe^x + 1

2secAe^x = e^[2x] + 1

secA  = (e^[2x] + 1 )/ (2e^[2x])

cosA  = (2e^[2x] ) / ( e^[2x] + 1 )

Note that Melody gets an extraneous solution of cosA = 0 ......but this cannot be so, because this would imply that secA  = 1/cosA  = 1/0     and this would be undefined in the original assumption

You didn't state what 1,850 is. Kilometers, Miles???

Let us take as kilometers, then:

1,850 / 3.7 =500:1, or

The scale on the map is: 1cm for every 500 km on the globe.

Does some have an answer,need help ASAP

A metric ton (tonne) is 1000KG

or    180,000 kg   or  396832.071933 lbs      or  198.416035966 SAE (US) tons

2.03188292

its 81

I assume that  f(x)  = x^2

So......f(-3) just means to sub in -3    and evaluate.......so we have

(-3)^2   = 9

Here's another approach........let the shorter side of the rectangle = x.......then the longer side = (7/5)x

So......the perimeter is given by :

2x + 2(7/5)x = 96     multiply through by 5

10x + 14x  = 480

24x = 480

x = 20     and (7/5)x = 28

So....the area = 20 * 28 =  560cm^2

Go online to this link and learn how to use the Quadratic Formula there:

http://www.purplemath.com/modules/quadform.htm

2a+1-4(1-a) how to calculate

2a + 1 - 4 + 4a

6a - 3 That is it.