Write the equation of a parabola whose directrix is y=9.75 and has a focus at (8, 0.25).
Answers
Answer:
y = (-1/19)(x - 8)² + 1521/76
Step-by-step explanation:
A parabola moves in such a way that it's distance from it's focus and directrix are always equal.
Now, we are given that directrix is y = 9.75 and focus is at (8, 0.25). Focus can be rewritten as (8, ¼) and directrix can be rewritten as y = 39/4
If we consider a point with the coordinates (x, y), it means the distance from this point to the focus is;
√((x - 8)² + (y - ¼)²)
Distance from that point to the directrix is; (y - 39/4)
Thus;
√((x - 8)² + (y - ¼)²) = (y - 39/4)
Taking the square of both sides gives;
((x - 8)² + (y - ¼)²) = (y - 39/4)²
(x - 8)² + y² - ½y + 1/16 = y² - (39/2)y + (39/4)²
Simplifying this gives;
(x - 8)² - (39/4)² = (½ - 39/2)y
(x - 8)² - 1521/4 = -19y
(x - 8)² - 1521/4 = -19y
Divide both sides by -19 to get;
y = (-1/19)(x - 8)² + 1521/76
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An attacker at the base of a castle wall 4 m high throws a rock straight up with speed 7.5 m/s from a height of 1.5 mabove the ground.(a) Will the rock exceed the top of the wall?(b) If so, what is its speed when it reaches the top of the wall? Page 4 of 74(c) If we don’t want the stone to exceed the top of the wall (we want the top of the wall to be the maximum height)what the initial speed that the stone must have?
b. rhombus
c. square
d. trapezoid
Answers
rhombus, square, and trapezoid are all their own shapes, parallelogram is a four-sided plane rectilinear figure with opposite sides parallel. So basically a parallelogram is a shape with four sides.
Hope this helps.
Answer:
parallelogram
Step-by-step explanation:
Answers
The y-value for the E coordinate after the translation of the points will be 9.
What is translation?
The process of changing the location of the image on the coordinate system will be known as the translation.
A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
Given that triangle, EFG with the coordinates E (-3,5), F(-3, 1), (1, 1) is translated as 2 units left and 4 units up.
E(-3,5) translated 2 units left would be (-5,5), then translated 4 units up would be (-5,9).
Therefore, the y-value for the E coordinate after the translation of the points will be 9.
To know more about translation follow
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Answer:
the y value would be 9
full translation(-5,9)
Step-by-step explanation:
E(-3,5) translated 2 units left would be (-5,5), then translated 4 units up would be (-5,9)
Choose 1 answer
84%
86%
88%
92%
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Answer:
84%
Step-by-step explanation:
Answer:
84%
Step-by-step explanation:
on Khan Academy
PLS HELP ME!!!
Answers
The answer to the question is 25.
Answers
Answer:
- the hypotenuse side, c = 23.1 cm
- angle A = 41.26 ⁰
- angle B = 48.74 ⁰
Step-by-step explanation:
Given;
first leg of the right triangle, a = 15.21 cm
second leg of the right triangle, b = 17.34 cm
Angle C = 90 ⁰
The missing parameters;
- the hypotenuse side = c
- angle A
- angle B
Use Pythagoras theorem to calculate the missing side "c", which is the hypotenuse
c² = a² + b²
c² = (15.21)² + (17.34)²
c² = 532.02
c = √532.02
c = 23.1 cm
The missing angle A is calculated as;
The missing angle is calculated as;
B = 90⁰ - A
B = 90⁰ - 41.26⁰
B = 48.74⁰
Answers
Answer:
Step-by-step explanation:
statment/reason
1) HK≅JK / given (S)
2) IK bisects ∠HKJ / given
3) ∠3≅∠4 / angle bisectors form congruent angles (A)
4) HK≅JK / given
5) IK ≅IK / reflexive propriety (S)
6) ΔIHK≅ΔIJK / SAS theorem of congruency
7) ∠1≅∠2 / corsponding parts of congruent Δs are ≅
8) IK bisects ∠HIJ / angle bisectors form congruent angles