Mathematics, 20.05.2021 17:20 karebareyo

The volume of a cylinder is 40 f3. Which expression represents the volume of a cone with the same base and height as the cylinder?
O 3(40) ft
O
1
40
O (40) At
o 3 (402)

The volume of a cylinder is 40 f3. Which expression represents the volume of a cone with the same b

Answers: 3

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Answer from: nestergurl101

Option (3)

Step-by-step explanation:

Volume of the cylinder = 40 ft³

Since, volume of a cylinder is given by the expression,

V = $\pi r^{2}h$

Here, r = radius of the circular base

h = Height of the cylinder

40 = $\pi r^{2}h$

$h=\frac{40}{\pi r^2}$ ------(1)

Volume of a cone = $\frac{1}{3}\pi r^{2} h$

By substituting the value of 'h' from equation (1)

Volume of the cone = $\frac{1}{3}\pi r^{2}(\frac{40}{\pi r^{2} } )$

= $\frac{1}{3}(40)$ ft³

Therefore, Option (3) will be the correct option.

Answer from: Quest

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints

Answer from: Quest

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range:

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The volume of a cylinder is 40 f3. Which expression represents the volume of a cone with the same ba...