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CaHeK987 [17]
3 years ago
8

A cardboard sheet is cut in the shape of a triangle, with vertices at (0,0), (20,0), and (3,4) units. the thickness of the sheet

is uniform. what is the x-coordinate of its center of mass?
Mathematics
1 answer:
kenny6666 [7]3 years ago
6 0
This problem can be solved in two ways, the long way, or the short way.

1. The long way
We know that the base of the triangle is along the x-axis, and the length of the base is 20.
The centre of mass is located at 2/3 of the distance from vertex (3,4) along the median, which cuts the base at (10,0).
Therefore the centre of mass is located at
x=3+(10-3)*2/3=23/3
y=4/3

2. The short way
It turns out that the centre of mass of a triangle sheet is located at the mean of the coordinates of the three vertices, i.e.
CG=((0+20+3)/3, (0+0+4)/3)=(23/3, 4/3)  as before.
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at a small school, one male and one female are selected to represent the student body at the PTSCA meetings. if there are 41 mal
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It is given that there are 41 males and 48 females in the small school.

So, the number of ways a male student can be chosen from 41 males is ^{41}C_1

Likewise, the number of ways a female student can be chosen from 48 females is ^{48}C_1.

Thus, the total number of ways in which 2-person combinations are possible to represent the student body at the PTSAC meetings will be given by:

^{41}C_1\times ^{48}C_1=1968


7 0
3 years ago
Which statement best explains the value of 16-(-3)
Alja [10]

Answer: 48

Step-by-step explanation:

It is the negative of 16 times the negative of 3.

Not sure if this is the answer but I hope it helps!

3 0
3 years ago
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The royal fruit company produces two types of fruit drinks the first type is 70% pure fruit juice and the second type is 95% pur
Ipatiy [6.2K]
This is a typical mixture problem where using a table is the best thing.
                 pints juice        % juice     =      total % juice
juice A            x                  .70          =        .70x
juice B        60-x                 .95          =    .95(60-x)
total              60                  .75          =    60(.75)

The last row gives you a total that you need to use, so do that multiplication to get 45. You now to need to add the last columns together for rows 1 and 2 and set them equal to 45: .7x +.95(60-x) = 45. When you do that math, you'll get that x = 48. This means that you need 48 pints of juice A and 60-48 pints of juice B, which is 12 pints.
6 0
3 years ago
The numbers of students in the four sixth-grade classes at Northside school are 26,19,34 and 21. Use properties to find the tota
san4es73 [151]
Basically there are 3 addition properties and they are associative property, identity property, and commutative property. 

Commutative property is just changing the order of the addends. Example: 26+19+34+21= 21+34+19+26

Identity Property is just adding a 0 to the number that doesnt change anything. Example: 26+19+34+21 +0 = 100

Associative property is just changing the grouping of the addends. Example: (26+19) + (34+21) 
6 0
3 years ago
Find x<br><br> -x = 7x - 56
solmaris [256]

Answer:

the answer is 7

Step-by-step explanation:

Add the same term to both sides of the equation

-x=7x-56

−x=7x−56

−x−7x=7x−56−7x

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