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I took your equation to mean: (1/5)^(4x) - 3 = 5

Solve for x over the real numbers:
5^(-4 x) - 3 = 5

Add 3 to both sides:
5^(-4 x) = 8

Take the logarithm base 5 of both sides:
-4 x = (log(8))/(log(5))

Divide both sides by -4:
Answer: |x = -(log(8))/(4 log(5))=-0.3230074185550.....

This just says the the Kinetic Energy of an object is given by  1/2 times the mass of the object  times the velocity of the object squared.

Anything that goes into 70 evenly and NOT 71- 78 will work

35   10  

Missing masses??!!. Look for them!!.

I will assume 8% to be compounded monthly. Use this formula to calculate the payment:

PV=P{[1 + R]^N - 1.[1 + R]^-N} R^-1

20,934 =P {[1 + 0.08/12]^(12*12) -1 x [1 + 0.08/12]^-(12*12) x (0.08/12)^-1}, solve for P.

20,934 =P x 92.3830538.... divide both sides by 92.3830538

P = $226.60 Your monthly payment.

Nick invested $6399 in an account at 7% compounded daily.  Calculate the compound interest C after 6 years.

FV = PV [ 1 + R]^N

FV =6,399[1 + 0.07/365]^(6*365)

FV =6,399[1 + 0.00019178]^2,190

FV =6,399 x 1.00019178^2,190

FV =6,399 x 1.52189753....

FV =$9,738.64 what Nick will have in his account after 6 years @ 7% comp. daily.

$9,738.64 - $6,399 =$3,339.64 total interest that Nick will have earned in 6 years @ 7% comp. daily.

x = 2

I converted the decimals to fractions.

Thew american billion is   1,000,000,000

and this equals   1000*1000000

There are many products (times)  that equal a billion or a trillion :D

90 x $9.25 =$832.50 total collected from all students.

$832.50 - $315.00 = $517.50 money left over for students' lunch.

$517.50 / 90 =$5.75 that each student will get to spend on lunch.

Ball is thrown at 42m/s and travels 18m. How long does it take for the ball to reach its destination?

Well assuming there is no curve and the speed is totally constant. (which of course it will not be) then

Speed= distance /time

time*speed=distance

time=distance / speed

 You can work all this out with the units too.

\(time=distance \div speed \\ =18m \div \frac{42m}{s}\\ = \frac{ 18m}{1} \times \frac{s}{42m} \\ \qquad \text{The metres cancel}\\ = \frac{ 18s}{42} \\ \approx 0.429 \;seconds\)

0.41 x 100/100 =41/100

1,250,000.

N can any number of this form:

78N + 8, so:

1 =78+8 =86 the smallest number

2 =156 + 8 =164

3 =234 + 8 =242........and so on.

Thanks very much Alan :)  

Let z = 3^h

lnz = h*ln3

(1/z)dz/dh = ln3

dz/dh = ln3*z → ln3*3^h

d3^h/dh = ln3*3^h

1/3=.3 repeating

Taylor series of function f(h):  f(h) = f(0) + df/dh₀*h + (d²f/dh²)₀*h²/2! + ...

If f(h) = 3^h then df/dh = ln3*3^h,  d²f/dh² = (ln3)²*3^h, etc. 

So, noting that 3⁰ = 1, we have:  3^h = 1 + ln3*h + (ln3)²*h²/2! + ...

(the ... indicates terms involving higher powers of h)

Hence 3^h - 1 = ln3*h + (ln3)²*h²/2! + ...

(3^h - 1)/h = ln3 + (ln3)²*h/2! + ...

As h → 0 all but the first term on the right hand side go to 0, so in the limit we have

lim_h→0(3^h - 1)/h = ln3 

(much easier using l'Hopital's rule though!)

It is still infinity :)

It is still infinity :)

I'd like to see this one done too please :)

Also

As a slightly seperate issue...

Why is

\(\frac{d}{dh}\;3^h =\;3^h\;log3\)

|5x-2|=3

You have to solve 2 equations and there will be 2 answers

5x-2=3                   and                  5x-2=-3

now you can do that :)

That would be like 50 dollars for me so no

Bring it up

Thx