It is given that AB is parallel to CD and points E, G, H, and F are collinear. The measure of ZEGF is 180°, by the definition of
a straight angle. ZAGE and ZAGF are
adjacent, so the measure of ZAGE plus the measure of ZAGF equals the measure of EGF, by the Angle Addition Postulate. Then, substituting for the measure of ZEGF
it can be said that the measure of ZAGE plus the measure of ZAGF equals 180°. so the measure of ZCHE plus the measure of ZAGF equals 180°.
Substituting once again means that the measure of ZAGE plus the measure of ZAGF equals the measure of ZCHE plus the measure of ZAGF. The measure of ZAGE
is equal to the measure of ZCHE
Finally, by the definition of congruence, ZAGE is congruent to ZCHE.
OZCHE and ZAGF are alternate interior angles; using the Addition Property of Equality
OZCHE and ZAGF are alternate interior angles; using the Subtraction Property of Equality
OZCHE and ZAGF are same-side interior angles; using the Subtraction Property of Equality
ZCHE and ZAGF are same-side interior angles; using the Addition Property of Equality
adjacent, so the measure of ZAGE plus the measure of ZAGF equals the measure of EGF, by the Angle Addition Postulate. Then, substituting for the measure of ZEGF
it can be said that the measure of ZAGE plus the measure of ZAGF equals 180°. so the measure of ZCHE plus the measure of ZAGF equals 180°.
Substituting once again means that the measure of ZAGE plus the measure of ZAGF equals the measure of ZCHE plus the measure of ZAGF. The measure of ZAGE
is equal to the measure of ZCHE
Finally, by the definition of congruence, ZAGE is congruent to ZCHE.
OZCHE and ZAGF are alternate interior angles; using the Addition Property of Equality
OZCHE and ZAGF are alternate interior angles; using the Subtraction Property of Equality
OZCHE and ZAGF are same-side interior angles; using the Subtraction Property of Equality
ZCHE and ZAGF are same-side interior angles; using the Addition Property of Equality
1 answer:
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Answer:
0
Step-by-step explanation:
We want to compute the curve integral (or line integral)
where the force field F is defined by
F(x,y) = (y, -x)
and C is the path consisting of the line segment from (1, 5) to (0, 0) followed by the line segment from (0, 0) to (0, 9).
We can write
C =
where
= line segment from (1, 5) to (0, 0)
= line segment from (0, 0) to (0, 9)
so,
Given 2 points P, Q in the plane, we can parameterize the line segment joining P and Q with
<em>r(t) = tQ + (1-t)P for 0 ≤ t ≤ 1 </em>
Hence can be parameterized as
for 0 ≤ t ≤ 1
and can be parameterized as
for 0 ≤ t ≤ 1
The derivatives are
and
In consequence,
Answer:
Yes, the zoo needs to order more fencing. The zoo has 54 ft of fence remaining for the unknown side.
If the unknown side is assumed to have this length, sin (θ) = 1.2857. which is not possible, so the triangle cannot be formed.
Step-by-step explanation:
Let a be the length of the third side of the triangle.
a = 127 - 73 = 54 ft
Let the angle that a makes with the barn be θ
The diagram of this question is attached to this solution.
Using the sine rule, we can examine if the remaining fencing material would be enough by checking if (sin θ) is realistic.
Using sine rule,
[a/(sin 72°)] = [73/(sin θ)]
[54/sin 72°] = [73/sin θ]
sin θ = (73 × sin 72°)/54 = 1.2857
sin θ = 1.2857
This is obviously not a realistic value for sin θ since it is known that sin θ ranges between 0 and 1.
The 54 ft is obviously not enough.
Hence, the zoo needs more fencing material to be able to complete the outdoor triangular giraffe exhibit.
Hope this Helps!!!
