All Answers 358093 Answers

Look at it this way:

Let        x = 0.9999999999.....

Then  10x = 9.9999999999...

Subtract the first from the second to get

10x - x = 9.999999999.... - 0.999999999...  

or 9x = 9

so x = 1

The area of a full circle is pi*radius², so the area of a semicircle is (1/2)pi*radius².

$$\left({\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right){\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{{\mathtt{7.89}}}^{{\mathtt{2}}} = {\mathtt{97.785\: \!370\: \!015\: \!268\: \!583\: \!8}}$$

area ≈ 97.79 cm² 

Sin(a) and sin(b) are both negative which means that a and b have to be in the 3rd or 4th quadrant.

 $$cos(a+b)\\\\
=cos(a)cos(b)-sin(a)sin(b)\\\\
=\pm\frac{4}{5}\times \pm \frac{12}{13}- \;\;\frac{-3}{5}\times \frac{-5}{13}\\\\
=\pm\frac{48}{65}- \;\;\frac{15}{65}\\\\
=\frac{-15-48}{65}\;\;or\;\;\frac{-15+48}{65}\\\\
=\frac{-63}{65}\;\;or\;\;\frac{33}{65}\\\\$$

$$2sin120cos120\\
=sin(120+120)\\
=sin240\\
=sin(180+60) \qquad (third\;\;quadrant\;\;so\;\;negative)\\
=-sin60\\
=\frac{-\sqrt3}{2}$$

If the domain is from x=0 to x = 4 then the range of y = x² is from y = 0 to y = 16.  It includes all real numbers not just integers.

It often helps to draw a graph:

2 sin 120 cos 120    ?

$$\\\sin{(\alpha+\beta)}=
\sin{(\alpha)}
*
\cos{(\beta)}
+
\cos{(\alpha)}
*
\sin{(\beta)}
\\
\sin{(\alpha+\alpha)}=
\sin{(\alpha)}
*
\cos{(\alpha)}
+
\cos{(\alpha)}
*
\sin{(\alpha)}\\\\
\boxed{
\sin{(2*\alpha)}=
2*\sin{(\alpha)}
*
\cos{(\alpha)}}\\\\
\sin{(2*120\ensurement{^{\circ}} )}=
2\sin{(120\ensurement{^{\circ}} )}
\cos{(120\ensurement{^{\circ}} )}=
\sin{(240 \ensurement{^{\circ}} ) =-0.86602540378$$

$$\\ \sin{(240 \ensurement{^{\circ}} )
=
\sin{(360\ensurement{^{\circ}-120 \ensurement{^{\circ} } )
=
-\sin{(120 \ensurement{^{\circ} } )
=-\frac{\sqrt{3} } {2}
=-0.86602540378$$

3/15 divided by 7/10  ?

$$\begin{array}{rcl}
\dfrac { \frac {3}{15}} {\textcolor[rgb]{1,0,0}{\frac {7}{10} }}
=
\frac {3}{15}\times\textcolor[rgb]{1,0,0}{\frac {10}{7}}
=
\frac {3*\textcolor[rgb]{1,0,0}{10 }}{15*\textcolor[rgb]{1,0,0}{7}}
=
\frac {3*\textcolor[rgb]{1,0,0}{2*5 }}{3*5*\textcolor[rgb]{1,0,0}{7}}
=
\frac {3*\textcolor[rgb]{1,0,0}{5*2 }}{3*5*\textcolor[rgb]{1,0,0}{7}}
=\frac {\textcolor[rgb]{1,0,0}{2}}{\textcolor[rgb]{1,0,0}{7}}\end{array}
=0.28571428571$$

Hi anonymous,

Good thinking but your logic is a little floored because there are an infinite number of 0s before the 1.  

So the 1 is never reached.

$$\\\frac{1}{3}=0.33333333.......\\\\
\frac{2}{3}= 0.66666666........\\\\
\frac{3}{3}=0.999999999....... = 1$$

but 1- 0.9999999999...=o.ooooooooooooooooooooooooo1

and since 0.00000000000000001 does not = 0

0.999999999999999 does not = 1

0.9 repeater equals 1

3x + y = -4

$$\Rightarrow x=-{1\over3}y-{4\over3}$$ 

$$\\\text{Y axis Segment } = -\frac{4}{3} \\\\
\text{Gradient to the Y axis} = -\frac{1}{3} \quad \text{(+ clockwise; - counterclockwise)}$$

Me too. I think I got it wrong too.

I think I got it wrong ._.

Awkward moment when there are two answers. And the feeling that you got it wrong.

DragonSlayer. Good Try, I see what you did. But you seemed to have calculated this as Simple Interest. For this question, you need to solve it as Compound Interest. Lets start.

Let me first introduce you to the Compound Interest Formula.

Principal X (1 + Periodic Rate) ^ Number of Periods = Future Amount

Principal is the amount in the account in one yeat given that this is an annual interest.

So lets add the Principal:

$${\mathtt{35}}{\mathtt{\,\times\,}}{\mathtt{12}} = {\mathtt{420}}$$

The Principal is 420.

So lets add that in:

420 * (1 + Period rate) ^ Number of Periods. = Future Amount.

Now the period rate is 7%. So lets turn that into a decimal.

0.07. Lets place that in

420 * (1 + 0.07) ^ Number of Periods. = Future Amount.

Number of Periods is the Year.

420 * (1 + 0.07) ^ 30= Future Amount.

$${\mathtt{420}}{\mathtt{\,\times\,}}{\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{0.07}}\right)}^{{\mathtt{30}}} = {\mathtt{3\,197.147\: \!117\: \!918\: \!052\: \!266\: \!8}}$$

The amount would then be 3,197.14 Dollars.

However, providing that Money is deposited every month... I will solve it on the next post.

The Future Value of an Annuity is given by:

FV = P [(1 + r)ⁿ - 1] / [r].........where

P = periodic payment..... ($35)

n = number of periods......(360)

r = rate per period = (.07/12) = 0.0058333333333333

So we have......

35 [(1 + 0.0058333333333333)³⁶⁰ - 1)] / (0.0058333333333333) ≈ $42698.98

CPhill, I know that there are many solutions to the problem. That's what I wrote.

I tried my best. Don't give me negative points, please.

Let me try.

$35*12=$420

$420*30=$12,600

$12,600*7%=$882

I don't know if the question asks for tha annual rate of 7% per year or what. If it is for 1 year, the answer is right below.

$882

$12,600-$882=$11,718

So, the answer is $11,718.

Hope it helps!

admin wanted to call it like that. I don't know why it is called like that.

Math would never hurt you. It hurts a little when you fail, or when you think and the answer doesn't come. And Melody, how would people make books that are taller than humans?

The answer is 78,125. Hope it helps.