All Answers 358110 Answers

The area of the triangle is 15.

Let the length of the 2nd piece ==L

Then, the length of the 1st piece==3L

The length of the shortest piece ==3L - 40

[L + 3L + 3L  -  40] ==100, solve for L

7L ==100  +  40

7L ==140

L ==140 / 5 ==20 feet - length of the 2nd piece

20  x  3 ==60 feet - length of the 1st piece.

60 - 40 ==20 feet - length of the 3rd piece.

Note: The 3rd piece must be 40 feet shorter than the FIRST and NOT the SECOND piece.

The Cubs are playing the Red Sox in the World Series. To win the world series, a team must win 4 games before the other team does. If the Cubs win each game with probability 1/4 and there are no ties, what is the probability that the Cubs will win the World Series? Express your answer as a percent rounded to the nearest whole percent.  

Read the set up:  "If the Cubs win each game with probability 1/4..."  

If the Cubs win each game, it doesn't matter what the probability had 

been that they would have won each game.  A win is a win and that's 

all that matters.  The Cubs sweep the Series in four games.  100%. 

a ==5,880,  b==6,048,  c==6,370

GCD(a, b) ==GCD(5,880, 6,048) ==168

GCD(a, c) ==GCD(5,880, 6,370) ==490

GCD(b, c) ==GCD(6,048, 6,370) ==14

\(h^{-1}(5) = 2/3\)

Oh, you were right!  The answer was 6!

its b

thank you but that doesn't really answer my question 

The height of the balcony is, essentially, the height of the ball when after 0 seconds.

This means that the answer is the value when you substitute 0 for t. 

My answer is    \(5^{(\frac{5}{16})}\)

Unless I made a careless error (which there is no evidence of) this is the exact answer.

The 2 guest answers are not correct because  they do not account for the ... after the 4th term.

There is an infinite number of terms here, not just 4.

Hi Melody:

When multiplied together, you get the following number:

(5^(1/5)) * (25^(1/25)) * (125^(1/125)) * (625^(1/625)) ==1.64801169512666976301802035295......etc.

1 - Guest #1 answer ==5^(4/13) ==1.64084551246609057805181222444......etc.

2 - Guest #2 answer==5^(194/625)==1.64801169512666976301802035295....etc.

3 - Melody's answer ==5^(5/16) ==1.65359110076253520866303943290......etc.

How about you write something of what you have done for yourself.

It seems like you just want to copy an answer.

Find all possible values of RT. 

Hello Guest!

X-Y coordinate system

\(R(0,\sqrt{25-16})\\ R(0,3)\\ m_{PT}=tan\ \frac{3}{4}\\ PT(x)=m(x-x_R)+y_R=0.75(x-0)+3\\ PT(x)=0.75x+3 \)

\(ST(x)=\sqrt{9^2-(x-8)^2}\\ \sqrt{9^2-(x-8)^2}=0.75x+3\\ 81-(x^2-16x+64)=0.5625x^2+4.5x+9\\ x\in \{-0.64,\ \color{blue}8\}\\ y\in \ \{\ 3.52\ ,\ \color{blue}9\}\)

          invalid

\(\color{blue}T(8,9)\ R(0,3)\ P(-4,0)\ Q(4,0)\ S(8,0)\)

\(\overline{RT}=+\sqrt{(y_T-y_R)^2+(x_T-x_R)^2}=+\sqrt{(9-3)^2+(8-0^2)^2}\\ \color{blue}\overline{RT}=10\)

  !

Thanks guests :)

P = 5^{1/5} \cdot 25^{1/25} \cdot 125^{1/125} \cdot 625^{1/625} \dotsm

\(P = 5^{1/5} \cdot 25^{1/25} \cdot 125^{1/125} \cdot 625^{1/625} \dotsm\\ P = 5^{1/5} \cdot 5^{2/5^2} \cdot 5^{3/5^3} \cdot 5^{4/5^4} \dotsm\\ P = 5^{(\frac{1}{5}+\frac{2}{5^2}+\frac{3}{5^3}+\frac{4}{5^4}\dotsm\\)} \\ log_5 P = {(\frac{1}{5}+\frac{2}{5^2}+\frac{3}{5^3}+\frac{4}{5^4}\dotsm)} \\ log_5 P = {(\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}\dotsm)} + {(\frac{1}{5^2}+\frac{1}{5^3}+\frac{1}{5^4}\dotsm)} +{(\frac{1}{5^3}+\frac{1}{5^4}+\frac{1}{5^5}\dotsm)+ \dots}\\ log_5 P =(\frac{1}{5}\div \frac{4}{5})+(\frac{1}{25}\div \frac{4}{5})+(\frac{1}{125}\div \frac{4}{5})+ \dots\\ log_5 P =(\frac{1}{5}\times \frac{5}{4})+(\frac{1}{25}\times\frac{5}{4})+(\frac{1}{125}\times\frac{5}{4})+ \dots\\ log_5 P =(\frac{1}{4})+(\frac{1}{20})+(\frac{1}{100})+ \dots\\ log_5 P =\frac{1}{4}\div \frac{4}{5}\\ log_5 P =\frac{1}{4}\div \frac{4}{5}\\ log_5 P =\frac{1}{4}\times \frac{5}{4}\\ log_5 P =\frac{5}{16}\\ P=5^{\frac{5}{16}}\\ P\approx 1.65359 \)

LaTex

P = 5^{1/5} \cdot 25^{1/25} \cdot 125^{1/125} \cdot 625^{1/625} \dotsm\\
P = 5^{1/5} \cdot 5^{2/5^2} \cdot 5^{3/5^3} \cdot 5^{4/5^4} \dotsm\\
P = 5^{(\frac{1}{5}+\frac{2}{5^2}+\frac{3}{5^3}+\frac{4}{5^4}\dotsm\\)} \\
log_5 P = {(\frac{1}{5}+\frac{2}{5^2}+\frac{3}{5^3}+\frac{4}{5^4}\dotsm)} \\

log_5 P = {(\frac{1}{5}+\frac{1}{5^2}+\frac{1}{5^3}\dotsm)} 
+ {(\frac{1}{5^2}+\frac{1}{5^3}+\frac{1}{5^4}\dotsm)}
+{(\frac{1}{5^3}+\frac{1}{5^4}+\frac{1}{5^5}\dotsm)+ \dots}\\

log_5 P =(\frac{1}{5}\div \frac{4}{5})+(\frac{1}{25}\div \frac{4}{5})+(\frac{1}{125}\div \frac{4}{5})+ \dots\\
log_5 P =(\frac{1}{5}\times \frac{5}{4})+(\frac{1}{25}\times\frac{5}{4})+(\frac{1}{125}\times\frac{5}{4})+ \dots\\
log_5 P =(\frac{1}{4})+(\frac{1}{20})+(\frac{1}{100})+ \dots\\
log_5 P =\frac{1}{4}\div \frac{4}{5}\\
log_5 P =\frac{1}{4}\div \frac{4}{5}\\
log_5 P =\frac{1}{4}\times \frac{5}{4}\\
log_5 P =\frac{5}{16}\\
P=5^{\frac{5}{16}}\\
P\approx 1.65359

break the mods into their prime factors

6=2*3

7

8=2*2*2

9=3*3

So  6,7,8 and 9 will all go into  2*3*7*2*2*3=  6*7*4*3 = 504

There will be 1 solution less than 504 and then 1 solution for each following product of 504

6*7*8*9 = [6*7*4*3]* 6

So there will be 6 solutions less than   6*7*8*9

Where c >= a. What is c - a?

Hello Guest!

\(y = x^2 + 4x + 6 \)

\(y = 1/2*x^2 + x + 4\)

(a,b),(c,d)

\(x^2 + 4x + 6 =\frac{1}{2}x^2 + x + 4\\ \frac{1}{2}x^2+3x+2=0\\ x^2+6x+4=0\\ x=-3\pm \sqrt{9-4}\\ x\in \color{blue}\{(-\sqrt{5}-3),(\sqrt{5}-3)\}\)

                  a                   c

\(b = (-\sqrt{5}-3)^2 + 4(-\sqrt{5}-3) + 6 \\ \color{blue}b=12.472\\ d=(\sqrt{5}-3)^2 + 4(\sqrt{5}-3) + 6 \\ \color{blue}d=3.528\)

c > a

\(c-a=(\sqrt{5}-3)-(-\sqrt{5}-3)\\ \color{blue}c-a=2\sqrt{5}\)

  !

What is your guess ?

Have you tried some different possibilities?

Whawt have you tried?

Written as a complex number, the answer is -242+110i

(11-5i)(11i)(2i)=

(11*11i-5*11i²)*2i=

(55+121i)(2i)=

(55)(2i)+(121i)(2i)=

110i-242=

-242+110i

the answer was 8

it wasnt 6

By the distance formula, the sum of all possible values of r is 6.

Find the domain of the real-valued function

Hello Guest!

\(f(x) = -\sqrt{-10x^2 - 4x + 6}\\ (-10x^2 - 4x + 6)\geq 0\\ x^2+ \frac{2}{5}x-\frac{3}{5}\\ x=-\frac{1}{5}\pm \sqrt{\frac{1}{25}+\frac{3}{5}}\\ x=-\frac{1}{5}\pm \sqrt{\frac{16}{25}}\)

\(x\in\{-1,\frac{3}{5}\}\)

\(\color{blue}D=\{x\in \mathbb R\ |\ -1\leq x\leq \frac{3}{5}\}\)

\(\)

  !

Simplify the following:
5^(1/5) 25^(1/25) 125^(1/125) 625^(1/625)

625^(1/625) = (5^4)^(1/625):

5^(1/5) 25^(1/25) 125^(1/125)×5^(4/625)

125^(1/125) = (5^3)^(1/125):

5^(1/5) 25^(1/25)×5^(3/125)×5^(4/625)

25^(1/25) = (5^2)^(1/25):

5^(1/5)×5^(2/25)×5^(3/125)×5^(4/625)

5^(1/5)×5^(2/25)×5^(3/125)×5^(4/625) = 5^(1/5 + 2/25 + 3/125 + 4/625):

5^(1/5 + 2/25 + 3/125 + 4/625)

Put 1/5 + 2/25 + 3/125 + 4/625 over the common denominator 625. 1/5 + 2/25 + 3/125 + 4/625 = 125/625 + (25×2)/625 + (5×3)/625 + 4/625:

5^(125/625 + (25×2)/625 + (5×3)/625 + 4/625)

25×2 = 50:
5^(125/625 + 50/625 + (5×3)/625 + 4/625)

5×3 = 15:

5^(125/625 + 50/625 + 15/625 + 4/625)

125/625 + 50/625 + 15/625 + 4/625 = (125 + 50 + 15 + 4)/625:

5^((125 + 50 + 15 + 4)/625)

125 + 50 + 15 + 4 = 194:

5^(194/625)