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Romashka [77]
2 years ago
9

Which conclusions are valid given that ABCD is a parallelogram? Select True or False for each statement.

Mathematics
1 answer:
Burka [1]2 years ago
4 0

it is true not false true

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An hourglass consists of two sets of congruent composite figures on either end. Each composite figure is made up of a cone and a
belka [17]
Answer: third option 268.8

Explanation:

For this kind of proble it is very important that you attach the figure because it contains important information to understand the question.

I have attached the figure for better understanding.

1) The top portion (and the bottom is congruent but rotated 180°) of the hourglass is a figure equivalent to a cylinder on top and a cone on bottom.

So the total volume contained in the top portion is the volume of a cylinder + the volume of a cone.

This is how you calculate the volume of the top portion:

1) The height of the cylinder is 54 mm - 18 mm = 36 mm

2) The formula for the volume of a cylinder is V = π (radius)^2 * height

radius = 8 mm
height = 36 mm

=> V = π(8mm)^2 * 36 mm = 2304π (mm)^3

3) The formula for the volume of a cone is V = (1/3)π(radius)^2 * height

radius = 8 mm
height = 18 mm

V = (1/3)π(8mm)^2 * 18 mm = 384π (mm)^3

4) The total volume of the top portion is volumen of the cylindrical part + voume of the cone:

Total voluem = 2304π (mm)^3 + 384π (mm)^3 = 2688π (mm)^3

5) To find the number of seconds <span>it take until all of the sand has dripped to the bottom of the hourglass you have to divide the total volumen of sand by the rate:

time in seconds = total volume of sand / rate of dripping

time in seconds = [2688 π (mm)^3 ] / [10π (mm)^3 / s] = 268.8 s

That is the answer: 268.8 s
</span>

4 0
3 years ago
Read 2 more answers
Thirteen less than eight times a number is three more than four times the number.
Lisa [10]

Answer:

Step-by-step explanation:

Let the number = x

8x - 13 = 4x + 3              Add 13

8x = 4x + 3 + 13             Combine

8x = 4x + 16                   Subtract 4x

8x - 4x = 16                    Combine

4x = 16                           Divide by 4

x = 16/4

x = 4

6 0
3 years ago
Write the ratio as a fraction in simplest form 25 to 45
brilliants [131]

Answer:

5/9

Step-by-step explanation:

3 0
3 years ago
What are ALL the factors of 15
Sophie [7]
1&15 and 3&5 are factors of 15
3 0
3 years ago
Optimization problem: what are the dimensions of the lightest open-top right circularcylindrical can that will hold a volume of
vivado [14]
So Volume of cylinder is pi*r^2*h = 1,000 

Then lightest one means you have the smallest surface area. Which is one base and then the area of the surface. SA = pi*r^2 + 2pi*r*h 

So now you have 2 equations, so: 

h = 1,000/(pi*r^2) 
So then SA = pi*r^2 + 2pi*r*(1,000/(pi*r^2) = pi*r^2 + 2,000/r 

Derivative of SA is then 2pi*r -2,000/r^2. Set to 0 

2pi*r-2,000/r^2 =0 --> 2pi*r^3 = 2,000 --> r^3 = 1,000/pi --> r = 10/pi^(1/3) 

Now go back to the volume function: pi*r^2*h =1,000 --> 1,000/(pi*100/pi^(2/3)) = h 
<span>h = 10 / pi^(1/3)</span>
3 0
3 years ago
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