All Answers 358108 Answers

sum_(n=1)^9 1/((n + 1)^3 - n - 1) = 27/110

By the Cosine Law, cos angle BAD = sqrt(7)/3.

P(8) = 1/10.

Circumference==2 x Radius  x  Pi

                           ==2  x  8  x  3.14 ==50.24 feet - that is how far the horse will walk.

The sum of all possible values of z is 47.

a^2+b^2+2ab=(a+b)^2 so (-1)^2=1

a + b + c==60,  a - 7==b +7,  b + 7==c/7, solve for a, b, c

a ==41/3,   b== - 1/3,   c==140 / 3

N ==41/3 - 7 ==20/3............(a)

N == - 1/3 + 7==20 /3.........(b)

N==[140/3] /7==20/3.........(c)

The perimeter of triangle A_3B_3C_3 is 128.

i=0;a=1; b=1;d= (a + 8) * a*(a + 8) ; if(d==40*b and gcd(40,b)==(a+8) and lcm(40,b)==a*(a+8), goto5, goto7);i++;printi,"=",(a, b); a++;if(a<2000, goto3, 0);a=1;b++;if(b<2000, goto3, 0)

The smallest possible value of the 2nd integer ==1,280

GCD[40, 1280] ==40 ==[x + 8], where x==32

LCM[40, 1280]==1280 ==x[x + 8], where x==32

Average speed==Total distance / Total time

Average speed ==[2 x 1 km] /[30/60  +  10/60]

Average speed ==2 km /[2/3]==2 x 3 / 2 ==3 km/h - her average speed back and forth.

productfor(n, 10, 25, n)==427,447,366,714,368,00,000

Thanks for the equine dental lessen Ginger :)

Let the original number of garments ==G

0.80G  +  0.20G ==shirts and pants they had in April

1.25 * 0.80G ==1G - number of shirts sewn in May

0.20G x 3 ==0.60G - number of pants sewn in May

0.80G + 0.20G + 1G + 0.60G ==840 + G

2.60G  - G ==840

1.60G ==840

G==840 / 1.60 ==525 - original number of garments.

[525 x  0.80]==420 shirts sewn in April

420  x  1.25 ==525 shirts sewn in May

Compute the value of 

1-2+3-4+...+2019-2020+2021

(1+3+5+ ..... +2021) - ( 2+4+6+ ..... +2020)

these are just arithmetic progresstions

The sum of an AP = \(\frac{n}{2}(a+L)\)

There are 2021 terms in total  half that 1010.5   so there are 1010 even numbers and 1011 odd numbers

(1+3+5+ ..... +2021) - ( 2+4+6+ ..... +2020)

\(=[\frac{1011}{2}(1+2021)]-[\frac{1010}{2}(\color{red}{2} \color{black}+2020)]\\ =[1011*(1011)]-[505*(2022)]\\ =1022121 - 1021110\\ =1011\)

I found my careless error, the corrected number is in red.

This is an idiom when used to describe humans. Human teeth do not continue to grow after formation and eruption.

This is literal (not an idiom) when used to describe an animal’s age –specifically horses. Estimating a horse’s age by examining its teeth is a centuries-old practice that is still commonly used today. Note that along with the length of the teeth, wear patterns and irregular “floats” are considered too.  

While horses’ gums do recede as they age, their teeth also grow an average of about 75 mm (3 inches) per year during their lifespan. Horse’s teeth naturally wear as they eat hay, and especially as they forage for grass, which is chewed with sand. Some horses will intentionally chew on small mouthfuls of sand to accelerate the wear. This behavior is commonly seen among horses that are heavily grain-fed, as they forage less.  (I heard that from the horse’s mouth.)

Modern horses that are properly cared for will have their teeth refloated once or twice a year by a veterinarian or keeper who is trained and skilled in the process.  Even with this process it is still possible to estimate the age of a horse by teeth wear patterns and gum recession.  

During the annual or semiannual oral care exams, excessively long teeth are shaved and ground to optimum levels along with the refloating procedures, and dental carry restoration. Yes, horses get cavities. Unlike humans, equine cavities will grow out. This is a great natural advantage considering that (some) horses have only had human dentists caring for their oral health for a century or so... (One less thing to be down in the mouth about.)

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Hi Ron,

I’m sure you are long in the tooth, assuming you still have at least one of them. 

How’s Gracie?

 It's foolish to bet on a horse without talking to him first. I know it seems silly to ask a horse who's going to win a race - but it's no sillier than asking anyone else. –Gracie Allen

GA

--. .-

$\sqrt[3]{3 - x} = -3/2$

$3 - x = -27/8$

$x = -3/8$

A scientist records the motion of a particle.  A graph of that motion is shown below.

Hello DumpDude!

a) What is the period of one complete cycle?                    

           \(\color{blue}4\ units_t\)

b) What is the range of this function?                              

        \(\color{blue}\{range-f(t)\}=\{\mathbb d\ |\ -1\leq d\leq 3\}\ [units_d]\)
c) If the particle can survive for twenty complete cycles  before deteriorating,

determine the domain of the function.                                 

         \(\color{blue}\mathbb D=\{t\ |\ 0\leq t\leq 80\}\ [units_t]\)
d) Determine the equation of the axis.                             

         \(\color{blue}d=f(t)=2\ cos\ (\frac{\pi}{2} t)+1\ [units_d]\)
e) Determine the amplitude.                                               

        \(\color{blue}2\ units_d\)

  !

It' says it's wrong

Consider

\(y=3-x   \;\;where\;\; x\le3\\ when \;\;x\le3,\;\;y\ge0\)

\(y=3-x   \;\;where\;\; x\le3\\ -x=y-3\\ x=3-y\\ \text{the inverse will be}\quad y=3-x\;\;where\;\;x\ge 0 \)

since I only am asked for the inverse values in this domain I do not need to concern myself with the original function when x>3 as this would give an inverse function domain of x<0

To show you,   if 

f(x)=-x^3+2x^2+3x then

f(3)=-27+18+9 = 0    for values bigger than 3 the value will be negative.   

\(f^{-1}(0)=3-0=3\\ f^{-1}(6)=3-6=-3\\ \)

Any question?  ask away :)

 Here is the actual graph

\(5x^2=20^3\\x^2=1600\\ x=\pm \sqrt{1600}\\ \color{blue}x\in\{-40;40\}\)

x^2=1600

x=40

Atlas 

uphill speed=33 1/3 km/h

downhill speed=100km/h

use harmonic mean=0.02999100269*2=0.59 aproximately

Answer to first one

32.86cis(4.06) :)

sin(30) = 1/2

cos(60) = 1/2

tan(45) = 1

so...

sin(30)*cos(30)*tan(45) = 1/2 * 1/2 * 1 = 1/4

Find BC in the following triangle, to two decimal places.