1) The answer for both includes a circle. You would rotate the shape around the axis of symmetry, creating an infinite number of 2-d circles stacked on top of each other, creating the cone or cylinder. In the case of a cylinder, the other shape is a rectangle, and in the case of a cone, a right triangle with one line serving as the axis of symmetry.
2) The volume of a cone is the area of the base, multiplied by height, divided by 3. This means that the volume of a cone is 1/3 the volume of a cylinder of equal height and base area. The volume of a cylinder is the area of the base times height. The volume of a pyramid, similar to a cone, is the area of the base (length x width) times the height, divided by three.
3) One definition of density is mass/volume, or mass per unit of volume. For example, if a 5 kg object has a volume of 10 cm³, than the density would be 0.5kg/cm³. In population density, relative to our example, area takes the place of volume and population takes the place of mass. This means that population density is population/area. For example, if 10,000 people occupy an area of 5 square miles, then the population density is 2,000 people/ square mile.
4) As you are clearly learning in this class, the volume of an object is not only determined by its dimensions, such as base, width, and height, but its shape. Let's review the cone example. If a cone and a cylinder have the same base area and height, the cone has a volume of 1/3 that of the cylinder.
5) When might you want to use volume in your daily life? Here is a depressing example. Say your corporate job in the Accounting Department has you feeling blue, and your only break is your daily trip to the water cooler. The cups at the cooler are cone-shaped. Not only is this inconvenient because you can't stand them up without getting the rim dirty, but these cups contain 1/3 the water that a perfectly cylindrical cup of the same base/height could provide. You may tell your manager this, and earn yourself some fancy new cylindrical paper cups!
Answer:
Step-by-step explanation:
Remark
You are going to use the Pythagorean Theorem. The trick is to find the length of the leg making up the base of the triangle.
That base is equal to the difference between the two bases.
Solution
The base of the triangle = 2x + 1 - (x + 3) Remove the brackets.
base = 2x + 1 - x - 3
base = x - 2
Now the height of the trapezoid is also the second leg of the triangle. Apply the Pythagorean Theorem.
c^2 = a^2 + b^2
a = x - 2
b = x + 4
c = 2x
4x^2 = (x - 2)^2 + (x + 4)^2 Expand the brackets
4x^2 = x^2 - 4x + 4 + x^2 + 8x + 16 Collect like terms
4x^2 = 2x^2 + 4x + 20 Subtract the right side from the left.
4x^2 - 2x^2 - 4x - 20 = 0
2x^2 - 4x - 20 = 0 Divide by 2
2x^2/2 - 4x/2 - 20/2 = 0
x^2 - 2x - 10 = 0
x = - b +/- sqrt(b^2 - 4*a*c)/ 2a
a = 1
b = - 2
c = - 10
x = (- -2 + / - sqrt((-2)^2 - 4*(1)*(-10) ) / 2
x = (2 + / - sqrt(4 + 40 ))/2 Only the plus root has any meaning.
x = ( 2 + sqrt(44 ) )/2
x = ( 2 + 2*sqrt(11) ) / 2
x = 1 + sqrt(11)
sqrt(11) = 3.3166
x = 1 + 3.3166
x = 4.3166
Add the ratios together: 2 + 3 +4 = 9
Divide the total tips by 9:
77.40 / 9 = 8.60
Multiply each portion of the ratio by 8.60:
2 x 8.60 = 17.20
3 x 8.60 = 25.80
4 x 8.60 = 34.40
The ratios are in order of the people:
Paul got 17.20
Colin got 25.80
Brian got 34.40
Brian got 34.40 - 17.20 = 17.20 more than Paul
Answer:
the price per cup is $4.64
Step-by-step explanation:
so 1 gallon is 4 cups and so what you do is 4×3=12 then divide 12 to $55.68 and you'll get $4.64 and if you wanna double check just do $4.64×12 then divide 12 by 3 and you'll get 4 cups that which equal a gallon
Q+P =180 so (Q is 137) p=s so (s is 43) and q = r so (r is 137)
