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2 years ago

A snake at the zoo is 4 feet long. A scale model of the snake is 2 inches long. What is the scale factor?

Mathematics

1 answer:

trapecia [35]2 years ago

8 0

1/24 4 feet = 48 inches. 48 divided by 2 = 24. Therefore 48 divided by 1/24 = 2

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14.7x + 4x = 0*(46y+39y) Y=14, Solve for X

Dovator [93]

14.7x + 4x = 0*(49y+39y) y = 14

18.7x = 0(686 + 546)

18.7x = 0

x = 0

4 0

3 years ago

Derivative, by first principle <img src="https://tex.z-dn.net/?f=%20%5Ctan%28%20%5Csqrt%7Bx%20%7D%20%29%20" id="TexFormula1"

vampirchik [111]

$\displaystyle\lim_{h\to0}\frac{\tan\sqrt{x+h}-\tan x}h$

Employ a standard trick used in proving the chain rule:

$\dfrac{\tan\sqrt{x+h}-\tan x}{\sqrt{x+h}-\sqrt x}\cdot\dfrac{\sqrt{x+h}-\sqrt x}h$

The limit of a product is the product of limits, i.e. we can write

$\displaystyle\left(\lim_{h\to0}\frac{\tan\sqrt{x+h}-\tan x}{\sqrt{x+h}-\sqrt x}\right)\cdot\left(\lim_{h\to0}\frac{\sqrt{x+h}-\sqrt x}h\right)$

The rightmost limit is an exercise in differentiating $\sqrt x$ using the definition, which you probably already know is $\dfrac1{2\sqrt x}$ .

For the leftmost limit, we make a substitution $y=\sqrt x$ . Now, if we make a slight change to $x$ by adding a small number $h$ , this propagates a similar small change in $y$ that we'll call $h'$ , so that we can set $y+h'=\sqrt{x+h}$ . Then as $h\to0$ , we see that it's also the case that $h'\to0$ (since we fix $y=\sqrt x$ ). So we can write the remaining limit as

$\displaystyle\lim_{h\to0}\frac{\tan\sqrt{x+h}-\tan\sqrt x}{\sqrt{x+h}-\sqrt x}=\lim_{h'\to0}\frac{\tan(y+h')-\tan y}{y+h'-y}=\lim_{h'\to0}\frac{\tan(y+h')-\tan y}{h'}$

which in turn is the derivative of $\tan y$ , another limit you probably already know how to compute. We'd end up with $\sec^2y$ , or $\sec^2\sqrt x$ .

So we find that

$\dfrac{\mathrm d\tan\sqrt x}{\mathrm dx}=\dfrac{\sec^2\sqrt x}{2\sqrt x}$

7 0

3 years ago

Juan lives 2.5 miles from the park. It took him 12 minutes to ride his bicycle to the park. What was Juan's average speed, in mi

Thepotemich [5.8K]

His average speed is 12.5 mph

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3 years ago

A store uses the expression –2p + 50 to model the number of backpacks it sells per day, where the price, p, can be anywhere from

Rus_ich [418]

Revenue = price * number of backpacks
number of backpacks = -2p + 50

p = 9 ; -2(9) + 50 = -18 + 50 = 32
revenue = 9 * 32 = 288

p = 12 ; -2(12) + 50 = -24 + 50 = 26
revenue = 12 * 26 = 312

p = 12.50 ; -2(12.50) + 50 = -25 + 50 = 25
revenue = 12.50 * 25 = 312.50 GIVES THE MAXIMUM REVENUE

p = 15 ; -2(15) + 50 = -30 + 50 = 20
revenue = 15 * 20 = 300

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3 years ago

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How do you write 60% as a fraction in simplest form?

saveliy_v [14]

60/100
6/10
3/5

Hope this helps :)

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4 years ago

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