All Answers 358348 Answers

\(x^{8+y}+x^9+x^{10+z} = x^8(x^y+x+x^{z+2}) \)

I really can't edit it , connection problems or website problem , I don't know either

that's why I made a reply instead of editing 

Well , Melody's answer is correct if you don't need to proove it 

but if you need proof

\(\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides} \)

\(6\sin \left(2x\right)-8\cos \left(x\right)+9\sin \left(x\right)-6=0\)

\(Use \: \sin \left(2x\right)=2\cos \left(x\right)\sin \left(x\right)\)

\(-6-8\cos \left(x\right)+9\sin \left(x\right)+2\cdot \:6\cos \left(x\right)\sin \left(x\right)=0\)

factoring gives us \(\left(4\cos \left(x\right)+3\right)\left(3\sin \left(x\right)-2\right)=0\)

so either the first term or the second equivalent to 0 , we will check them both

\(4\cos \left(x\right)+3=0,\:\frac{-\pi }{2}\le \:x\le \frac{\pi }{2}\)

there are no solution in this range for x , you can check yourself

\(\sin \left(x\right)=\frac{2}{3}\)

in the range \(\frac{-\pi }{2}\le \:x\le \frac{\pi }{2}\)

there is only one solution for sinx= 2/3 in the range -pi/2 to pi/2

it is 

d. x = 0.730

Well,

you could just substitute each of those values into the left hand side and see which one gives and answer closest to 6.

Now the probability that he either chooses an apple or not an apple is 1. Now if you subtract the probability that he does choose an apple you are left with the probability that he does not. In this case there is a .6 probability that he does choose an apple, so 1-.6 = a .4 chance that he does not choose an apple. Now next we tackle the pear question. Again there is the probability of 1 that he chooses something. If we subtract the probability of that thing not being a pear we get the probability of the pear. So 1- 0.6- 0.3 = .1 change that he chooses a pear.

So:

A) .4 Chance (40%)

and 

B) .1 Chance (10%)

Hope this helps you.

-G

How I do this is i use point-slope form. So this is how i solved it. First i plugged in the point and got the equation     y+8=1/4(x-4) Now next i distributed the 1/4 and got y+8 = 1/4x -1 Now next to get standard for the x and y need to me arranged as such: Ax +By= C so the c had to be moved over by subtracting it from both sides so we got y- 1/4x +8= -1

Now next we need to move the 8 over, seeing as it is part of C. so we get y -1/4x =-9 Now I forgot to do this earlier but you should switch the y and x in this case so you have Ax + By not By + Ax so it should really be -1/4x + y =-9 Now to make it standard form all of the numbers have to be integers and Ax has to be a positive integer, so we have to multiply the whole equation by -4. This gives us the final answer of x- 4y= 36 which is all there is to it really. Hope this helps.

-G

Could you present you last answer properly in LaTex please pro35hp?  

It is correct :)

\(\mathrm{Use\:the\:following\:identity}:\quad \sin \left(2x\right)=2\cos \left(x\right)\sin \left(x\right)\)

\(1.5\cos \left(x\right)+2\cos \left(x\right)\sin \left(x\right)=0\)

\(=\cos \left(x\right)\left(2\sin \left(x\right)+1.5\right)\)

\(\cos \left(x\right)=0\:\:\:\mathrm{or}\:\:\:\:2\sin \left(x\right)+1.5=0\)

\(\cos \left(x\right)=0\quad :\quad x=\frac{\pi }{2}+2\pi n,\:x=\frac{3\pi }{2}+2\pi n\)

\(2\sin \left(x\right)+1.5=0\quad :\quad x=2\pi n-0.84806,\:x=2\pi n+\pi +0.84806\)

\(x=2\pi n+\pi +0.84806,\:x=2\pi n-0.84806,\:x=\frac{3\pi }{2}+2\pi n,\:x=\frac{\pi }{2}+2\pi n\)

solve each x between 0 and 2pi

\(0<2\pi n-0.84806<2\pi\)

\(\frac{0.84806}{2pi}<n<1+ \frac{0.84806}{2pi }\)

hence , n = 1 , plug it in the previous equation \(2\pi -0.84806=5.435\)

So without calculating other equation

we have choices

and the true choice is 

e. x = 1.571, 3.990, 4.712, 5.435 

if you want to complete just solve each other x between 0 and 2 pi and don't forget that n is an integer number

Bill invested $500 for 3 years at 4.5% per year simple interest.

Find the total interest. 

$500 x 4.5/100 =$22.50 interest earned for 1 year.

$22.50 x 3 =$67.50 total interest earned in 3 years.

Go ask Siri.

Express 17 1/2% as a fraction in its lowest terms

\(\frac{17.5}{100}=\frac{175}{1000}=\frac{175\div25}{1000\div25}=\frac{7}{40}\)

Not sure what you mean

\(x^8+5x^6\\ x^6*x^2+x^6*5\\ =x^6(x^2+5)\)

does that help ??

Thanks Michael,

Your first bit is good but then I am not sure what you did ://

Anyway, I want to take a quick look myself.     :)

\( 60.1 − 43.9 cos\frac{ πt}{ 6}\ge 77\\ − 43.9 cos\frac{ πt}{ 6}\ge 16.9\\ cos\frac{ πt}{ 6}\le -16.9/43.9\\ cos\frac{ πt}{ 6}\le -0.385\\ \frac{ πt}{ 6}\le cos^{-1}(-0.385)\\ \frac{ πt}{ 6}\ge 1.966\\ πt\ge 11.796\\ t\ge3.75 \)

I will assume that 1 is the END of January SO   4 is the end of April.

So sales will be exceeded in April

Here is a graph that might help you to understand.  Although the equation itself actually makes little sense.

Thanks Chris :)

60.1 − 43.9 cos πt/ 6 ≥ 77 
− 43.9 cos πt/ 6 ≥ 16.9 

cos πt/6 ≤ - .38496... 

consider cos πt/6 = - .38496... 
I know cos 1.1756.. = +.38496 

so πt/6 = π - 1.1756 = appr 1.966 
t = 3.755 

or 

πt/6 = π + 1.1756.. = 4.3172.. 
t = 8.245 

1233

That is excellent Michael.     

So the answer is    0.2*6 = $1.20        

Pro35hp,

Why are you calling someone that you do not even know 'dear'

It sounds sarcastic and it is not polite.

Would you like me to to tell you. "Sorry dear but you are wrong." ?  It would be a put down!

Would you call your teacher, or even another boy in your class,  "dear" - of course not - it would be very rude.

a) 1 kg = 1000g

b) 0.2 kg

log 10 = x/log60 + 2log10 solve x

I will assume base 10

1 = x/log60 + 2*1 

-1 = x/log60

x= -log 60

-log(60) = -1.7781512503836436

Hi Michael,      

I'd like you to answer a couple of questions for me.

1) How many grams in a kilogram.    Google it is you do not know.

2) What fraction of a kg is 200 grams?

1revolution = 360 degrees

90 revolutions = 90*360 degrees

1 minute = 60 seconds

Therefore wheel turns through 90*360/60 → 540 degrees per second

.