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1 year ago

Identify the scale factor. Wingspan of airplane: 90ft Wingspan of model of airplane: 6ft

Mathematics

1 answer:

Debora [2.8K]1 year ago

8 0

The scale factor of the model of the airplane is 1 feet : 15 feet.

<h3>What is the scale factor?</h3>

A scale drawing is a reduced form in terms of dimensions of an original image / building / object. The scale drawing is usually reduced at a constant dimension using the scale factor.

Scale factor = original dimensions / dimensions of the scale drawing

90 / 6 = 15

1 : 15

To learn more about scale drawings, please check: brainly.com/question/26388230

#SPJ1

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Morgarella [4.7K]

Answer:

$f'(x)=-\frac{2}{x^\frac{3}{2}}$

Step-by-step explanation:

So we have the function:

$f(x)=\frac{4}{\sqrt x}$

And we want to find the derivative using the limit process.

The definition of a derivative as a limit is:

$\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Therefore, our derivative would be:

$\lim_{h \to 0}\frac{\frac{4}{\sqrt{x+h}}-\frac{4}{\sqrt x}}{h}$

First of all, let's factor out a 4 from the numerator and place it in front of our limit:

$=\lim_{h \to 0}\frac{4(\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x})}{h}$

Place the 4 in front:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}$

Now, let's multiply everything by (√(x+h)(√(x))) to get rid of the fractions in the denominator. Therefore:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}(\frac{\sqrt{x+h}\sqrt x}{\sqrt{x+h}\sqrt x})$

Distribute:

$=4\lim_{h \to 0}\frac{({\sqrt{x+h}\sqrt x})\frac{1}{\sqrt{x+h}}-(\sqrt{x+h}\sqrt x)\frac{1}{\sqrt x}}{h({\sqrt{x+h}\sqrt x})}$

Simplify: For the first term on the left, the √(x+h) cancels. For the term on the right, the (√(x)) cancel. Thus:

$=4 \lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }$

Now, multiply both sides by the conjugate of the numerator. In other words, multiply by (√x + √(x+h)). Thus:

$= 4\lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }(\frac{\sqrt x +\sqrt{x+h})}{\sqrt x +\sqrt{x+h})}$

The numerator will use the difference of two squares. Thus:

$=4 \lim_{h \to 0} \frac{x-(x+h)}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Simplify the numerator:

$=4 \lim_{h \to 0} \frac{x-x-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}\\=4 \lim_{h \to 0} \frac{-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Both the numerator and denominator have a h. Cancel them:

$=4 \lim_{h \to 0} \frac{-1}{(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Now, substitute 0 for h. So:

$=4 ( \frac{-1}{(\sqrt{x+0}\sqrt x)(\sqrt x+\sqrt{x+0})})$

Simplify:

$=4( \frac{-1}{(\sqrt{x}\sqrt x)(\sqrt x+\sqrt{x})})$

(√x)(√x) is just x. (√x)+(√x) is just 2(√x). Therefore:

$=4( \frac{-1}{(x)(2\sqrt{x})})$

Multiply across:

$= \frac{-4}{(2x\sqrt{x})}$

Reduce. Change √x to x^(1/2). So:

$=-\frac{2}{x(x^{\frac{1}{2}})}$

Add the exponents:

$=-\frac{2}{x^\frac{3}{2}}$

And we're done!

$f(x)=\frac{4}{\sqrt x}\\f'(x)=-\frac{2}{x^\frac{3}{2}}$

5 0

2 years ago

Please help me find the answer! Please explain how you got it!

Ksenya-84 [330]

Answer:

B. 4.5c + 4 = 24

Step-by-step explanation:

T = cx + py is the equation you are given.

T = 24 because it is the total amount of money you can spend.

x = 4.5 because each phone case costs 4.50 dollars

p = 2 because you bought 2 pop sockets.

y = 2 because each pop socket costs 2 dollars.

There is no c because you don't know the number of phone cases you bought.

Now, we have to substitute the values into the equation:

24 = 4.5x + 2(2)

24 = 4.5x + 4

4.5x + 4 = 24 <--- This is your answer

Hope this helps!

7 0

2 years ago

How do you do 2 divided by 7

laiz [17]

Do long division but the answer is 2/7 or 0.2857

6 0

3 years ago

What is the graph of the function f(x) = -x^2+x+20/x+4

mr_godi [17]

F(x) = (-x²+x+20) / (x+4)

-x²+x+20 | x+4
+x²+4x -x+5
\\\\ 5x+20
-5x-20
\\\\\\\\\

f(x) = (x+4)(-x+5) / (x+4)

f(x) = (-x+5)

The graph is a decreasing line, with origin from 5.

3 0

2 years ago

What percent of 126 is 22?

LenaWriter [7]

17.46% of 126 is 22

Divide 22 by 126:
$22 \div 126 = 0.1746$

Change the decimal into a percentage by multiplying the decimal by 100:
$0.1746 \times 100 = 17.46$

6 0

3 years ago

Read 2 more answers