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Travka [436]
3 years ago
7

A funnel is made up of a partial cone and a cylinder as shown in the figure. The maximum amount of liquid that can be in the fun

nel at any given time is 16.59375 cubic centimeters. Given this information, what is the volume of the partial cone that makes up the top part of the funnel?
Mathematics
2 answers:
BARSIC [14]3 years ago
7 0

Answer:

15.75 pi cm^3

Step-by-step explanation:

I got this question on a test and this was the right answer

zavuch27 [327]3 years ago
5 0
The volume of the partial cone is the volume of the entire funnel minus the volume of the cylindrical part.

The volume of a cylinder is given by:

V=\pi r^2h
where: r is the radius of the cylinder and h is the height of the cylinder.

Given that the cylindrical part of the funnel has a height of 1.5 cm and a diameter of 1.5 cm, thus the radius is 1.5 / 2 = 0.75 cm and the volume is given by:

V=\pi(0.75)^2(1.5)=0.84375\pi=2.65072cm^3

Therefore, the volume of the partial cone is given by 16.59375 - 2.65072 = 13.94303 cubic cm.
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The first and second terms of a linear sequence (A.p) are 3 and 8 respectively. Please determine the least Number of terms of Ap
Alla [95]

Answer:

To rewrite your question, you are looking for the smallest    that fulfills the inequality:

∑=1>250

First, we must find the sequence    in explicit form. We can think of it as a line we are trying to get the slope-intercept form of. We have the points (1, 3) and (2, 8). Therefore, the slope is  8−32−1=51=5 . Now we just need the y-intercept. We can find it through substitution:

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In order to solve for   , we can plug in one of the points that we were already given. I will choose the point (1, 3). Note that this point just means that when  =1 ,  =3 .

3=5(1)+

3=5+

=−2

Now for the original question.

∑=1(5−2)>250

((5(1)−2)+(5()−2)2)>250

(5+12)>250

522+12>250

2+15>100

2+15+1100>100+1100

(+110)2>100+1100

(+110)2>10001100

+110>±10001100‾‾‾‾‾‾‾√

+110>±11010001‾‾‾‾‾‾√

>−110±11010001‾‾‾‾‾‾√

Since we are looking for the smallest value, we will subtract for the plus or minus sign.

>−110−11010001‾‾‾‾‾‾√≈−10

Since that is negative, we will have to add instead.

>−110+11010001‾‾‾‾‾‾√≈9.9

Therefore, the smallest integer    that makes sense and satisfies the inequality is 10.

So, the first 10 numbers must be added.

Honestly, it would have been quicker just to brute-force this.

Step-by-step explanation:

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How do I write three and one fourth as a percent
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