Find the constant of variation k for the direct variation. x f ( x ) 0 0 2 –1 4 –2 7 –3.5 k = 0.5 k = –2 k = –0.5 k = 0
1 answer:
Answer:
Option C is correct.
Constant of variation k = -0.5
Step-by-step explanation:
The direct variation says that:
then, the equation is of the form: .....[1] where k is the constant of variation.
Given the table:
x f(x)=y
0 0
2 -1
4 -2
7 -3.5
Consider any values from the tables
x = 4 and y=f(x) = -2
Substitute these values in equation [1] we have;
Divide both sides by 4 we get;
Therefore, the constant of variation is, -0.5
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Answer:
D)4x + 6/(x + 1)(x - 1)
Step-by-step explanation:
A field is basically a rectangle, so to find the perimeter of our field we are using the formula for the perimeter of a rectangle
where
is the perimeter
is the length
is the width
We know from our problem that the field has length 2/x + 1 and width 5/x^2 -1, so and
.
Replacing values:
Notice that the denominator of the second fraction is a difference of squares, so we can factor it using the formula where
is the first term and
is the second term. We can infer that
and
. So,
. Replacing that:
We can see that the common denominator of our fractions is . Now we can simplify our fraction using the common denominator:
We can conclude that the perimeter of the field is D)4x + 6/(x + 1)(x - 1).
by pythagorean formula, the last side is √(61)
by cos rule
cos A
A = 39.81