All Answers 358087 Answers

cos(sec^(-1)(sqrt(5)))=1/ sqrt(5)

=39.72 inches

Okay...if you have a graphing calculator...then you would press the blue button that says "2nd" and in the middle of the calculator there should be a button thqat says "sin" , press it, then it will show the word "sin" on our screen like this: sin(, that is when you anter the number 0.47 and make sure you press the close parantheses button after that which is ")" and then press enter....then number you get is the solution.

Hope I helped :)

2/3r=26

2r=26*3

2r=78

r=78/2

r=39

the square root of 16.222 is 4.0276544042407611

I like dust in the wind but mr. Bojangles is an ok song.

What about Dust in the Wind by Kansas?

Or Mr. Bojangles by Nitty Gritty Dirt Band. 

2/3r=26

\(\frac{2}{3}r=26\\ r=26*\frac{3}{2}\\ r=13*\frac{3}{1}\\ r=39\)

How do i work out an angle using soh,cah,toa.

Energy=mass * speed of light in vacuum^2

It's the region above the dotted line but below the solid line in the graph below:

.This region continues to ever higher x values of course!

.

Have a look at https://en.wikipedia.org/wiki/Cubic_function for the solution to this cubic equation.

A fraction is just a fancy way to write a division problem.

please

Hello guest!

how much greater is 5970000000000000000000000

than 10000000000000000000007.34

written in scientific notation?

5 970 000 000 000 000 000 000 000

         - 10 000 000 000 000 000 000 007.34

= 5.97 * 10²⁴ - 10²² - 7.34

= 10²² * (5.97 * 10² - 1) - 7.34

= 10²² * 596 - 7.34

= 5 960 000 000 000 000 000 000 000.00

                                                         - 7.34

= 5 959 999 999 999 999 999 999 992.66

= 5. 959 999 999 999 999 999 999 99266 * 10²⁴

5.97 * 10²⁴ is greater than (10²² + 7.34)

                  to  5. 959 999 999 999 999 999 999 99266 * 10²⁴

Greeting asinus : )

 !

FV=PV[ 1 + R]^N

FV=15,000[1 + .03]^4

FV=15,000 x 1.12550881

FV=$16,882.63

MWizzard, take a look at my answer   :)

Jill’s husband Jim invests $15 000 with compound interest at 3% pa. Ch 3 How much does he have after 4 years?

It depends on how often it is compounded bur I will assume it is compounded yearly 

15000 (1+0.03)^4  = 15000*1.03^4 

15000*1.03^4 = 16882.63215

$16,882.63

According to the rules asinus is correct :))

However,

I expect you really meant

4^(1/5)*(4^0.3) = 4^0.2 * 4^0.3  = 4^0.5  = sqrt4  = 2

I have another method for the second question.  I found the exact answer and used no trig.

As others have already shown, triangle BEC is isosceles so BE=BC=8

DE=8-2=6 units.

Let angle ECD= alpha

It follows that in triangle BCD

< BCD = theta-alpha

< CDB =180-theta

< DBC = alpha

Now consider triangle ABE

<ABE = theta-alpha

<BEA=180-theta

<EAB = alpha

so 

Triangle BCD is similar to triangle ABE       (3 equal angles)

Hence

\(\frac{AB}{BE}=\frac{BC}{DC}\\ \frac{AB}{8}=\frac{8}{DC}\\ AB=\frac{64}{DC}\\\)

Also triangle ABC and triangle CED are both isosceles triangles with base angles of theta degrees so they are also similar.

so

\(\frac{AB}{BC}=\frac{DC}{DE}\\ \frac{AB}{8}=\frac{DC}{6}\\ AB=\frac{4*DC}{3}\\~\\ so\\~\\ \frac{64}{DC}=\frac{4*DC}{3}\\ \frac{64*3}{4}=DC^2\\ DC=\frac{8*\sqrt3}{2}\\ DC=4\sqrt3\;\;units\\\)

\(AB=\frac{64}{DC}\\ AB=\frac{64}{4\sqrt3}\\ AB=\frac{16}{\sqrt3}\\ AB=\frac{16\sqrt3}{3}\;\;units\\~\\ AB \approx 9.2376\;\;units\)

CH₄ + 2O₂ = CO₂ + 2H₂O

Molecular weight of methane = 16

Molecular weight of carbon dioxide = 44

Mass of carbon dioxide = mass of methane×44/16  →  6.30×10−3×44/16  → 0.017 g

Jill’s husband Jim invests $15 000 with compound interest at 3% per year. How much does he have after 4 years?

Interest -> $15 000 × [100% + (4 × 3%)]

= $15 000 × (100% + 12%)

= $15 000 × 112%

= $16 800

from MathWizard2004 A.K.A. mathw0122

P.S. January 22, 2004 is not my birthday! (gotten from Inside Out)

Here's another way to approach this question:

The equation can be written as 3x = e^-x

e^-x can be written as a series: 1 - x + x²/2 - x³/6 + x⁴/24 - x⁵/120 + ...

So 3x = e^-x can be written as 3x = 1 - x + x²/2 - x³/6 + x⁴/24 - x⁵/120 + ...

Subtract 3x from both sides to get  0 = 1 - 4x + x²/2 - x³/6 + x⁴/24 - x⁵/120 + ...

Now approximate this by  0 ≈ 1 - 4x₀  so that x₀ ≈ 0.25  

Take the next term to get   0 ≈ 1 - 4x₁ + x₁²/2   Solve this to get x₁ ≈ 0.258  (ignoring the other solution which is bigger than 1, so the series would diverge, and is clearly not a solution to the original equation).

The true solution lies between 0.25 and 0.258  (the question allows for an interval as a solution!).

It is easy enough to take higher order approximations numerically to tighhten the interval if required.

.

[cos(a)cos(b)+sin(a)sin(b)][cos(a)cos(b)-sin(a)sin(b)]=?

\(\begin{array}{rcll} && [~ \cos(a) \cos(b)+ \sin(a) \sin(b) ~] \cdot [~ \cos(a)\cos(b)- \sin(a) \sin(b) ~] \\ &=& \cos^2(a) \cos^2(b) - \cos(a) \cos(b)\sin(a) \sin(b)+ \sin(a) \sin(b)\cos(a)\cos(b) -\sin^2(a) \sin^2(b) \\ &=& \cos^2(a) \cos^2(b) + 0 -\sin^2(a) \sin^2(b) \\ &=& \cos^2(a) \cos^2(b) -\sin^2(a) \sin^2(b) \\ &=&[~ 1-\sin^2(a) ~] \cos^2(b) -\sin^2(a) [~ 1-\cos^2(b) ~] \\ &=& \cos^2(b) -\sin^2(a) \cos^2(b) -\sin^2(a) +\sin^2(a)\cos^2(b) \\ &=& \cos^2(b) -\sin^2(a) -\sin^2(a) \cos^2(b) +\sin^2(a)\cos^2(b) \\ &=& \cos^2(b) -\sin^2(a) +0 \\ &\mathbf{=}&\mathbf{ \cos^2(b) -\sin^2(a) }\\ \end{array}\)

x=1/(3*e^x)

solve for x (or give an interval that satisfies the equation)

We use the product log function, also called Lambert W-Function:

If the function is \(x\cdot e^x = z\), then \(x = W(z)\)

\(\begin{array}{rcll} x &=& \dfrac{1} {3\cdot e^x} \qquad & | \qquad \cdot e^x \\ x\cdot e^x &=& \frac13\\ \mathbf{ x } & \mathbf{=} & \mathbf{ W(\frac13) } \end{array}\)

\(x = 0.257627653049736704282916201626097790909692647503204491533\dots\)

Let the number you say, anything, be x.

Now let's test the properties of division (by zero)

Property 1: (for x ≠ 0)

\(\frac{x}{0} = ∞\) 

Property 2: (for x ≠ 0)

\(\frac{0}{x} = 0\)  

Property 3: (for x ≠ 0)

\(\frac{x}{x} = 1\)    

However, when x = 0 in all properties,

\(\frac{0}{0}\)     could be infinity (property 1), 0 (property 2), or 1 (property 3).

But, this equation does not make sense, since you cannot share nothing to nobody.

Therefore, there is no solution to \(\frac{0}{0}\)     

Therefore, dividing by zero does NOT make sense at all.

from MathWizard2004 A.K.A. MathW0122