An isosceles trapezoid ABCD with height 2 units has all its vertices on the parabola y=a(x+1)(x−5). What is the value of a, if p
oints A and D belong to the x−axis and m∠BAD=60°
2 answers:
Answer:
The value of a = ±(√3)/(6)
Step-by-step explanation:
Points A and D belong to the x−axis.
All vertices on the parabola y = a (x+1)(x−5) = a (x² - 4x - 5)
So, points A and D represents the x-intercept of the parabola y
To find x-intercept, put y = 0
∴ a (x+1)(x−5) = 0 ⇒ divide both sides by a
∴ (x+1)(x−5) = 0 ⇒ x = -1 or x = 5
so, the x-coordinate of Point A is -1 or 5
And given that: m∠BAD=60°
So, the tangential line of the parabola at point A has a slope of 60°
∴ y' = tan 60° = √3
∴ y' = a (2x-4)
∴ a (2x-4) = √3
∴ a = (√3)/(2x-4)
Substitute with x = -1 ⇒ a = (√3)/(-6)
Substitute with x = 5 ⇒ a = (√3)/(6)
So, The value of a = ±(√3)/(6)
Also, see the attached figure, it represents the problem in case of a = (√3)/(-6)
You might be interested in
Answer:
The cost is $9.70 per kilogram.
Step-by-step explanation:
This can be solved by a rule of three.
In a rule of three problem, the first step is identifying the measures and how they are related, if their relationship is direct of inverse.
When the relationship between the measures is direct, as the value of one measure increases, the value of the other measure is going to increase too. In this case, the rule of three is a cross multiplication.
When the relationship between the measures is inverse, as the value of one measure increases, the value of the other measure will decrease. In this case, the rule of three is a line multiplication.
In this problem, the measures are the weight of the cheese and the price. As the weight increases, so does the price. It means that this is a direct rule of three.
Solution:
The problem states that cheese costs $4.40 per pound. Each kg has 2.2 pounds. How many kg are there in 1 pound. So:
1 pound - xkg
2.2 pound - 1 kg
kg
Since cheese costs $4.40 per pound, and each pound has 0.45kg, cheese costs $4.40 per 0.45kg. How much does is cost for 1kg?
$4.40 - 0.45kg
$x - 1kg
The cost is $9.70 per kilogram.
Answer: - 2.5
Step-by-step explanation:
Using the attached number line has reference, the distance between each integer on the number line attached is 1, and the numbers are ordered in ascending order from - 10 to + 10. The point R exists in between the point marked - 2 and - 3 respectively. This shows that that point R is a number between the two integers, a number greater than - 3 but less than - 2.
From the picture attached the blue dot sits directly at the midpoint between - 3 and - 2. Hence the position can be a obtained by averaging the two integers.
(-3 + - 2) / 2 = - 5/2 = - 2.5
