Answer:
13x-10y
Step-by-step explanation:
Combine like terms;
10x+3x = 13x
-8y-2y = -10y
So it would give the equation of 13x-10y
Given the lengths of the three sides of the triangular fence, the angle by
which the fence line changes direction can be found by cosine rule.
The angle by which the fence line change direction is approximately <u>44</u>
The given parameters are;
AB = 290 yards = LK
BC = 248 yards = ML
AC = 499 yards = MK
Let AB = a, BC = b, and AC = c, by cosine rule, we have;
c² = b² + a² - 2·b·a·cos(C)
Therefore;
499² = 248² + 290² - 2×248×290×cos(C)
2×248×290×cos(C) = 248² + 290² - 499² = -103397
143840×cos(C) = -103397
∠C = ∠ABC = ∠MLK ≈ 135.95°
The angle by which the fence turns is a supplementary angle to angle
∠MLK, which is therefore;
?° + ∠MLK = 180°
?° = 180° - ∠MLK
∴ ?° ≈ 180° - 135.95° ≈ 44°
The angle by which the fence change direction is approximately <u>44</u>
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Answer:
For the first one its: Volume = 402.12in³
For the second one its: Volume = 201.0619 in³
Step-by-step explanation:
For the first one work:
Volume = 3.1416 x 42 x 8
= 3.1416 x 16 x 8
For the second one work:
Volume = 3.1416 x 42 x 4
= 3.1416 x 16 x 4
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!
