The focus of a parabola is (0, -3) and the directrix is y = 3. What is the equation of the parabola?
Answers
Answer:
The equation of the parabola is [tex]y = -12\cdot x^{2}[/tex].
Step-by-step explanation:
Since the directrix is of the form [tex]y = a[/tex], the parabola is vertical. The vertex of the parabola ([tex]V(x,y)[/tex]) is the midpoint between the focus ([tex]F(x,y)[/tex]) and a point of the directrix ([tex]P(x,y)[/tex]), that is to say:
[tex]V(x,y) = \frac{1}{2}\cdot F(x,y) + \frac{1}{2}\cdot P(x,y)[/tex] (1)
If we know that [tex]F(x,y) = (0, -3)[/tex] and [tex]P(x,y) = (0, 3)[/tex], then the coordinates of the vertex of the parabola:
[tex]V(x,y) = \frac{1}{2}\cdot (0, -3) + \frac{1}{2}\cdot (0, 3)[/tex]
[tex]V(x,y) = (0, 0)[/tex]
The vertex factor ([tex]p[/tex]) is the distance of the focus with respect to the vertex:
[tex]p = \sqrt{[F(x,y)-V(x,y)]\,\bullet \,[F(x,y)-V(x,y)]}[/tex] (2)
If we know that [tex]F(x,y) = (0, -3)[/tex] and [tex]V(x,y) = (0, 0)[/tex], then the vertex factor is:
[tex]p = \sqrt{0^{2}+(-3)^{2}}[/tex]
[tex]p = -3[/tex]
The equation of the parabola in the vertex form is described below:
[tex]y - k = 4\cdot p \cdot (x-h)^{2}[/tex] (3)
Where:
[tex]x[/tex] - Independent variable.
[tex]y[/tex] - Dependent variable.
[tex]h, k[/tex] - Coordinates of the vertex.
If we know that [tex](h,k) = (0, 0)[/tex] and [tex]p = -3[/tex], then the equation of the parabola is [tex]y = -12\cdot x^{2}[/tex].
Related Questions
Each square represents 1 whole. Which of the following are represented by the model shown? Select the three correct answers.
Answers
Answer:
(52/10)
5 (2/10)
5.2
Step-by-step explanation:
What is the volume of a cube with a side length that measures 1 1/2 ft? Enter your answer in the box.
Answers
9514 1404 393
Answer:
3 3/8 ft³
Step-by-step explanation:
The volume of a cube is the cube of the side length.
V = s³
V = (1.5 ft)³ = 3.375 ft³ = 3 3/8 ft³
A rectangle has a width of 6 and a length of 2x+8. The area is 108 squared, what is the value of x?
Answers
Answer:
x = 5
Step-by-step explanation:
108 = 6(2x + 8)
108/6 = 18
18 = 2x + 8
18 - 8 = 10
10 = 2x
10/2 = 5
5 = x
If f(x) = x3 – 2x2, which expression is equivalent to f(i)?
0-2 + 1
O-2-1
O
2 + 1
O 2-1
PLS HELP
Answers
Answer:
[tex]2 - i[/tex]
Step-by-step explanation:
Substitute i for x. Remeber i means imaginart number.
[tex] {i}^{3} - 2 {i}^{2} [/tex]
Use the Imaginary number exponents rules
[tex] {i}^{2} = - 1[/tex]
[tex] {i}^{3} = - i[/tex]
[tex]i {}^{4} = 1[/tex]
Simplify the equation.
[tex] - i - ( - 2)[/tex]
[tex] - i + 2[/tex]
Write as a complex number in form a+bi
[tex]2 - i[/tex]
Please ASAP! All I know is that the pH is 3
Answers
Answer:
B
Step-by-step explanation:
this is simply logarithm
3 = -log(H)
-3 = log H
H= 10^-3
H= 0.001
A developer is building a scale model of the city. From the roof of an apartment complex, the developer points two lasers at the taller office building across the street. The first laser points to the base of the building and the second laser points to the top of the building. The first laser beam has an angle of depression of 36° and is 155.7 feet long. The second has an angle of elevation of 32° and is 148.6 feet long. How tall is the office building? How far apart are the apartment complex and the office building? Round your answers to the nearest foot.
Answers
Answer:
a. 170 ft b. 126 ft
Step-by-step explanation:
a. How tall is the office building?
The two laser lights with the length of the taller office building, L form a triangle with sides 155.7 feet, 148.6 feet and L with angle 36° + 32° = 68° facing the taller office building.
We use the cosine rule to find the length of taller office building.
So, L² = 155.7² + 148.6² - 2(155.7)(148.6)cos68°
L² = 24242.49 + 22081.96 - 46,274.04(0.3746)
L² = 46324.45 - 17334.56
L² = 28989.89
L = √28989.89
L = 170.26 ft
L ≅ 170 ft
b. How far apart are the apartment complex and the office building?
Using one of the lights, the distance between the buildings, d, the laser light(being the hypotenuse side) and the building (being the opposite side)form a right angled triangle.
So, using the 155.7 feet light at 36 angle,
cos36 = d/155.7
d = 155.7cos36
d = 155.7(0.8090)
d = 125.96 ft
d ≅ 126 ft
What do patterns do you notice about finding the area of a triangle?
Answers
Step-by-step explanation:
heres the formula A=12b(base)h(hight)
Answer:
Step-by-step explanation:
It has (1/2) included in the formula to find area
pls help thannnnkkkss <33
Answers
Answer: You would put the parentheses here 24 divided by 6 x 2 - (1 +4)
Have a nice day!
Evaluate using suitable property. Write the needed steps. Use proper brackets.
20 x 399 x 5
Answers
Step-by-step explanation:
20 x 399 x 5
= (20×5) × 399
= 100×399
= 39,900
Plzz help me I need help I am stumped.... will mark brainliest plzz help
Answers
Answer:
x = -11
Step-by-step explanation:
3x + 4(3-5x) =1
3x + 12 - 2x = 1
1x + 12 = 1
- 12 - 12
1x/1 -11/1 ×=-11
The winter clothing drive has received donations of 5 coats,23 pairs of gloves, 19 scarves, and 3 hats so far.
Answers
Answer:
0.54 percent chance
Step-by-step explanation:
5+23+19+3=50
=54
help me plzz
4X + 24 - X + 5 ≤ 62
Answers
Answer:
Combine like terms:
3x + 29 ≤ 62
-29 -29
3x = 33
Divide by 3 on both sides.
x = 11!
Answer:
x is 11
Step-by-step explanation:
4X + 24 - X + 5 ≤ 62
24 + 5
is 29
29-3x ≤ 62
-3x ≤ 33
-x ≤ 11
x ≥ 11
Please help me solve these questions
Answers
2= 12
Hope this helps
Im just trying to see if this answer is correct could someone check
Answers
Answer:Its 81.25
Step-by-step explanation:
right on acellus
Solve the question below.
A + C =5
C + D = 4
C - A = 1
What is D + A?
Answers
Answer:
9
Step-by-step explanation:
The area of the shape is [ ]
square meters.
(50 points ^^)
Answers
Answer:
44m²
Step-by-step explanation:
GIVEN :-
Lengths of all the sides of the figure.TO FIND :-
Area of the figureSOLUTION :-
Divide the whole figure into 2 rectangles.
Dimension of 1st rectangle = 6m × 2mDimension of 2nd rectangle = 8m × 4mArea of 1st rectangle = 6 × 2 = 12m²
Area of 2nd rectangle = 8 × 4 = 32m²
∴ Area of the whole figure = 32 + 12 = 44m²
Find the perimeter of the shape below. 4 cm 8 cm 14 cm 4 cm 6 cm 8 cm
Answers
Answer:
44cm
Step-by-step explanation:
4+4+6+8+8+14 =
8 + 14 + 22=44
Maria has a bag with 6 red marbles, 6 blue marbles, and 4 green marbles looking Maria picks one . She does not replace it and she picks another oneOn the first pick, Maria gets a green marble. What is the probability that she gets a red marble on her second pick?
Answers
Answer: Hello there!
initially Maria has 6 red marbles, 6 blue marbles, and 4 green marbles.
You know that in the first pick, Maria gets a green marble ( this means that now there are 3 green marbles left)
Now we want to know the probability that she gets a red marble on the second pick.
Now there are 6 + 6 + 3 = 15 marbles in the bag, and 6 of them are red ones. Then the probability of getting one red is the number of red ones divided by the total amount ( which is the ratio of red marbles to total marbles)
this is 6/15.
now you can see that there is no 6/15 in the options, so we need to see which one is equivalent.
if we took the option C, 2/5, and multiply both denominator and numerator by 3, we get (3*2)/(3*5) = 6/15, then 2/5 and 6/15 are equivalents.
Then the correct answer is C.
Step-by-step explanation:
please help! i need this in 10 minutes!!
Answers
Answer:
That would be 105
Step-by-step explanation:
1 nurse 1 doctor
2/210 = 105.
Laura is bowling 5 games. Her first 4 scores were 103, 143, 101, and 110.
To end up with an average score of at least 126.8, what is the lowest score Laura will need in the fifth
game?
Answers
Answer:
The least 5th score is 177
Step-by-step explanation:
Given
[tex]First\ 4: 103, 143, 101, 110.[/tex]
[tex]Average = 126.8[/tex]
Required
The least 5th score
Represent the 5th score with x.
The average is calculated as:
[tex]Average = \frac{\sum x}{n}[/tex]
So, we have:
[tex]126.8 = \frac{103 + 143 + 101 + 110 + x}{5}[/tex]
[tex]126.8 = \frac{457 + x}{5}[/tex]
Multiply both sides by 5
[tex]634= 457 + x[/tex]
Solve for x
[tex]x = 634- 457[/tex]
[tex]x = 177[/tex]
HELP, ASAPPP, Unit 1: Performing Transformations
Answers
Step by step solution: see photo
IF YOU AWNSER THIS ILL GIVE U 5$
Answers
Answer:
choose 1 ball from a bag with 1 red ball and 4 white balls
Step-by-step explanation:
410 people were surveyed about their favorite color. The circle graph created from the results shows that the slice for red measures 130 degrees. How many people said their favorite color was red?
Answers
Since we know that the total number of people is 410, we know that the whole circle is equal to 410 people. We know that a full circle is 360 degrees, so our group would be 130 degrees of those 360, or 130/360. Since one complete circle is 410 people, we multiply this by 130/360 to find the number of people that said red is their favorite color is 148.
Can someone help me plz
Answers
Answer:
n^15
Step-by-step explanation:
n x 15 is n15 added to the power of will give you your answer
Solve for x. Enter the solutions from least to greatest. 5x^2 - 20x + 15 = 0
Answers
Answer:
x = {1, 3}Step-by-step explanation:
5x² - 20x + 15 = 0x² - 4x + 3 = 0x² - 4x + 4 = 1(x - 2)² = 1√(x - 2)² = √1x - 2 = ± 1x = 2 ± 1x = 1, x = 3X=1
A man earns 15000 in a month. if he spends 20% on food and 10% in his children's education.
a) what is his total expenditure?
b) how much does he save in a month?
Answers
Step-by-step explanation:
Total money=15000
food=20%
edu.=10%
food AMT=20% of 15000
=20/100*15000
= 3000
education AMT= 10/100*15000
=1500
savings = 15000-1500-3000
=Rs10500
total expenditure=1500+3000
=4500
x^2-3=0 solve for all real values of x
Answers
Step-by-step explanation:
x²-3=0
x²=3
x=√3
stay safe healthy and happy.Answer:
x = √3
x = - √3
Step-by-step explanation:
x^2 - 3 = 0 Add 3 to both sides
x^2 = 3 Take the square root of both sides.
sqrt(x^2) = sqrt(3)
x = +/- sqrt(3)
Remember that the - root is also a solution to the question. Also for this question don't put the - sign under the root sign. That is an entirely different question.
I need help with problem number 3 if someone can help me with that
Answers
2(-2)-5 = -9
Your table is as follows:
(-2,-9)
(-1,-7)
(0,-5)
(1,-3)
9. Find the measure of angle
a
36°
57°
Answers
Answer:
no clue bro
Step-by-step explanation:
1. Which of the following equations would not
contain the point (4, 12)?
A.y = 2X + 9
B.y = -2x + 14-x1
C. y = 2x + 8
D. y = -2x + 20