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3 years ago

A model train is 6 inches the real train is 42 feet what is the scale factor in inches

2 answers:

7 0

1 foot = 12 inches
42 feet = (42 x 12) = 504

The factor of (6 inches / 42 feet) is (6 inches / 504 inches) = 1 / 84 .

The scale factor is not in inches. It's a factor, and has no units.
A 1-ft model would represent a real 84 feet.
A 1-meter model would represent a real 84 meters.
A 1-yard model would represent a real 84 yards.

soldier1979 [14.2K]3 years ago

7 0

Answer:

42/6 = 7

SCALE FACTOR: 7 feet = 1 inch

Step-by-step explanation:

You might be interested in

The population of a certain community is known to increase at a rate proportional to the number of people present at time t. If

attashe74 [19]

Answer:

$t=7.85 years$

Step-by-step explanation:

We can write this rate as an ordinary differential equation.

$\frac{dP}{dt}=aP$

Where a is proportional constant, P the population variable, and t the time.

$\frac{dP}{P}=adt$

Integrating each side of the equation.

$\int \frac{dP}{P}=\int adt$

$ln(P)=at+c$

$P=e^{at+c}$

$P=e^{c}e^{at}=Ce^{at}$

To find C we need to use the initial condiction, it means evaluae P at t=0.

$P_{0}=Ce^{0}=C$

$P=P_{0}e^{at}$

Now, we use the sentence the population has doubled in 5 years.

$2P_{0}=P_{0}e^{a5}$

We can find "a" in this condition.

$2=e^{a5}$

$ln(2)=a5$

$a=\frac{ln(2)}{5}$

$a=0.14$

Finally, let's find how long will it take to triple.

$3P_{0}=P_{0}e^{0.14t}$

$3=e^{0.14t}$

$t=\frac{ln(3)}{0.14}$

$t=7.85 years$

I hope it helps you!

4 0

2 years ago

Write out the sample space for the given experiment. Use the following letters to indicate each choice: W for white, Y for yello

allochka39001 [22]

Answer:

S={WG, WE, WM, YG, YE, YM, BG, BE, BM}

Step-by-step explanation:

There are three possible color choices for the game room (White, Yellow or Blue), and three possible choices for the entertainment center (Gray, Ebony or Maple). This means that there are 9 possible outcomes, therefore, the sample space for the experiment is:

S={WG, WE, WM, YG, YE, YM, BG, BE, BM}

4 0

2 years ago

What is b in 4b+61 in math

aniked [119]

Set up the equation like 4b+61=0, subtract 61 from both sides, and that'll be 4b=-61. Divide both sides by 4. b=15.25

5 0

2 years ago

Mr Nelson paid $3.84 tax he pay the sales tax rate of 8% how much was item he was buying before sales tax was added

UkoKoshka [18]

Answer:

Mr. Nelson paid $48 befor tax.

Step-by-step explanation:

Let x be the price of the item before tax.

108 % * x - x = 3.84 (the tax itself)

27/25x - x = 3.84

2/25 x = 3.84

x = 48

3 0

2 years ago

Find dy/dx if f(x) = (x + 8)^3x.

vlabodo [156]

This is quite a complex problem. I wrote out a really nice solution but I can't work out how to put it on the website as the app is very poorly made. Still, I'll just have to type it all in...

Okay so you need to use a technique called logarithmic differentiation. It seems quite unnatural to start with but the result is very impressive.

Let y = (x+8)^(3x)

Take the natural log of both sides:

ln(y) = ln((x+8)^(3x))

By laws of logarithms, this can be rearranged:

ln(y) = 3xln(x+8)

Next, differentiate both sides. By implicit differentiation:

d/dx(ln(y)) = 1/y dy/dx

The right hand side is harder to differentiate. Using the substitution u = 3x and v = ln(x+8):

d/dx(3xln(x+8)) = d/dx(uv)

du/dx = 3

Finding dv/dx is harder, and involves the chain rule. Let a = x+ 8:

v = ln(a)
da/dx = 1
dv/da = 1/a

By chain rule:

dv/dx = dv/da * da/dx = 1/a = 1/(x+8)

Finally, use the product rule:

d/dx(uv) = u * dv/dx + v * du/dx = 3x/(x+8) + 3ln(x+8)

This overall produces the equation:

1/y * dy/dx = 3x/(x+8) + 3ln(x+8)

We want to solve for dy/dx, achievable by multiplying both sides by y:

dy/dx = y(3x/(x+8) + 3ln(x+8))

Since we know y = (x+8)^(3x):

dy/dx = ((x+8)^(3x))(3x/(x+8) + 3ln(x+8))

Neatening this up a bit, we factorise out 3/(x+8):

dy/dx = (3(x+8)^(3x-1))(x + (x+8)ln(x+8))

Well wasn't that a marathon? It's a nightmare typing that in, I hope you can follow all the steps.

I hope this helped you :)

8 0

3 years ago