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11 days ago

14

A cone-shaped paper drinking cup is to be made to hold 33 cm3 of water. find the height and radius of the cup that will use the

smallest amount of paper. (round your answers to two decimal places.)

1 answer:

Svet_ta [12.7K]11 days ago

6 0

To minimize the amount of paper used, the dimensions should be perfectly matched such that the diameter equals the height. Therefore, if we denote the diameter as x, then the height equals x and the radius is x/2.
Consequently, the cone's volume is expressed as:
V=1/3πr^2h
=1/3*π*(x/2)^2*x
=0.262x^3
From this, we can derive that:
33=0.262x^3
thus, we find x^3=125.95
solving gives x=(125.95)^(1/3)
resulting in x=5.0126=5.01 cm
thus, the diameter and height are both 5.01cm.

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Gerry has 50 sports trading cards. Of those cards one fifth of them are baseball cards, one teenth of them are football cards, a

zzz [12365]

Gerry has 25 more basketball cards than he does baseball cards. Step-by-step explanation: Gerry owns a total of 50 sports trading cards. Among these, one-fifth are baseball cards, meaning he has 10 baseball cards. One-tenth of his collection consists of football cards, so he has 5 football cards. The remainder are basketball cards, leading to the conclusion that he has 35 basketball cards. The difference in quantity between his basketball and baseball cards is 25.

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24 days ago

What algebraic expression represents GK, if GK =37, what are GH and JK. GJ=4x+2 and HK=6x-1

Inessa [12570]

The outcome is "GK=37, GH=14, and JK=19".

The problem references a missing attachment file, thus please find it attached.

The provided values are:

GJ=4x+2

HK=6x-1

Given GK =37

Need to calculate:

HJ=?

From GK: GK = GJ+JK yields GJ+(HK-HJ)

= 4x+2+((6x-1)-x) yields

9x+1...(a)Substituting (a) into the equation gives: 9(4)+1 yields 37 solves to x=4... for answer (b) and (c). Substituting x=4 yields:

GH=14 and JK=19.

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1 month ago

What other points are on the line of direct variation through (5, 12)? Check all that apply. (0, 0) (2.5, 6) (3, 10) (7.5, 18) (

Inessa [12570]

It is established that

A correlation between two variables, x and y, demonstrates a direct variation if it can be written in the format $y/x=k$ or $y=kx$

For this question, we have

the point $(5,12)$ lies on the direct variation line

therefore

Determine the constant of proportionality k

$y/x=k$ -------> substitute ------> $k=12/5$

The equation is

$y=\frac{12}{5}x$

Keep in mind that

If a point is located on the direct variation line

then

the point has to fulfill the direct variation equation

we will now validate each point

case A) point $(0,0)$

$x=0\ y=0$

Insert the values of x and y into the direct variation equation

$0=\frac{12}{5}*0$

$0=0$ -------> is valid

thus

the point $(0,0)$ lies on the direct variation line

case B) point $(2.5,6)$

$x=2.5\ y=6$

Insert the values of x and y into the direct variation equation

$6=\frac{12}{5}*2.5$

$6=6$ -------> is valid

thus

the point $(2.5,6)$ lies on the direct variation line

case C) point $(3,10)$

$x=3\ y=10$

Insert the values of x and y into the direct variation equation

$10=\frac{12}{5}*3$

$10=7.2$ -------> is not valid

thus

the point $(3,10)$ does not lie on the direct variation line

case D) point $(7.5,18)$

$x=7.5\ y=18$

Insert the values of x and y into the direct variation equation

$18=\frac{12}{5}*7.5$

$18=18$ -------> is valid

thus

the point $(7.5,18)$ lies on the direct variation line

case E) point $(12.5,24)$

$x=12.5\ y=24$

Insert the values of x and y into the direct variation equation

$24=\frac{12}{5}*12.5$

$18=30$ -------> is not valid

thus

the point $(12.5,24)$ does not lie on the direct variation line

case F) point $(15,36)$

$x=15\ y=36$

Insert the values of x and y into the direct variation equation

$36=\frac{12}{5}*15$

$36=36$ -------> is valid

thus

the point $(15,36)$ lies on the direct variation line

ultimately

the solution is

$(0,0)$

$(2.5,6)$

$(7.5,18)$

$(15,36)$

5 0

1 month ago

Read 2 more answers

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babunello [11817]

This may be a bit awkward to explain in writing, so please bear with me:)

You are given the equations. Begin by focusing on ad = 11.6. Treating variables normally, this reads as a times d = 11.6.
From that, d = 11.6/a by dividing both sides by a.

With d expressed, substitute (11.6/a) into cd = 6.7. Then isolate c by multiplying both sides by a/11.6, yielding c = (6.7a)/11.6.

Now that c is known, insert (6.7a)/11.6 for c in bc = 8.3. The algebra becomes a bit messy, but solving for b gives approximately 14.3705 / a. Since you need ab, multiply both sides by a, and rounding to one decimal place produces ab = 14.4

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29 days ago

By selling a school blazer for Rs 1215, the shopkeeper earns a profit of 8%. Find

Svet_ta [12734]

Detailed explanation:

Thus,

100% plus 8% equals 108%

108% equals 1215

1% corresponds to 11.25

Therefore, 100% amounts to 1125 rs

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1 month ago