Answer:
D) 3.8 cm
Step-by-step explanation:
There are several ways this problem can be solved. Maybe the easiest is to use the Law of Cosines to find angle BAC. Then trig functions can be used to find the length of the chord.
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In triangle BAC, the Law of Cosines tells us ...
a² = b² +c² -2bc·cos(A)
A = arccos((b² +c² -a²)/(2bc)) = arccos((8² +6² -3²)/(2·8·6)) = arccos(91/96)
A ≈ 18.573°
The measure of half the chord is AB times the sine of this angle:
BD = 2(AB·sin(A)) ≈ 3.82222
The length of the common chord is about 3.8 cm.
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<em>Additional comment</em>
Another solution can be found using Heron's formula to find the area of triangle ABC. From that, its altitude can be found.
Area ABC = √(s(s-a)(s-b)(s-c)) . . . . where s=(a+b+c)/2
s=(3+8+6)/2 = 8.5
A = √(8.5(8.5 -3)(8.5 -8)(8.5 -6)) = √54.4375 ≈ 7.64444
The altitude of triangle ABC to segment AC is given by ...
A = 1/2bh
h = 2A/b = 2(7.64444)/8 = 1.911111
BD = 2h = 3.822222
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Subtract (8-4) and you get 4 as the total and then times it by 2 which will give u 8, the answer is 8
Answer:
The height of water in the second tank is 2ft
Step-by-step explanation:
In this question, we are asked to calculate the height of water in a second tank if the content of a first tank is poured into the second tank.
The plot twist to answering this question is that we need to note the volume of water in the first tank. Although the first tank has dimensions of 2ft by 3ft by 2ft height, the water in the tank only rose to a height of 1 feet.
Hence, to calculate the volume of the water in the first tank, the width and the length of the tank still remain the same, the only difference here is that we work with a height of 1 feet since the Water is not full.
Mathematically, the volume of water present in the tank will be;
V = l * b * h
V = 4 * 3 * 1 = 12 cubic feet
Now, this content is emptied into a second tank. Since the volume of water here is the same; this means;
12 cubic feet = 3 * 2 * h
We ignore the 4ft height as it is just the height of the tank and not the height of the water in the tank
6h = 12 cubic feet
h = 12/6 = 2 ft
Answer: percent
Step-by-step explanation: i know stuff and btw i hope this helps