A hyperbola is centered at the origin and opens either horizontally or vertically. It passes through the points (-3, 4), (-2, 0)
, and (t, 2). Find t^2.
1 answer:
Answer:
5.25
Step-by-step explanation:
The fact that the graph crosses the x-axis means the hyperbola opens to the left and right. Hence its equation is ...
x^2/a - y^2/b = 1
The point (-2, 0) helps us find "a":
(-2)^2/a - 0/b = 1
4 = a
Then we can find "b" from the other fully-specified point.
(-3)^2/4 - 4^2/b = 1 . . . . . . substitute (-3, 4) for (x, y)
b = 16/(9/4 -1) = 64/5 . . . . solve for b
Then the third point will satisfy ...
t^2/4 - (5/64)·2^2 = 1 . . . . . . substitute (t, 2) for (x, y)
t^2 = 4·(1 +5/16) = 4 +5/4 . . . . solve for t^2
t^2 = 5.25
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Answer:
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The length of the football field is 360 feet.
Step-by-step explanation:
Let w represent width of the football field.
We have been given that the length is 200 ft more than the width, so the length of the field would be .
We are also told that the perimeter is 1,040 ft. We know that football field is in form of rectangle, so perimeter of field would be 1 times the sum of length and width. We can represent this information in an equation as:
Let us solve for w.
Therefore, the width of the football field is 160 feet.
Upon substituting in expression
, we will get length of field as:
Therefore, the length of the football field is 360 feet.
Answer:
The area of the triangle formed by origin, and the points (4,5) and (-2,5) will be 15 sq. units.
Step-by-step explanation:
The two parabolas are and y = x² - 2x - 3.
Now, solving those two equations we will get the points of intersection.
So,
⇒ - (x - 1)² + 24 = 3x² - 6x - 9
⇒ -x² + 2x - 1 + 24 = 3x² - 6x - 9
⇒ 4x² - 8x - 32 = 0
⇒ x² - 2x - 8 = 0
⇒ x² - 4x + 2x - 8 = 0
⇒ (x - 4)(x + 2) = 0
So, x = 4 or - 2.
Now, for x = 4 , y = 4² - 2(4) - 3 = 5 and the point of intersection is (4,5).
Or, for x = - 2, y = (- 2)² - 2(- 2) - 3 = 5 and the point of intersection is (-2,5).
Now, points (4,5) and (-2,5) make a straight line parallel to the x-axis at a perpendicular distance of 5 units from origin and its length is (4 - (- 2)) = 6 units.
So, the area of the triangle formed by origin, and the points (4,5) and (-2,5) will be = 0.5 × 5 × 6 = 15 sq. units. (Answer)