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I believe  that  the  surface  area  is minimized when all three dimensions  are equal

So

s^3  =  437

s = (437)^(1/3)     where s  is  any dimension  of the  prism

The minimum  surface  area  is

6  [ (437)^((1/3) * (437)^(1/3)  ]   ≈  345.52 cm^2

thanks!

Thank you 😊.

y = k / (sqrtx)       sub in the values to calculate the proportionality constant  'k'

15 = k/(sqrt25)

k =75

3 = 75/(sqrtx)

75/3 = sqrt x

625 = x

$\sqrt{x}*y=k$

$5*15=k$

$k=75$

$\sqrt{x}=\frac{75}{3}$

$x=625$

JP

The rectangular  prism will   have  a square base of  6  on each side  and  a height  of  18

Its  volume is      6^2 * 18   =   648 cm^3

The  cylinder  will  have a radius of 3  and a height of 18

Its volume is  pi ( 3^2) * 18   ≈   508.9 cm^3

The cylinder  wastes less space

Cylinder volume = 3²pi * 18 ≈ 508.938

Prism volume = 6² * 18 = 648

Nvm answer is 4

5x+8y-17=0

Formula for distance between point (p, q) and line ax+by+c=0 is:  

distance=$\frac{\left|ap+bq+c\right|}{\sqrt{a^2+b^2}}$ 

since in this case, p=k and q=$k\sqrt{3}$ , a=5, b=8, and c=-17, we can substitute:

$\frac{\left|ap+bq+c\right|}{\sqrt{a^2+b^2}}=\frac{\left|5k+8k\sqrt{3}-17\right|}{\sqrt{5^2+8^2}}=\frac{\left|5k+8k\sqrt{3}-17\right|}{\sqrt{89}}$

Since the distance is 4, $\frac{\left|5k+8k\sqrt{3}-17\right|}{\sqrt{89}}=4$

                                      solving this, we get $k=-\frac{\left(-4\sqrt{89}+17\right)\left(5-8\sqrt{3}\right)}{167}$ or $\:k=-\frac{\left(4\sqrt{89}+17\right)\left(5-8\sqrt{3}\right)}{167}$

                                      tell me if I'm wrong, because this is a pretty complicated solution. 

JP

From the graph    2009 games won = 10      2011 games won = 22 games

rate of change     (22-10 ) games  / ( 2 years ) = 6 games/yr

Remember the formula for surface area of cone: it's $a=\pi r\left(r+\sqrt{h^2+r^2}\right)$

You have the surface area of the cone, and the radius of the cone. Just substitute both and solve for the height. 

Thank you!

Volume of a cone = 1/3 pi r^2 h

70 .5    = 1/3  (5.2 /2)²   h                           solve for 'h' 

70.5 * 3  / ( 5.2/2)² = ___________ cm

v is colume, r is radius, and h is height. 

formula for volume of cone: $V=πr²\frac{h}{3}$

just substitute 

x + 3y = -5.        re-arrange

y = - 1/3 x - 5    slope = - 1/3   parallel slope is the same   -1/3

y = - 1/3 x   + b       sub in the given point to calculate 'b'

2 = - 1/3 (-7) + b      so b = -1/3

y = -1/3 x  - 1/3    multiply by 3 to get rid of the fraction

3y = -x -1

x + 3y = -1

-3x-9y= 3             you can finish

She has four options for Entrees. 

She has 2 options for drinks

She has 2 options for desserts. 

4*2*2=16

But some possibilities go over her budget. These are the possibilities: 

P-L-FY=8

P-S-FY=7.75

F&C-L-FY=8

F&C-S-FY=7.75

FR-S-C=8

FR-S-FY=9

FR-L-C=8.25

FR-L-FY=9.25

these are 8 possibilities. 

So, she has 16-8=8 distinct possible meals. 

JP

period = 1 week

# periods in 5 years = 5 * 52 = 260 periods

interest per period =  .045 / 52

5435.55 =  orig * ( 1 + .045/52)²⁶⁰

orig invest = 4340.80

$Z= -5/2 -I(5\sqrt{3}/2$
 

Im pretty shure this is the right answer.

Find slant height via pythagorean theorem =

    sqrt ( 28^2 + 12^2) = 30.46 cm

slant height *  height * pi = lateral surface area

     30.46   * 28    * pi              and we need 4 of these

30.46 * 28 * pi * 4 = 10718.7  cm^2     = 1.072 m²  

The diagonal through the rectangular prism will be

  sqrt ( 100^2 + 50^2 + 20^2)       and you will need TWO times this distance   = 227.16 meters

answer????

C(t)= 0.2t^2 - 10t + 650      if graphed, this is a bowl shaped parabola

    the minimum will occur at   t = - b/2a = - (-10)/(2* .2) = 10/ .4 = 25  cars

Cost of 25 cars will be  :      C (t) = 0.2 (25²) - 10 (25) + 650 = ___________                   you can do the calcs.....

Hint:

The angle at the centre of a circle will be twice the angle at the circumference if both are standing on the same arc.

The arc both these angles is on is LM 

This is quite an interesting fence. 

=^._.^=