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jeka57 [31]
2 years ago
13

What is the average rate of change from x=0 to x=5

Mathematics
2 answers:
zmey [24]2 years ago
6 0
80-40/5-0=40/5=8 through the slope formula
Liono4ka [1.6K]2 years ago
4 0

Answer:

-8

I just answered this one

Step-by-step explanation:

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A cone-shaped paper drinking cup is to be made to hold 27 cm of water. Find the height h and radius r of the cup that will use t
andreyandreev [35.5K]

Answer:

  • r = 2.632 cm
  • h = 3.722 cm

Step-by-step explanation:

The formula for the volume of a cone of radius r and height h is ...

  V = (1/3)πr²h

Then r² can be found in terms of h and V as ...

  r² = 3V/(πh)

The lateral surface area of the cone is ...

  A = (1/2)(2πr)√(r² +h²) = πr√(r² +h²)

The square of the area is ...

  T = A² = π²r²(r² +h²)

Substituting for r² using the expression above, we have ...

  T = π²(3V/(πh))((3V/(πh) +h²) = 9V²/h² +3πVh

We want to find the minimum, which we can do by setting the derivative to zero.

  dT/dh = -18V²/h³ +3πV

This will be zero when ...

  3πV = 18V²/h³

  h³ = 6V/π . . . . . multiply by h³/(3πV)

For V = 27 cm³, the value of h that minimizes paper area is ...

  h = 3∛(6/π) ≈ 3.7221029

The corresponding value of r is ...

  r = √(3V/(πh)) = 9/√(π·h) ≈ 2.6319242

The optimal radius is 2.632 cm; the optimal height is 3.722 cm.

_____

The second derivative test applied to T finds that T is always concave upward, so the value we found is a minimum.

__

Interestingly, the ratio of h to r is √2.

8 0
3 years ago
A rectangle or exercise mat has a perimeter of 48 feet the length of the mat Is twice The lift right and solve any questions to
Misha Larkins [42]

Answer:

The equation to determine the length is 4w+2w=48.

The Length of the exercise mat is 16 feet.

Step-by-step explanation:

Given:

Perimeter of Rectangular mat = 48\ ft

Let the length of the mat be denoted by 'l'

And width be denoted by 'w'.

Also Given:

The length of the mat is twice the width of the mat.

So we can say that;

l=2w  ⇒ equation 1

Now we know that;

Perimeter of Rectangle is equal to twice the sum of length and width.

framing in equation form we get;

2(l+w)=48 ⇒ equation 2

Now Substituting equation 1 in equation 2 we get;

2(2w+w)=48

Applying Distributive property we get;

2\times2w+2\times w=48\\\\4w+2w=48

Hence, The equation to determine the length is 4w+2w=48.

On Solving the above equation we get;

4w+2w=48\\\\6w=48

Dividing both side by 6 we get;

\frac{6w}{6}=\frac{48}{6}\\\\w=8\ ft

Now Substituting the value of 'w' in equation 1 we get;

l=2w=2\times8=16\ ft

Hence The Length of the exercise mat is 16 feet.

3 0
3 years ago
A statement can help you organize the numbers to answer a question about percents
Semenov [28]

Answer:

<u> $50</u> is <u>27.02%</u> of <u>$185</u>.

Step-by-step explanation:

Money spent on clothing = $50

Money spent on Groceries = $100

Money spent on Gas = $35

Total money spent = $185

Our question is to find the percentage of total money that is spent on clothing.

Percentage money on clothing = \frac{Money spent on clothing}{Total money} × 100

                                                   = \frac{50}{185} × 100

                                                   = 27.02% (approx)

Hence,<u> $50</u> is <u>27.02%</u> of <u>$185</u>.  

5 0
2 years ago
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Please help me on this I need help and nobody is really helping
Nady [450]
I believe the answer is (0,0)
3 0
2 years ago
Read 2 more answers
A pet store has 5 tanks of fish. Each tank has the same number of fish. The store has 50 fish total. How many fish are in each t
Romashka-Z-Leto [24]

answer : 10 fish in each tank because 10 time 5 equals 50 and there 5 tanks sotaht mean 50 divided by 5 it will be 10 fish

8 0
2 years ago
Read 2 more answers
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