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Inessa05 [86]
3 years ago
12

The average length of a ladybug can range from 0.08 to 0.4 inches. Find two lengths that are within the given span.Write them as

fractions in simplest form.
Mathematics
1 answer:
Alenkinab [10]3 years ago
7 0
The average length of a ladybug can range from 0.08 to 0.4 inches.

So two lengths within the given span are 0.1 inch and 0.3 inches.

In  \: fraction: \\  \\ 0.1 \: inch =  \frac{1}{10}  \: inch \\  \\ 0.3 \: inch =  \frac{3}{10}  \: inch
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The volume of sphere is increaseing
Artemon [7]

Volume of a sphere:

<em>V</em> = 4/3 <em>π</em> <em>r</em> ³

Differentiate <em>V</em> with respect to time <em>t</em> :

d<em>V</em>/d<em>t</em> = 4<em>π</em> <em>r</em> ² d<em>r</em>/d<em>t</em>

Surface area of a sphere:

<em>A</em> = 4<em>π</em> <em>r</em> ²

Differentiate <em>A</em> with respect to <em>t</em> :

d<em>A</em>/d<em>t</em> = 8<em>π</em> <em>r</em> d<em>r</em>/d<em>t</em>

<em />

You're given that the volume is increasing at a constant rate, d<em>V</em>/d<em>t</em> = 10 cm³/s, so

10 cm³/s = 4<em>π</em> <em>r</em> ² d<em>r</em>/d<em>t</em>

Solve for d<em>r</em>/d<em>t</em> (the rate of change of the sphere's radius):

d<em>r</em>/d<em>t</em> = 5/(2<em>π</em> <em>r</em> ²) cm³/s

Substitute this into the equation for d<em>A</em>/d<em>t</em> :

d<em>A</em>/d<em>t</em> = 8<em>π</em> <em>r</em> (5/(2<em>π</em> <em>r</em> ²) cm³/s)

d<em>A</em>/d<em>t</em> = 20/<em>r</em> cm³/s

At the moment the radius is <em>r</em> = 5 cm, the surface area is increasing at a rate of

d<em>A</em>/d<em>t</em> = 20/(5 cm) cm³/s = 4 cm²/s

When the surface area is increasing at a rate of d<em>A</em>/d<em>t</em> = 2 cm²/s, the radius <em>r</em> is such that

2 cm²/s = 20/<em>r</em> cm³/s

which happens when the radius is

<em>r</em> = 20/2 (cm³/s) / (cm²/s) = 10 cm

4 0
3 years ago
Please help mee I don't understand this for some reasonnnn!!
Vesnalui [34]

Answer:

bivariate data

Scatter plot

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nonlinear assocciaton

clustering

outlier

Step-by-step explanation:

7 0
2 years ago
How would you translate this situation below into an algebraic expression?
Natasha2012 [34]
Dime value: $0.10
Nickel value: $0.05

For this word problem, you are asked to create an algebraic expression (an equation) for the unknown variables. 

Now, we know that a dime is worth $0.10 or 10 cents and a nickel is worth $0.05 or 5 cents. So, all you would have to do is create an equation that takes those values into account. 
5n + 10d

Your algebraic expression would be B. 5n + 10d

I hope this helps!
5 0
3 years ago
3/10+4/100+9/1000 as a decimal
Kipish [7]

Answer:

0.349

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
What is the volume of the rectangular prism?
11Alexandr11 [23.1K]
The volume is 288

because V = w h l = 6•4•12 = 288
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2 years ago
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