There are two of them.

I don't know a mechanical way to 'solve' for them.

One can be found by trial and error:

x=0 . . . . . 2^0 = 1 . . . . . 4(0) = 0 . . . . . no, that doesn't work
x=1 . . . . . 2^1 = 2 . . . . . 4(1) = 4 . . . . . no, that doesn't work
x=2 . . . . . 2^2 = 4 . . . . . 4(2) = 8 . . . . . no, that doesn't work
x=3 . . . . . 2^3 = 8 . . . . . 4(3) = 12 . . . . no, that doesn't work
x=4 . . . . . 2^4 = 16 . . . . 4(4) = 16 . . . . Yes ! That works ! yay !

For the other one, I constructed tables of values for 2^x and (4x)
in a spread sheet, then graphed them, and looked for the point
where the graphs of the two expressions cross.

The point is near, but not exactly, x = 0.30990693...

If there's a way to find an analytical expression for the value, it must involve
some esoteric kind of math operations that I didn't learn in high school or
engineering school, and which has thus far eluded me during my lengthy
residency in the college of hard knocks. If anybody out there has it, I'm
waiting with all ears.

7 0

2 years ago

Read 2 more answers

Answer the question and get Brainly, A sail for a boat is in the shape of a right Tiangle. The longest side is 20 ft. long. One

lana66690 [7]

Answer:

<h3>The answer is D.</h3>

Step-by-step explanation:

Explanation:

The rule of a triangle is that it the other two sides could not be longer than longest side of the triangle. If the two sides added up together is greater than the longest side, the triangle would no longer be connected. Since 8 + 12 ft still works for the longest side of the triangle, it will be considered the length of the third side.

3 0

2 years ago

Read 2 more answers

An investment company pays 8% compounded semiannually. You want to have $12,000 in the future. (A) How much should you deposit

Leno4ka [110]

Before we start answering the question, let's define the compound interest formula:
$A = P(1+ \frac{r}{n}) ^{nt}$
Where:
'A' is the amount of money in dollars
'P' is the principal amount of money in dollars
'r' is the interest rate (decimal)
'n' is the number of times interest is compounded per year
't' is the time in years

(A) Find Principal Amount
Given:
A = 12,000
P = ?
r = 0.08
n = 2 (semiannually)
t = 5
Now we plug our values in and solve:
$12,000 = P(1+ \frac{0.08}{2}) ^{(2)(5)}$
$12,000 = P(1.04) ^{10}$
$P = 8106.77$
∴ You would have to deposit $8106.77 in order to have $12,000 in 5 years from now.

(B) Find Principal Amount
Same given values as above, with the exception of 't' which is now 10 instead of 5.
$12,000 = P(1+ \frac{0.08}{2}) ^{(2)(10)}$
$12,000 = P(1.04) ^{20}$
$P = 5476.64$
∴ You would have to deposit $5476.64 in order to have $12,000 in 10 years from now.

Hope this helps!

4 0

3 years ago