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3 years ago

9

A right circular cylinder is inscribed in a sphere of radius r. Find the dimensions of such a cylinder with the largest possible

volume (your answer may depend on r).

1 answer:

Burka [1]3 years ago

3 0

Answer:

Largest volume in terms of r = 4r^3π/ 3√3 or you could write it as 4√3r^3π/9.

Step-by-step explanation:

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50,000 contestants participate in an on-line game. The game randomly eliminates 20% of the contestants each day. Determine the n

irga5000 [103]

Answer:10,486 contestants

Step-by-step explanation:

First day:

Total number of contestants at the beginning = 50,000

After first day, 20% 0f 50,000 are removed.

That is, (20/100)×50,000 = 10,000

Contestants remaining after first day = 50,000-10,000 = 40,000

Second day:

Contestants= 40,000

20% removed

That is (20/100)×40000=8000

Balance =40000-8000=32,000

Third day:

Contestants= 32000

20% removed

That is (20/100)×32000=6400

Balance =32000-6400=25,600

Fouth day:

Contestants= 25,600

20% removed

That is (20/100)×25,600=5,120

Balance =25,600-5,120=20,480

Fifth day:

Contestants= 20,480

20% removed

That is (20/100)×20,480=4096

Balance =20,480-4096=16,384

Sixth day:

Contestants= 16,384

20% removed

That is (20/100)×16,384=3276.8

Balance =16,384-3276.8=13,107.2

Seventh day:

Contestants= 13,107.2

20% removed

That is (20/100)×13,107.2=2621.44

Balance =13107.2-2621.44=10485.76

Therefore, number of contestants remaining after one week equals 10,486.

6 0

3 years ago

Solve y = f(x) for x. Then find the input(s) when the output is 10.

elixir [45]

The inputs are 1 and -1 when the output is 2.

Step-by-step explanation:

The given function is

f(x) = 10 x²

Then we set y = f (x)

y = 10 x²

By dividing each side by 10 we get

x² = y/10

Then we solve for x

x = ± $\sqrt{y/2}$

Now we have to find the input(s) when the output is 10

x = ± $\sqrt{10/10}$

x = ± 1

Hence, the inputs are 1 and -1 when the output is 2.

The final solution is x =1 and x = -1.

7 0

3 years ago

How do you write (243)^ 3/5 in radical form? THEN simplified?! *PLEASE HELP

SOVA2 [1]

Answer:

27

Step-by-step explanation:

If you have an exponent that is a fraction, you need to make a radical with the index from the denominator and an exponent of the radicand from the numerator.

(243)^3/5=( $\sqrt[5]{243}^3$ )

This would come out as $\sqrt[5]{14348907^}$ . this further simplifies down to the final answer of 27

6 0

3 years ago

I need help really fast

topjm [15]

The Answer is letter a

8 0

3 years ago

The sales tax in one state is 5%. Write a function rule for finding the total cost of an item with selling price x. Then find th

Aneli [31]

Answer:

The sales tax in one state is 5%. Write a function rule for finding the total cost of an item with selling price x. Then find the total cost of a CD player with a selling price of $110.

A. f(x) = 5 + x; $111.05

B. f(x) = 0.05x; $5.50

C. f(x) = x � 5; $108.95

D. f(x) =1.05x; $115.50

total cost = (price) + (5% of price)

f(x) = x + 0.05x

f(x) = 1.05x

So the function is f(x) = 1.05x

Plug in x = 110 to get

f(x) = 1.05x

f(110) = 1.05*110

f(110) = 115.50

The item costs $115.50 (after tax is added on)

Step-by-step explanation:

1: the total cost of a CD player would be 104.76

2: Total Cost = (price) + (5% of price)

f(x) = x + 0.05x

f(x) = 1.05x

So the function is f(x) = 1.05x

Plug in x = 110 into the function

f(110) = 1.05*110

f(110) = 115.50

The item costs $115.50

3: Answer:

f(x) = .05x; $5.50

Step-by-step explanation:

f(x) = .05x

f(110) = .05(110) = $5.50

7 0

3 years ago