A cat keeps eating to gain weight while a dog keeps doing exercise to lose weight.
1 answer:
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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
Answer:
We have the equation:
x - y = 4
We can write this as a linear equation in the slope-intercept form if we isolate the variable y.
We get:
y = x - 4
Now to graph this function, we need to evaluate x in two different points and get two points (x, y) of the line.
If we use x = 1 and x = 2, then we get:
y(1) = 1 - 4 = - 3
Then we have the point (1, -3)
and:
y(2) = 2 - 4 = - 2
Then we have the point (2, - 4)
Now we need to draw these two points in the coordinate axis, and draw a line that connects the points, the example can be seen in the image below.
a) To use the graph, we need to locate the value x= 7 in the x-axis.
Then draw a vertical line
In the point where the vertical line intersects the graph, we draw an horizontal line.
The y-value will be the value at which this horizontal line intersects the y-axis
In this case, is at y = 3.
Then when x = 7, y = 3.
(you can see it in the graph)
ii) The coordinate at which the graph intersects the x-axis can be seen in the graph, it is the point (0, 4)
