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Masja [62]
3 years ago
12

The function g has an inverse. The function g − 1 determines the number of folds needed to give the folded paper a thickness of

t mm. Write a function formula for g − 1 .
Mathematics
1 answer:
Amanda [17]3 years ago
4 0

Answer:

\mathbf{g^{-1} (t) = log _2  \ 20 \ t}

Step-by-step explanation:

Here is the full question

A standard piece of paper is 0.05 mm thick. Let's imagine taking a piece of paper and folding the paper in half multiple times. We'll assume we can make "perfect folds," where each fold makes the folded paper exactly twice as thick as before - and we can make as many folds as we want.

Write a function g that determines the thickness of the folded paper (in mm) in terms of the number folds made, n. (Notice that g(0) 0.05,)

g(n )= (05)2^n

The function g has an inverse. The function g⁻¹ determines the number of folds needed to give the folded paper a thickness of t mm. Write a function formula for g⁻¹).

<u>SOLUTION:</u>

If we represent g(n) with  t;

Then

\mathbf{t = (0.05)2^n} \\ \\ \mathbf{\dfrac{t}{0.05} = 2^n} \\ \\ \mathbf{\dfrac {100 \ t }{ 5} = 2^n} \\  \\ \mathbf{20 t = 2^n}

Taking logarithm of both sides; we have :

\mathbf{log (20 t) = n log 2}    \ \ \    \mathbf{(since  \ ,  log  \ a^b = b \ log \ a) }  \\ \\ \mathbf{n =  \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) =  \dfrac{log \ 20 t }{log \ 2 }} \\ \\ \mathbf{g^{-1} (t) = log _2  \ 20 \ t}

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An object is launched from ground level with an initial velocity of 120 meters per second. For how long is the object at or abov
babunello [35]

Answer:

D) 14 seconds

Step-by-step explanation:

First we will plug 500 in for y:

500 = -4.9t² + 120t

We want to set this equal to 0 in order to solve it; to do this, subtract 500 from each side:

500-500 = -4.9t² + 120t - 500

0 = -4.9t²+120t-500

Our values for a, b and c are:

a = -4.9; b = 120; c = -500

We will use the quadratic formula to solve this.  This will give us the two times that the object is at exactly 500 meters.  The difference between these two times will tell us when the object is at or above 500 meters.

The quadratic formula is:

x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}

Using our values for a, b and c,

x=\frac{-120\pm \sqrt{120^2-4(-4.9)(-500)}}{2(-4.9)}\\\\=\frac{-120\pm \sqrt{14400-9800}}{-9.8}\\\\=\frac{-120\pm \sqrt{4600}}{-9.8}\\\\=\frac{-120\pm 67.8233}{-9.8}\\\\=\frac{-120+67.8233}{-9.8}\text{ or }\frac{-120-67.8233}{-9.8}\\\\=\frac{-57.1767}{-9.8}\text{ or }\frac{-187.8233}{-9.8}\\\\=5.3242\text{ or }19.1656

The two times the object is at exactly 500 meters above the ground are at 5 seconds and 19 seconds.  This means the amount of time it is at or above 500 meters is

19-5 = 14 seconds.

6 0
3 years ago
Niles and Bob sailed at the same time for the same length of time. Niles' sailboat traveled 36 miles at a speed of 6 mph, while
kykrilka [37]

Answer:

Niles and Bob were traveling for 6 hours.

Step-by-step explanation:

The speed or rate at which an object is moving can be computed using the formula:

s=\frac{d}{t}

Here:

<em>s</em> = speed

<em>d</em> = distance traveled

<em>t</em> = time taken

It is provided that Niles and Bob sailed at the same time for the same length of time.

Speed of Niles sailboat is, <em>s</em>₁ = 6 mph.

Distance traveled by Niles' sailboat is, <em>d</em>₁ = 36 miles.

Speed of Bob's sailboat is, <em>s</em>₂ = 16 mph.

Distance traveled by Bob's sailboat is, <em>d</em>₂ = 96 miles.

It took both Niles and Bob the same time to travel the respective distance.

Compute the time it took Niles to travel 36 miles at 6 mph speed as follows:

t_{1}=\frac{d_{1}}{s_{1}}

   =\frac{36}{6}\\=6

It took Niles 6 hours to travel 36 miles at 6 mph speed.

Compute the time it took Bob to travel 96 miles at 16 mph speed as follows:

t_{2}=\frac{d_{2}}{s_{2}}

   =\frac{96}{16}\\=6

It took Bob 6 hours to travel 96 miles at 16 mph speed.

Thus, Niles and Bob were traveling for 6 hours.

7 0
3 years ago
Y=-x^2-x-3 find the X intercept for The parabola define by this equation
KengaRu [80]
To find the X intercept make y =0. Then factor out a negative on the side with the equation for each of the terms, so it becomes
0=-(x^2+x+3)
0=(x^2+X+3)
0-3=(x^2+X)
-3=x(X+1)
-3=X, X intercept -3,0
-3=(X+1)
-4=X, X intercept -4,0.
These are possible X intercepts you can check by using quadratic formula as well.
7 0
3 years ago
...........................
cupoosta [38]

Answer:

3/5 or 0.6

Step-by-step explanation:

Here, given the value of tan theta , we want to find the value of sine theta

Mathematically;

tan theta = 0pposite/adjacent

Sine theta = opposite/hypotenuse

Firstly we need the length of the hypotenuse

This can be obtained using the Pythagoras’ theorem which states that the square of the hypotenuse equals sum of the squares of the two other sides.

Let’s call the hypotenuse h

h^2 = 3^2 + 4^2

h^2 = 9 + 16

h^2 = 25

h = √(25)

h = 5

Now from the tan theta, we know that the opposite is 3

Thus, the value of the sine theta = 3/5 or simply 0.6

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3 years ago
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2 years ago
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