MATHEMATICS HIGH SCHOOL

A candle manufacturer sells cylindrical candles in sets of three. Each candle in the set is a different size. The smallest candle has a radius of 0.5 inches and a height of 3 inches. The other two candles are scaled versions of the smallest, with scale factors of 2 and 3. How much wax is needed to create one set of candles?

Answers

Answer 1

Answer:

Answer:

The amount of wax that is needed to create one set of candles is:

27π cubic inches.

Step-by-step explanation:

The radius(r) of the smallest candle=0.5 inches.

Height(h) of smallest candle= 3 inches.

Hence, Volume of smallest candle $V_1$ is:

$V_1=\pi r^2h$

Now the medium candle is one which is obtained by taking a scale factor of 2.

Hence, radius of medium candle=2r

Height of medium candle=2h

Hence, Volume of medium candle $V_2$ is:

$V_2=\pi* (2r)^2* (2h)\n\nV_2=8\pi r^2h$

Similarly the largest candle is one which is obtained by taking a scale factor of 3.

Hence, radius of largest candle=3r

Height of largest candle=3h

Hence, Volume of largest candle $V_3$ is:

$V_3=\pi* (3r)^2* (3h)\n\nV_3=27\pi r^2h$

The amount of wax required to create one set of candle is equal to total volume of all the three candles.

$\text{Amount\ of\ wax}=V_1+V_2+V_3\n\n\n\text{Amount\ of\ wax}=\pi r^2h+8 \pi r^2h+27\pi r^2 h\n\n\n\text{Amount\ of\ wax}=36\pi r^2h$

Now on putting the value of r and h in the expression we get:

$\text{Amount\ of\ wax}=36* \pi* (0.5)^2* 3\n\n\n\text{Amount\ of\ wax}=27\pi\ \text{cubic\ inches}$

Hence, the answer is:

27π cubic inches.

Answer 2

Answer: it is 27 π cubic inches

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Does the set of numbers 13, 21, and 24 form a Pythagorean triple? Explain. a. yes; 132 + 212 ≠ 242b. no; 132 + 212 = 242
c.no; 132 + 212 ≠ 242
d. yes; 132 + 212 = 242

Answers

For a Pythagorean triple:
a² + b² = c²
13² + 21² = 24²
169 + 441 = 576
610 ≠ 576
Answer:
C) No, 13² + 21² ≠ 24²

Answer:

No; no; 13^2 + 21^2 ≠ 24^2

Step-by-step explanation:

The sum of the squares of the legs is greater than the square of the hypotenuse, therefore this set of numbers DOES NOT form a Pythagorean triple. The sum of the squares of the legs must be equal to the square of the hypotenuse.

Find the lateral area of a regular pentagonal pyramid that has a slant height of 14 in. and a base side length of 6 in. A) 210 in^2 B) 240 in^2 C) 42 in^2 D) 420 in^2

Answers

The question ask to choose among the following choices that contains the value of the lateral area of a regular pentagonal pyramid that has a slant height of 14 in and a base side length of 6 in. Base on my calculation, the answer would be A. 210 inch^2. I hope this would help

The lateral area of a regular pentagonal pyramid has a slant height of 14 in is 210 inch^2.

We have given that ,

The lateral area of a regular pentagonal pyramid that has a slant height of 14 in. and a base side length of 6 in.

What is the pentagonal pyramid?

A pentagonal pyramid is a pyramid with a pentagonal base upon which are erected five triangular faces that meet at a point. Like any pyramid, it is self-dual. The regular pentagonal pyramid has a base that is a regular pentagon and lateral faces that are equilateral triangles.

The question ask to choose among the following choices that contain the value of the lateral area of a regular pentagonal pyramid that has a slant height of 14 in and a base side length of 6 in.

Base on my calculation, the answer would be A.

210 inch^2.

To learn more about the pyramid visit:

brainly.com/question/218706

#SPJ5

Functions 1 and 2 are shown below:Function 1: f(x) = −3x2 + 2
A graph of a parabola with x intercepts of negative 0.5, 0 and 2, 0 and a vertex of 0.5, 4 is shown.

Which function has a larger maximum? Type your answer as 1 or 2.

Answers

Answer:

The function 2 has a larger maximum.

Step-by-step explanation:

The vertex form of the parabola is

$f(x)=a(x-h)^2+k$ .... (1)

Where, (h,k) is the vertex.

The given functions are

$f(x)=-3x^2+2$ ..... (2)

Since the leading coefficient is negative, therefore it is a downward parabola. It means the vertex of the parabola is the maximum point.

On comparing (1) and (2), we get

$h=0,k=2$

Therefore the maximum value of the function is 2 at x=0.

The second function has x intercepts of (-0.5, 0) and (2, 0) and a vertex of (0.5, 4).

It is also a downward parabola because the parabola has two x-intercepts and the vertex lies above the x-axis.

Since the vertex is (0.5, 4), therefore the maximum value of the function is 4 at x=0.5.

$Maximum(F_1)=2$

$Maximum(F_2)=4$

Therefore function 2 has a larger maximum.

Answer:

the anwser is 2 guys. i got it correct

Express 4.26 as a mixed number.

Answers

4 13/50
4 is the whole number because it is a whole number
26/100 can be simplified to 13/50
is this problem a high school problem?

4.26 in mixed number.
4.26 = 426/100 ( improper fraction )
426/100 = 213/50 = 4 13/50 Ans

If n ≠ 0, which of the following must be greater than n?I 2n
II n²
III 2 - n

Answers

tbh, none of them
ex. 2n
you can have n=-1
2(-1)
-2<-1
ex. n^2
n=1
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rob is saving up to buy a new MP3 player for every $15 he earns babysitting he saves six dollars. on Saturday rob earned $75 babysitting how much money did he save

Answers

Answer : He saved $30 money.

Step-by-step explanation :

when he earned $15 from babysitting, he saved money = 6 dollars

when he earned $1 from babysitting, he saved money = $(6)/(15)$ dollars

when he earned $75 from babysitting, he saved money = $(6)/(15)* 75=30$ dollars

Therefore,He saved $30 money.

The total amount of money is 75 dollars
There are 5 fifteens in 75
There are 6 dollars saved everytime he makes 15 dollars
6 x 5 = 30
He saved 30 dollars

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