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dlinn [17]
3 years ago
14

Jesse is looking for the volume of the cone below, and she is using the formula V=(1/3)Bh. Which of the following is the value o

f "B",base?
Mathematics
1 answer:
Sidana [21]3 years ago
6 0

Answer:

B =  \pi *r^2

(Base of the cone)

Step-by-step explanation:

The volume of the cone is always 1/3 of the volume of a cylinder with the same radius and height.

Volume of the cylinder

V_cylin = ( \pi *r^2 )* h

Where

r is the radius

h is the height

This means the volume of the cone is equal to

V_cone = (1/3)* ( \pi *r^2 )* h

By looking to the equation of the problem

V=(1/3)Bh

We can easily deduce that

B =  \pi *r^2

(Base of the cone)

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Suppose we want to choose 4 colors, without replacement, from 18 distinct colors.
amm1812

Answers:

  • (a) 73440
  • (b)  3060

=====================================================

Explanation for part (a)

Consider four slots labeled A,B,C,D.

We have

  • 18 choices for slot A
  • 17 choices for slot B
  • 16 choices for slot C
  • 15 choices for slot D

We started at 18 and counted down until we filled the four slots. The countdown is because we cannot repeat a color. Multiply out those values to get the answer: 18*17*16*15 = 73440

You can use the nPr permutation formula as an alternative method

_nP_r = \frac{n!}{(n-r)!}

in this case n = 18 and r = 4. The exclamation marks indicate factorial.

-----------------------------------

Explanation for part (b)

Let's say we had color labels A,B,C,... all the way up to R which is the 18th letter in the English alphabet. From those 18 letters, we can only pick four. Let's say we pick D,E,F,G.

Focusing solely on the set {D,E,F,G}, we only have one set and the order doesn't matter. So {D,E,F,G} is the same as {D,E,G,F}.

There are 4*3*2*1 = 24 ways to arrange those four items meaning that we'll need to divide the result of part (a) by 24 to get the result of part (b)

73440/24 = 3060

You could use the nCr combination formula to get the same result

_nC_r = \frac{n!}{r!(n-r)!}

where n = 18 and r = 4 are the same from last time.

The connection between nPr and nCr is this

_nC_r = \frac{_nP_r}{r!}

which can be rearranged into

_nP_r = r!*\left( _nC_r \right)

these formulas are handy to help us go back and forth between nCr or nPr.

8 0
3 years ago
20 points!!
omeli [17]

34.1 degrees Farenheit

have a splendid evening

5 0
2 years ago
Find the area of a rectangle that is 5.8 cm long and 1.2 cm wide
Svetlanka [38]
<h2><em>6.96cm^2.</em></h2><h2><em>5.8 x 1.2 = 6.96cm^2.</em></h2>
5 0
3 years ago
Read 2 more answers
40, 10, 5/2 5/8... (fractions) is it arithmetic or geometric and what are the next two terms PLZ HELP DUE IN 10 MINS
patriot [66]

Answer:

Please check the explanation.

Step-by-step explanation:

Given the sequence

40,\:10,\:\frac{5}{2},\:\frac{5}{8}

A geometric sequence has a constant ratio 'r' and is defined by

\:a_n=a_0\cdot r^{n-1}

Computing the ratios of all the adjacent terms

\frac{10}{40}=\frac{1}{4},\:\quad \frac{\frac{5}{2}}{10}=\frac{1}{4},\:\quad \frac{\frac{5}{8}}{\frac{5}{2}}=\frac{1}{4}

The ratio of all the adjacent terms is the same and equal to

r=\frac{1}{4}

Thus, the given sequence is a geometric sequence.

As the first element of the sequence is

a_1=40

Therefore, the nth term is calculated as

\:a_n=a_0\cdot r^{n-1}

a_n=40\left(\frac{1}{4}\right)^{n-1}

Put n = 5 to find the next term

a_5=40\left(\frac{1}{4}\right)^{5-1}

a_5=40\cdot \frac{1}{4^4}

a_5=\frac{40}{4^4}

   =\frac{2^3\cdot \:5}{2^8}

a_5=\frac{5}{2^5}

a_5=\frac{5}{32}

now, Put n = 6 to find the 6th term

a_6=40\left(\frac{1}{4}\right)^{6-1}

a_6=40\cdot \frac{1}{4^5}

a_6=\frac{40}{4^5}

    =\frac{2^3\cdot \:5}{2^{10}}

a_6=\frac{5}{2^7}

a_6=\frac{5}{128}

Thus, the next two terms of the sequence 40, 10, 5/2, 5/8... is:

  • a_5=\frac{5}{32}
  • a_6=\frac{5}{128}
7 0
3 years ago
The Pythagorean Theorem ONLY works on which triangle?​
Gekata [30.6K]

Answer:

right triangle

Step-by-step explanation:

that's the condition for the Pythagorean Theorem hold true

8 0
3 years ago
Read 2 more answers
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