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Correct

Yes, At the turning points the gradient of the tangent must be 0

so

the first derivative at that point must be zero.

this is because

THE GRADIENT OF THE TANGENT IS GIVEN BY THE FIST DERIVATIVE

I think.

\(\text{P(each suit different)}=1* \frac{39*26*13}{52*52*52}\\ \text{P(each suit different)}= \frac{3}{4*2*4}\\ \text{P(each suit different)}= \frac{3}{32}\\ \)

OK, why not like this:  1/3 / √ 32 = 2^n

Hello guest from answer  #1!

\(\color{BrickRed}\frac{1}{3\cdot \sqrt{32}}=2^n\\ 3\cdot \sqrt{32}=2^{-n}\\ 3\cdot 2^{2.5}=2^{-n}\\ 3=\frac{2^{-n}}{2^{2.5}}\\ 3=2^{-n-2.5}\)

\(\frac{ln3}{ln2}=-n-2.5\)

\(n=-2.5-\frac{ln3}{ln2}\)

\(n=-4.08496\)

  !

 ∠DCB = ∠ECD = 42 degrees

1/3 √ 32 = 2^n

Hello Guest!

\(\frac{1}{3}\cdot \sqrt{2^5}=2^n\\ \sqrt{2^5}=3\cdot 2^n\\ 2^{\frac{5}{2}-n}=3\)

\(ln2\cdot ({\frac{5}{2}-n})=ln3\)

\(\frac{5}{2}-n=\frac{ln3}{ln2}\)

\(n=\frac{5}{2}-\frac{ln3}{ln2}\)

\(n=0.15037\)

  !

Thank you ElectricPavlov...

Melody..good morning,

Just to mention, the reason I looked at the 1st derivative as being one of the turning points, is that we do use the 1st derivitave also to calculate the x-coordinates of the turning points, by, once the derivitave is calculated, it is then factored to get the x-coordinates, and it was because of that, that I thought they gave us one of those turning points. but I will see it from now that they mean to supply us with gradient information....Thank you..

This question keeps cropping up!!

By the way, it should actually be:

work ou the value of n if:

1/3 / √ 32 = 2^n

The ratio is 5/8.

Randy has a cube with an edge of a = 21 cm. From in the middle of one face of this cube Randy cuts out and removes a cube with an edge of b = 3 cm. Find the change in surface area of the original cube.

Hello Guest!

\(S_1=6a^2=6\cdot (21cm)^2\)

\(S_1=2646cm^2\)

\(\Delta S=-b^2+5b^2=4b^2=4\cdot (3cm)^2\)

\(\Delta S=36cm^2\)

\(The\ cube\ changes\ its\ Surface\ by\ 36\ cm ^ 2.\)

\(S_2=S_1+\Delta S=2646cm^2+36cm^2\)

\(S_2=2682cm^2\)

  !

The probability is 4/33.

The length of arc YZ is 36*pi.

Thank you!

C_L = L / (A * .5 * r * V² )            L will equal the weight of the plane = 2 897 229 N   

                                                   A = 418 m²

                                                    r=air density   ..  we need the temperature (K)  of the air at 1625 m to calculate density

                                                             using STP and standard lapse rate of 2^o C per 1000 ft results in 4.34^o C = 277.48 K

                                                           pressure = 101.8 kPa    = 101.8 x 10^3  N/m²   = 101.8 x 10^{3  2}kg/(s²-m)  = 10377.17 kg/m²

                                                             using these parameters you can calc   r = 1.27 kg/m³

                                                              V = 99.4 m/s

I find C_L = 1.105      (not positive of this answer)

The perimeter of an isosceles triangle is 36 centimeters and two sides of the triangle are in the ratio 2:7. What is the number of centimeters in the length of the longest side?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

An isosceles triangle is a triangle with two equal sides.

If the ratio of the two sides is 2:7 then the ratio of all 3 sides is 2:7:7  

 The length of the longest side is:>         7(36 / 16) = 15.75 cm 

Multiply first equation by 3 to get

12x +  3x = 15      and add to the 2nd equation to get

 19x = 17

x = 17/19     use this value of x in one of the equations to calc  'y'

I need steps and details.

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Re-arrange to

x^2 - 10x + y^2 + 4y  = -c     now complete the squares for x and y

(x-5)^2      + (y+2)^2   = - c  + 25 + 4          The red portion = r²

-c + 25 + 4 = 1²

29 = 1 + c

28 = c

By AM-GM, there is no minimum value, and the maximum value is 756.25.

From a Google search
According to the first triangle inequality theorem, the lengths of any two sides of a triangle must add up to more than the length of the third side. This means that you cannot draw a triangle that has side lengths 2, 7 and 12, for instance, since 2 + 7 is less than 12.

Possible combos:

 2x + 7x    < 36-9x

18x < 36

x < 2                    

x =1      2   7  27     

x=2      4 14  18                   These do not meet the triangle inequality theorem above        

x = 1.5         5   17.5   13.5  <====  possible          5:17.5   =  2:7             longest = 17.5 cm

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