I think you have to do the derivative by hand  

i(t) = 4 sin 2t + 3t, when t = 0.6

i'(t)=4cos(2t)*2+3

i'(t)=8cos(2t)+3

i'(0.6)=8cos(2*0.6)+3

Make sue your calc is set to radians.

8*cos(2*0.6)+3=

that should give you the correct answer

$${\mathtt{8}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\frac{{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{0.6}}{\mathtt{\,\times\,}}{\mathtt{180}}}{{\mathtt{\pi}}}}\right)}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}} = {\mathtt{5.898\: \!862\: \!035\: \!816}}$$

My entry is different from what I told you to enter because I had to enter it in degrees!

dial 911

convert .182 to a faction?

I will try to demonstrate the method for this with a simpler number, then go onto your question.

If we take the number 1 and divide it by 2 we get half of 1 which is 0.5      $${\frac{{\mathtt{1}}}{{\mathtt{2}}}} = {\mathtt{0.5}}$$

So we can see that as a fraction and a decimal, and we could have probably guessed the answer.

in this we are saying that 0.5 is a fraction of 1, so could be written like this $${\frac{{\mathtt{0.5}}}{{\mathtt{1}}}} = {\frac{{\mathtt{1}}}{{\mathtt{2}}}} = {\mathtt{0.5}}$$

Sadly $${\frac{{\mathtt{0.5}}}{{\mathtt{1}}}}$$ is what we call an improper fraction, in that the top number (Numerator) or bottom number (denominator) are not whole numbers.

To convert $${\frac{{\mathtt{0.5}}}{{\mathtt{1}}}}$$ to a proper fraction, where the numerator and denominator are both whole numbers we multiply both terms by 10 until we loose the decimal point.

$${\frac{{\mathtt{0.5}}{\mathtt{\,\times\,}}{\mathtt{10}}}{\left({\mathtt{1}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}}$$ = $${\frac{{\mathtt{5}}}{{\mathtt{10}}}}$$  This is now a proper fraction but needs to be reduced or simplified down to it's simplest form by finding a number (their greatest common divisor) that could divide both the numerator and denominator to give us whole numbers for the numerator and denominator.

$${\frac{{\mathtt{5}}}{{\mathtt{10}}}}$$ divided by 5 is simplified to $${\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$ which we know as half of 1.

Now to answer your question; convert .182 to a faction?

We are saying that 0.182 is a fraction of 1 so would be written

$${\frac{{\mathtt{0.182}}}{{\mathtt{1}}}}$$   As in my example, we need to convert this to a proper fraction, so we multiply both the numerator and denominator by 10 until we lose the decimal point.

$${\frac{\left({\mathtt{0.182}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}{\left({\mathtt{1}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}}$$ = $${\frac{{\mathtt{1.82}}}{{\mathtt{10}}}}$$ We still have a decimal point to lose so we repeat the process

 $${\frac{\left({\mathtt{1.82}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}{\left({\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}}$$ = $${\frac{{\mathtt{18.2}}}{{\mathtt{100}}}}$$  Again, we still have a decimal point to loose so we repeat the process again

$${\frac{\left({\mathtt{18.2}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}{\left({\mathtt{100}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}}$$ = $${\frac{{\mathtt{182}}}{{\mathtt{1\,000}}}}$$  Finally, we have a proper fraction with no decimal points. 

This is a lengthy way to do it so we have a simpler method. In this process we can see that we had to multiply both the numerator and denominator by 10 3 times, that's 10*10*10. This coincides with the amount of numbers after the decimal point in the original 0.182

So, if we said that for every number after the decimal point, we have to multiply both the numerator and the denominator by 10 we would have

$${\frac{\left({\mathtt{0.182}}{\mathtt{\,\times\,}}{\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}{\left({\mathtt{1}}{\mathtt{\,\times\,}}{\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{10}}\right)}}$$ which is equivalent to $${\frac{\left({\mathtt{0.182}}{\mathtt{\,\times\,}}{\mathtt{1\,000}}\right)}{\left({\mathtt{1}}{\mathtt{\,\times\,}}{\mathtt{1\,000}}\right)}}$$ which equals $${\frac{{\mathtt{182}}}{{\mathtt{1\,000}}}}$$ , much quicker. This is effectively the same as in other math problems where we whish to move the decimal point.

Now all we have to do is simplify $${\frac{{\mathtt{182}}}{{\mathtt{1\,000}}}}$$ to it's simplest form by dividing it by it's greatest common divisor which is 2, $${\frac{{\mathtt{182}}}{{\mathtt{1\,000}}}}$$ divided by 2 equals $${\frac{{\mathtt{91}}}{{\mathtt{500}}}}$$, which is your answer.

Melody is correct, saseflower......we should check our answers....I forgot to do this today, and I gave a wrong answer....shame on me...!!!

There is a post about this in the sticky topics on the bottom right of your page.

Hi CPhill,

ditto!

hi Saseflower,

You can check your answer but substituting 13.3 in for x on the right hand side of the question and seeig if it equals 172.

like this

-6*13.3-4(4*13.3-10)

$${\mathtt{\,-\,}}{\mathtt{6}}{\mathtt{\,\times\,}}{\mathtt{13.3}}{\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\times\,}}\left({\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{13.3}}{\mathtt{\,-\,}}{\mathtt{10}}\right) = {\mathtt{\,-\,}}{\frac{{\mathtt{1\,263}}}{{\mathtt{5}}}} = -{\mathtt{252.6}}$$

It doesn't equal the left hand side which was 172 so  x cannot be equal to 13.3.  

Understand?  

100 x $.25  .... move the decimal two places to the right.....  so we have →  $25.00

a geometric progression with 28 as its first term has the sum to infinity of 70 .

find its common ratio

$$\text{sum: }
\begin{array}{rlccl}
s &=& 28 & + & 28r+ 28r^2 + 28r^3+28r^4+28r^5 +\dots+ \\
r*s &=& && 28r +28r^2+28r^3+28r^4+28r^5+\dots+ \\
\hline
s-r*s &=& 28 &\\
&&&\\
\hline
&&&\\
\end{array}$$

$$r*s = s - 28 \\ \\
r = \dfrac{s - 28}{s} \quad | \quad s = 70\\\\
r = \dfrac{70 - 28}{70} \\\\
r = \frac{42}{70} \\\\
r = \frac{21}{35} \\\\
r = \frac{3}{5} \\\\
r = 0.6$$

press your shift key on your keyboard

$${\frac{{\mathtt{2\,707}}}{{\mathtt{999}}}}$$  Normally we would try to reduce this down to it's simplest form by finding a number (their greatest common divisor) that could divide both the top number (numerator) and bottom number (denominator) to give us whole numbers for the numerator and denominator, this would be called a proper fraction.

e.g. $${\frac{{\mathtt{2}}}{{\mathtt{4}}}}$$ divided by 2 is simplified to $${\frac{{\mathtt{1}}}{{\mathtt{2}}}}$$

$${\frac{{\mathtt{2\,702}}}{{\mathtt{999}}}}$$ does not have a greatest common divisor to reduce or simplify it whilst keeping it as  proper fraction. Therefore, it is called an irreducible fraction and remains as it is.

I need help on my homework. Plox, I will give you a thank you in return. 9^x = 1 what is x  ?

$${{\mathtt{9}}}^{{\mathtt{x}}} = {\mathtt{1}}$$

$$9^x=1 \quad | \quad \ln() \\
x*\ln(9) = \ln(1) \quad | \quad \ln(1) = 0\\
x*\ln(9) = 0 \quad | \quad : \ln(9) \\\\
x = \dfrac{ 0 } { \ln(9) } \\ \\
x = 0 \\
\small{\text{
Proof:
$ 9^0 = 1 $ okay!
}}$$

amount 10000 rate 10% interst?

It is difficult to work this out with the limited information. I have tried to relate it to a few common scenarios.

1) This question could be referring to 10,000.00 of a currency in a savings/bank account and asking how much interest would be earned on it at a rate of 10%? 

2) This question could be referring to a debt of 10,000.00 of a currency on a loan/credit/charge card and asking how much interest would be charged on it at a rate of 10%?

Usually, rates of interest such as these are calculated per annum/year.

I will use the $ (dollar) sign for the currency to try to make it clearer as it's one of the most recognised currency symbols though this can easily be swapped for any other currency.

The calculations for this are the same;

You could start by determining what is 1% of $10,000.00

$${\frac{{\mathtt{10\,000}}}{{\mathtt{100}}}} = {\mathtt{100}}$$   So this shows that 1% of $10,000.00 is $100.00

Now we can easily find 10% 0f $10,000.00 by multiplying 1% ($100.00) by 10

$${\mathtt{100}}{\mathtt{\,\times\,}}{\mathtt{10}} = {\mathtt{1\,000}}$$   This shows that 10% of $10,000.00 is $1,000.00

In the case of example 1 above, this would mean that your $10,000.00 in your savings account would have increased by $1,000.00 to a total of $11,000.00

In the case of example 2 above, this would mean that your debt of $10,000.00 on your loan had increased by $1,000.00 to a total debt of $11,000.00

There are a few other ways you could calculate this;

$${\mathtt{10\,000}}{\mathtt{\,\times\,}}{\mathtt{0.1}} = {\mathtt{1\,000}}$$    The 0.1 being the decimal version of 10%, which gives the answer of $1,000.00, to be added to your original $10,000.00

$${\mathtt{10\,000}}{\mathtt{\,\times\,}}{\mathtt{1.1}} = {\mathtt{11\,000}}$$    The 1.1 being the decimal version of 110% which is the same as 100% (the original $10,000.00) plus the 10% (the $1,000.00) already added together for us. This being the quickest method as long as you can understand it.

If your calculator has a % button you could use this by typing $${\mathtt{10\,000}}{\mathtt{\,\times\,}}{\mathtt{10}}\% = {\mathtt{1\,000}}$$  to just find the interest or $${\mathtt{10\,000}}{\mathtt{\,\times\,}}{\mathtt{110}}\% = {\mathtt{11\,000}}$$ to find the interest with the original amount combined. I would not rely on this method though in case the calculator you were provided with for a test/exam didn't have this feature.

thank you very much both of you

Very nice Chris :)

I think it is  as it gives me 1$${\frac{{{\mathtt{9}}}^{{\mathtt{1}}}}{{\mathtt{9}}}}$$

how do you combine like terms to this problem

$$-2(j^2-k)-6(j^2+3k) \\
=-2j^2+2k-6j^2-18k \\
=-2j^2-6j^2+2k-18k \\
= j^2(-2-6)+k(2-18) \\
=j_2(-8)+k(-16)\\
=j_2(-8)+k(-2*8)\\
=j_2(-8)+k(2)(-8)\\
=(-8)(j^2+2k) \\
=-8(j^2+2k)$$

We have

28 / (1 - r)  = 70    rearrange

28/70  = 1 - r

r = 1 - 28/70  = 14/35

Oops.....i made a slight error here....I forgot to subtract the 28/70 from the 1...the correct answer is ..

1 - 28/70  = 42/70 = 21/35 = 3/5  .....now, it matches heureka's solution!!!!

Thanks for calling my attention to that, heureka...!!!  DOH !!!!

1/60 as a percentage

$$\frac{1}{60}\\\\
=\frac{1}{60}*\frac{100}{100}\\\\
=\frac{100}{60}*\frac{1}{100} \quad | \quad \frac{1}{100} = 1\ \%= \ \%\\\\
=\frac{100}{60} \ \% \\\\
=\frac{5}{3} \ \% \quad | \quad \frac{5}{3} = 1.\overline{6}\\\\
=1.\overline{6} \ \% \\$$

$$(-1)^5\\
=-1*-1*-1*-1*-1\\
= 1 *-1*-1*-1\\
= -1 *-1*-1\\
= 1 *-1\\
= -1$$

I just love it.   I have not stopped laughing.     That's hilarious!    Thanks Chris.

I do appear to be a very jolly dinosaur.      

determine the following lines are parrallel ?     x-y+1=0       6x-6y+7=0

$$\boxed{ \textcolor[rgb]{1,0,0}{a} *x + \textcolor[rgb]{0,0,1}{b} *y + c = 0 \qquad m = -\frac{ \textcolor[rgb]{1,0,0}{a} }{ \textcolor[rgb]{0,0,1}{b} } } \\$$

$$\\ \textcolor[rgb]{1,0,0}{1} *x \textcolor[rgb]{0,0,1}{-1} *y +1 = 0 \qquad m = -\frac{ \textcolor[rgb]{1,0,0}{1} }{ \textcolor[rgb]{0,0,1}{(-1)} } = 1
\\
\\
\textcolor[rgb]{1,0,0}{6} *x \textcolor[rgb]{0,0,1}{-6} *y +7 = 0 \qquad m = -\frac{ \textcolor[rgb]{1,0,0}{6} }{ \textcolor[rgb]{0,0,1}{(-6)} } = 1 \\$$

The lines are parrallel because m is equal.

$$32\div d-2= \frac{32}{d}-2$$

You cannot do anything more with this.

I do not understand what you are asking