All Answers 358149 Answers

Yes I am but just for lil bit of time as I'm a little busy since early morning! I had a SST test today  for which I had to study 3chapters and that's y I couldn't come here in morning for I was revising ! And today being busy I couldn't post " let's end the day with a laugh" but I'll surely try tomorrow ! 

Let's see how jboy314's answer was derived.

The "formula" for the monthly payment is given by:

M = P(1+r)ⁿ r / [(1+r)ⁿ-1]

Where

M = the Monthly Payment

P  = the amount financed ($20000)

r = the montly interest rate expressed as a decimal = .069/12 = .00575

So we have

M = (20000*(1+.00575)^60*.00575)/ ((1+.00575)^60 -1)) = $395.08

hahaha you came back! 

$395.08

5.8 since 1/2 * 11.6= 5.8

We seem to have a "variable length" pendulum, Jedithious !!!

We'll use 31cm and call it good.......(Sorry, I forgot that the question requested to the nearest cm!!...my bad)

1.   30% = .30 in decimal form

     "Of" means multiply

     "What Number" is "x"

     "Is" means "Equal To"

So we have

.30 * x = 14.1      divide both sides by .30

x = 47    and that's the "What Number"

2. I assume you want to convert 81 cm to inches......so we have

81cm *  (1 inch/2.54cm) = about 31.89 in.       .....notice that the "cm" "cancel" abd we're left with the desired unit (inches)

The radius is (1/2) of the diameter, so (1/2)* (11.6) = 5.8

Anonymous has answered correctly if we were setting the original expression = 0. That wasn't indicated in the question, but it may have been intended......I can't say......

6a(11a+5)=0

(6a * 11a) + (6a * 5)=0

66a^2 + 30a=0

66a^2 = -30a

66a^2/a = -30

66a = -30

a = -30/66 or -5/11

Using the distributive property, we have

6a(11a) + 6a(5)  =

66a² + 30a

To sum these, first express each with the same denominator.  This is easy to do once we notice that 34 is twice 17, so the fraction -3/17 can be written as -6/34.  Now the sum becomes 9/34 - 6/34, or (9-6)/34, or 3/34.

I guess I should also note that adding a negative number just means subtracting that number, so 9/34 + (-3/17) is the same as 9/34 - (3/17)

If she deposits 30% of her salary, she must spend 70% of her salary, so 70% of her salary is Rs.9800.  This means her salary must be Rs.9800/0.7 or Rs.14000

A picture helps:

1.  sin(θ) = 20/L  ;  L = 20/  sin(θ);    θ = 40°

$${\mathtt{L}} = {\frac{{\mathtt{20}}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{40}}^\circ\right)}}} \Rightarrow {\mathtt{L}} = {\mathtt{31.114\: \!476\: \!537\: \!185\: \!947\: \!2}}$$

L = 31 cm to nearest cm

2. Lcos(θ) + 7.3 = L;  L = 7.3/(1 - cos(θ));

$${\mathtt{L}} = {\frac{{\mathtt{7.3}}}{\left({\mathtt{1}}{\mathtt{\,-\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{40}}^\circ\right)}\right)}} \Rightarrow {\mathtt{L}} = {\mathtt{31.202\: \!507\: \!422\: \!010\: \!490\: \!6}}$$

L = 31 cm to nearest cm.

I think that both of the foregoing answers are misleading.

As an alternative method of solution, resolving the displaced pendulum to the vertical and adding the 7.3 gets you the equation

L*cos(40) + 7.3 = L, (the 20 isn't needed)

and from which L = 31.2025 (4 dp).

It would seem that we can't be sure of the first decimal place and that the best that we can do is to give the result correct to the nearest cm, as asked for in the question.

What are the factors of 45

$$\begin{array}{rcrcl}
1&\times&45&=&45\\
3&\times&15&=&45\\
5&\times&9&=&45\\
\left{(}
9&\times&5&=&45\\
15&\times&3&=&45\\
45&\times&1&=&45
\right{)}
\end{array}$$

The factors of 45 are: 1, 3, 5, 9, 15, 45

$$\\
\tan{(40\ensuremath{^\circ})}={20\;cm \over l-7.3\;cm}\\\\
(l-7.3\;cm)={20\;cm \over \tan{(40\ensuremath{^\circ})} }\\\\
l=7.3\;cm+{20\;cm \over \tan{(40\ensuremath{^\circ})} }\\\\
l=7.3\;cm + 23.8\;cm=31.1\;cm$$

The pendulum is 31.1 cm long

Awww! Poor little Zegroes got nothing else to say !!!!

and Zegroes if I'm little then I should start calling u Grandfather ! 

Soo r u ok grandfather!

Zegroes don't be so happy ! Ur talking the trophy of the c**p question ! And I don't like these kinda trophies so I leave it for u  ! I'm happy at least becoz of me u won  something though it was c**p only ! 

I've been giving some thought to this one....I believe Melody is correct.....our previous answers were incorrect with respect to allowing repeats.....I think that the answer is WAY larger.......

I see this as a "slot" problem with these considerations........

1. Choose any 4 of of 7 "slots" and let each slot be occupied by any one of 26 letters. Notice that order isn't a consideration, since, for example, "slots" 1-2-4-7  are the same as 2-1-4-7 or 1-4-2-7.

2. For each arrangement above, the other 3 "slots" can be occupied by any three digit combination utilizing numbers 0 through 5.......there are 556 of these possible combinations.......(000 through 555).

So we have:

C(7,4)* (4^26) * 556   = 87,640,048,748,629,852,160  combinations  !!!

Whew!!!....that's a pretty big number!!! (Note that the 4^26 part contributes to most of the "bigness".....)

Anyone else have any ideas on this??

Z. used the Rad mode. Come on Z, quit goofing off! Do the reverse quadratic for x= 9 and x=15. You said you don’t have time, but you had time to give the wrong answer for this very easy one here. I know Rosala wouldn’t have made that mistake.

CPhill’s method is very cool!

Jedithious may also be interested in this. It’s the Taylor series form. The signs alternate and the exponent and factorial are odd and the same. Convert the degrees to rads and plug into x.

This is how a calculator computes the value.

$$\sin x = x- \frac{x^3}{3!}+ \frac{x^5}{5!}- \frac{x^7}{7!}...$$

Ironically, you might need a calculator to do it. This is doable by pencil and paper at the cost of writer's cramp. You will need to do about 7 steps for accuracy to about 0.3 of a degree over 360 degrees.

 7UP

Let x be the number of adult tickets sold and let y be the number of children's tickets sold.

So     x + y  = 8400

And the number of adult tickets sold times the price for each plus the number of children's tickests sold times their price = $40,000   or, in equation form

6x + 4y = 40000         Now, if we subtract x from both sides of the first equation, we have that y = 8400 - x

And substituting for y in the second equation, we have

6x + 4(8400 - x) = 40000    .....simplifying, we have

6x + 33600 - 4x = 40000

2x + 33600 = 40000    ..... subtract 33600 from both sides

2x = 6400     ...... divide by 2 on both sides

x = 3200    .......so this is the number of adult tickets sold

And using y = 8400 - x,  we have y = 8400 - 3200 = 5200   ..and that's how many children's tickets were sold.

(1/2)^3 * 512 - (-216)   ?

$$\\({1\over 2})^3 * 512 - (-216)\\\\
={1\over 2^3} * 2^9 +216\\\\
={2^9\over 2^3} +216\\\\
=2^{9-3} +216\\\\
=2^6 +216\\\\
=64 +216\\\\
=280$$

just press atan 5 on the site calc.

arc tan is the same as inverse tan.

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{5}}\right)} = {\mathtt{78.690\: \!067\: \!525\: \!98^{\circ}}}$$

Zegroes answer is also correct but his is in radians.

1.373400767 radians