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ddd [48]
3 years ago
10

A frustum is made by removing a small cone from a similar large cone. Work out the volume of the frustum, below. Give your answe

r in terms of pie

Mathematics
1 answer:
AlekseyPX3 years ago
3 0

Answer:

Step-by-step explanation:

volume of cone=1/3 πr²h

volume of frustum=vol of larger cone-vol of smaller cone=1/3πR²H-1/3πr²h

=1/3π(R²H-r²h)

=1/3π(4.5²×9-3²×6)

=1/3π×9×3(4.5×1.5-2)

=9π(6.75-2)

=9π×4.75

=42.75π cm³

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In 2013, the moose population in a park was measured to be 5,100. By 2018, the population was measured again to be 5,200. If the
natka813 [3]

Answer:

P(t) = 5100e^{0.0039t}

Step-by-step explanation:

The exponential model for the population in t years after 2013 is given by:

P(t) = P(0)e^{rt}

In which P(0) is the population in 2013 and r is the growth rate.

In 2013, the moose population in a park was measured to be 5,100

This means that P(0) = 5100

So

P(t) = 5100e^{rt}

By 2018, the population was measured again to be 5,200.

2018 is 2018-2013 = 5 years after 2013.

So this means that P(5) = 5200.

We use this to find r.

P(t) = 5100e^{rt}

5200 = 5100e^{5r}

e^{5r} = \frac{52}{51}

\ln{e^{5r}} = \ln{\frac{52}{51}}

5r = \ln{\frac{52}{51}}

r = \frac{\ln{\frac{52}{51}}}{5}

r = 0.0039

So the equation for the moose population is:

P(t) = 5100e^{0.0039t}

5 0
3 years ago
Write an equation to model the sentence. How many cherries are left in a bowl of 52 cherries after you have eaten some?
Tresset [83]

Answer:

52 - x

Step-by-step explanation:

x \: is \: the \: cherries \: eaten

x is the cherries eaten

7 0
3 years ago
Factor the Following:<br><br>1.) 8<br>2.) -12<br>3.) -3y²<br>4.) 6x²+36x<br>5.) 7x -14x²​
Alex787 [66]

Answer:

1.) 8 = 8

2.) -12 = -12

3.) -3y² = -3y²

4.) 6x² + 36x = 6x(x + 6)

5.) 7x - 14x² = 7x(1 - 2x)

~

3 0
3 years ago
(10 POINTS AND BRAINLIEST)
bekas [8.4K]

Answer:

A.) 15.60=11.40+10x

Step-by-step explanation:

okay we know kathy spent 15.60 in total at the post office

so we know 15.60 will be after the equal sign.

she paid 11.40 only on the package

and rest of money was on stamps.

15.60-11.40= 4.20

so she used 4 dollars and 20 cents for stamps if she bought 10 we need to divied 4.20/10=0.42

0.42 cents for each stamps so we need a equation that will give us this answer.

Me i go thru each one and solve for x

lucky for me i just need to solve one

because equation A solves it correctly.

15.60=11.40+10x

subtract 11.40 on both sides

15.60-11.40

4.20=10x

now we divide 10 on each side

4.20/10=0.42

x=0.42

 

5 0
3 years ago
Read 2 more answers
The video club to which Lin belongs allows her to receive one free DVD for every three DVDS she rents. If she pays $3 for each D
Nesterboy [21]

Answer:

12

Step-by-step explanation:

Given:

On every 3 DVDs she rents, 1 DVD is received for free

Rent of each DVD = $3

Total amount paid = $114

Now,

The total number of DVDs she took on rent = \frac{\textup{Total amount paid}}{\textup{Rent of each DVD}}

or

The total number of DVDs she took on rent = \frac{\textup{114}}{\textup{3}}

or

The total number of DVDs she took on rent = 38

also,

For every 3 DVDs she gets 1 Free DVD

thus,

For every 1 DVD she gets \frac{\textup{1}}{\textup{3}} free DVD

therefore,

For  38 DVD she gets \frac{\textup{38}}{\textup{3}} free DVD

or

she gets 12.67 DVDs free

Since,

the DVDs cannot be given in fraction

Hence she will get 12 free DVDs

5 0
3 years ago
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