The center of an ellipse is located at (0, 0). One focus is located at (12, 0), and one directrix is at x = 14 1/12.
what is the equation that represents the ellipse?????????
Answers
[tex] \frac{(x-h)^{2}}{a^{2}} + \frac{(y-k)^{2}}{b^{2}} =1[/tex]
where
(h,k) = coordinates of the center
a, b = semi-major and semi-minor axes
Refer to the figure shown below.
The center of the ellipse is at (0,0).
Therefore, h=0, k=0.
One focus is at (12, 0)
Therefore
c = 12
One directrix is at 14 1/12 = 169/12.
Because the directrix is located at x = a²/c, therefore
a²/12 = 169/12
a² = 169/144
a = 13
Because c² = a² - b², obtain
b² = a² - c²
= 169 - 144 = 25
b = 5
Answer:
The equation for the ellipse is
[tex] \frac{x^{2}}{169} + \frac{y^{2}}{25} =1[/tex]
The equation that represents the ellipse with the given coordinates of the center, one focus, and one directrix is x^2/144 + y^2/(25/12) = 1.
Explanation:The equation that represents the ellipse with the center at (0, 0), one focus at (12, 0), and one directrix at x = 14 1/12 can be found using the standard form of the equation for an ellipse:
(x - h)^2/a^2 + (y - k)^2/b^2 = 1
where (h, k) is the center of the ellipse, a is the distance from the center to the vertices, and b is the distance from the center to the co-vertices.
Since the center is at (0, 0), the equation becomes:
x^2/a^2 + y^2/b^2 = 1
The distance from the center to one focus is 12, so the value of a is 12. To find the value of b, we need to use the distance from the focus to the directrix. Since the directrix is x = 14 1/12, the distance from the focus to the directrix is |14 1/12 - 12|. Simplifying, we get |14 1/12 - 12| = 2 1/12. Therefore, the value of b is 2 1/12.
Substituting these values into the equation, we get:
x^2/144 + y^2/(25/12) = 1
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Related Questions
how do you reduce the fraction of 28/49
Answers
reduce by 7
28/7 4
---- = ----
49/7 7
your answer will be: 4/7
hope this helps :D
28/7 4
---- = ----
49/7 7
your answer will be: 4/7
Determine the range of: f(x) = 13 - 20x - x^2 -3x^4. Also, find the max. And min. Values and state where those values occur
Answers
The range of the graph refers to the coverage of y-values of the curve. From the picture, we could see that it covers most of the negative y-axis. To know at which value, let's find the maxima. There is no minima for this graph as you can see because it extends downwards infinitely at both sides.
To find the maxima, differentitate f(x) with respect to x and equate to 0
f'(x) = 0 = -20-2x-12x^3=0
You can find the roots easily by using a scientific calculator using the mode EQN. For this equation, there are 2 complex root and 1 real root. Thus, x = -1.14. Substitute this to the original equation:
y = 13 - 20(-1.14) - (-1.14)^2 -3(-1.14)^4
y = 29.433
Thus, the maxima is at point (-1.14,29.433). It can't be seen clearly in the graph because of the close intervals.
If matrix A has dimensions 3 x 2 and matrix B has dimensions 3 x 2, can matrix A and matrix B be multiplied?
Answers
Matrix B has 3 rows, 2 columns
The number of columns in matrix A (which is 2) does not match up with the number of rows in matrix B (which is 3).
So the matrix multiplication A*B is undefined. We cannot multiply the matrices.
Answer:
we can not multiply matrix A and B.
Step-by-step explanation:
We have been given that
dimension of matrix A = 3 x 2
dimension of matrix B = 3 x 2
Rule of multiplying two matrices:
Two matrix can be multiplied if the column of first matrix is equal to the row of second matrix.
column of first matrix = row of second matrix
Here, we have
Column of first matrix A = 2
Row of second matrix b = 3
Since,, column of matrix A ≠ Row of matrix B
Hence, we can not multiply matrix A and B.
Please help :) :) :)
Answers
A motorboat
travels 222 km in 6 hours going upstream.
Rate = distance/time = 222/6 = 37 km/hr
----------------------
It travels 390 km going downstream in the same amount of time.
Rate = distance/time = 390/6 = 65 km/hr
---------
What is the rate of the boat in still water and what is the rate of the
current?
Equations:
Upstream: b-c = 37 km/hr
Downstrm: b+c = 65 km/hr
Add and solve
for "b":
(2)b = 102 km/hr
b = 51 km/hr (speed of the boat in still water)
-----
Solve for "c":
b+c = 65
51 + c = 65
c = 14 km/hr (speed of the current)
A bicycle wheel makes 5 revolutions. Determine how far the bicycle travels in feet. The diameter of the wheel is 32in.
Answers
Of the 240 shirts on a rack, 40 percent are size medium. How many shirts on the rack are size medium?
Answers
First, let’s check for the given:
Shirts on the rack = 240
Medium size shirts = 40% of 240
With the following given, we can now solve for the total
number of shirts on the rack that are size medium.
So, in order to solve for the problem, we multiply 40% to 240:
The decimal equivalent of 40% is 0.4.
240 shirts * .4 = 96 shirts
Therefore, out of 240 shirts on the rack, there are 96 shirts on the rack that are size medium.
To add, the number or ratio that represents a fraction of 100 is called a percentage.
A baseball was pitched at a speed of 75.2 miles per hour. a tennis ball was served at a speed 1.5 times faster than this. how much faster was the speed of the tennis ball than the speed of the baseball?
Answers
112.8+75.2=188
188-75.2=112.8
Answer:
75.2*1.5=112.8
112.8+75.2=188
188-75.2=112.8
find the area of the circle with diameter of 11mm leaving answer in terms of pi
Answers
r=d/2=11/2=5.5
area=π*30.25=30.25π
Find the measure of angle AOE in the diagram below.
Help will be appreciated!
Answers
Answer:
We choose D
Step-by-step explanation:
Given that:
∠BOA = (3x -28) degrees ∠COD = (66 -x) degrees ∠BOC = 90 degreesAs we know that ∠BOA + ∠COD + ∠BOC= 180 degrees because AD is a straight line, so we have:
(3x -28) + (66-x) +90 = 180
<=> 2x = 52
<=> x = 26 degrees.
=> ∠BOA = 3*26 - 28 = 50 degrees
As we can see that, ∠BOA = ∠DOE (The properties of two straight lines intersect)
<=> ∠DOE = 50 degrees
Once again, the AD is a straight line, so we have:
∠DOE + ∠AOE = 180
<=> ∠AOE = 180 - ∠DOE
<=> ∠AOE = 180 - 50 = 130 degrees
We choose D
If f(x)=6x and g(x) = 4x+1, find ( f o g)(x)
Answers
(f○g)(x)=6(4x+1)
(f○g)(x)=24x+6
The temperature at 9 a.m. is 2 degrees. The temperature rises 3 more degrees by noon. Which expression describes the temperature at noon?
2 + 3
2 + (–3)
–2 + (–3)
–2 + 3
Answers
it starts at 2 degrees which is not a negative number and temperature rises so it isn't a negative number either
so it would be 2+3
An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is A, 2+3.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given that the temperature at 9 a.m. is 2 degrees. Further, the temperature rises 3 more degrees by noon.
As two whole numbers are added together, the total quantity or sum of those values is obtained. Therefore, the expression that describes the temperature at noon is 2 + 3.
This is because the temperature is positive and after the temperature rises, the temperature will be added.
Hence, the expression that describes the temperature at noon is 2 + 3.
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Use the law of cosines to find the missing third side
Answers
a^2=7.4^2+15.8^2-2(7.4)(15.8)cos54°
a^2=304.4-233.84cos54°
a=√(304.4-233.84cos54°) units
a≈12.92 units (to the nearest hundredth of a unit)
The missing third side BC is approximately 16.93 units. To use the Law of Cosines to find the missing third side (BC), we'll use the formula:
[tex]c^2 = a^2 + b^2 - 2ab * cos(C)[/tex]
where:
c is the side opposite angle C (BC in this case)
a and b are the known sides (AC and AB, respectively)
C is the angle opposite side c (angle BAC in this case)
Given values:
Angle BAC (C) = 54 degrees
AC (a) = 7.4
AB (b) = 15.8
Now, we can plug the values into the formula and solve for BC (c):
[tex]BC^2 = 7.4^2 + 15.8^2 - 2 * 7.4 * 15.8 * cos(54)[/tex]
To find cos(54), we can use a calculator:
[tex]cos(54 degrees) \approx 0.5878[/tex]
Now, we can continue the calculation:
[tex]BC^2 = 54.76 + 249.64 - 2 * 7.4 * 15.8 * 0.5878\\BC^2 = 54.76 + 249.64 - 17.44\\BC^2 = 286.96[/tex]
Now, find the square root of both sides to get the value of BC:
[tex]BC = \sqrt{286.96} \\BC \approx 16.93[/tex]
So, the missing third side BC is approximately 16.93 units.
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Stuart is buying a pair of jeans that regularly cost $40. They are on sale for 20% off. If the tax rate is 8%,what is the sale price of the jeans including tax?
Answers
Five scouts took a white water rafting trip. The total cost of the trip was $721. Each person in the group received a student discount of $6. Write and solve an equation to find out how much each student paid before discount.
Answers
cost per student before discount = 721/5+6
721/5 = 144.20 +6 = 150.20
Suppose you roll two standard number cubes once. Find the probability. P(7 or even)
Answers
To roll a seven you could have (1,6) (6,1) (2,5) (5,2) (3,4) (4,3)
6 different ways so 6/36 reduces to 1/6 way of getting a 7
For getting an even number as sum, we can have (1,1) or (1.3) or (1,5) or (2,2) or (2,4) or (2,6) or (3,1) or (3,3) or (3,5) or (4,2) or (4,4) or (4,6) or (5,1) or (5,3) or (5,5) or (6,2) or (6,4) or (6,6) 18 ways, probability is 18/36 reduces to ½
So for either one you now have 1/6 + 1/2 = 6+2/12 = 8/12 reduced to 2/3
help someone plz
A student needs to make a rectangular cardboard piece that is 12 inches long. The area of the cardboard piece should be between 60 square inches to 300 square inches. The function f(w) relates the area of the cardboard, in square inches, to the width w in inches. Which of the following shows a reasonable domain for f(w)?
A: 2 ≤ w ≤ 5
B: 5 ≤ w ≤ 25
C: 25 ≤ w ≤ 60
D: 60 ≤ w ≤ 300
Answers
area = L x w
60 = 12 x w
w=60/12 = 5
300 = 12 x w
w = 300/12 = 25
so B is the correct answer
Answer:
Option B
[tex]5 \leq w \leq 25[/tex]
Step-by-step explanation:
Let
L------> the long of the cardboard piece
W-----> the width of the cardboard piece
The area of cardboard piece is equal to
[tex]A=L*W[/tex]
In this problem we have
[tex]L=12\ in[/tex]
so
[tex]A=12W[/tex]
[tex]f(W)=12W[/tex]------> equation A
[tex]f(W)\geq 60\ in^{2}[/tex] ------> inequality B
[tex]f(W)\leq 300\ in^{2}[/tex] ------> inequality C
Substitute equation A in the inequality B
[tex]12W\geq 60\ in^{2}[/tex]
[tex]W\geq 60/12[/tex]
[tex]W\geq 5\ in[/tex]
Substitute equation A in the inequality C
[tex]12W\leq 300\ in^{2}[/tex]
[tex]1W\leq 300/12[/tex]
[tex]1W\leq 25\ in[/tex]
The domain for the function f(W) is equal to the interval------> [tex][5,25][/tex]
Evaluate the expression : (0.4)^3=
Answers
The expression when evaluated, can be found to be 0. 064.
How to evaluate the expression ?( 0 . 4 ) ³ means raising the number 0. 4 to the power of 3 , which is the same as multiplying 0. 4 by itself three times. This is how the expression is evaluated.
Start with:
0 . 4 * 0 . 4 * 0 . 4
Calculate each multiplication step:
1st multiplication: 0 . 4 * 0 . 4 = 0 . 16
2nd multiplication: 0 . 16 * 0 . 4 = 0 . 064
So, when you multiply 0. 4 by itself three times ( 0 . 4 * 0 . 4 * 0 . 4), you get the result of 0 . 064.
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Answer this please image below
Answers
A histogram never provides information regarding how many for an exact number. A histogram measures frequency by looking at and comparing several ranges.
The last answer includes information that can't be drawn from the histogram.
It ask for a specific number of bottles when the histogram utilizes a range to sort the amount of bottles collected.
Hope this helps!
25/150 in simplest form
Answers
Divide bothe the numerator and denominator by 25 to get the simplest form.
25/25=1
150/25=6
Final answer: 1/6
if a polynomial has one root in the form a+√b , it has a second root in the form of a_√b
Answers
That is,
The conjugate of (a + √b) is (a - √b) and vice versa.
To show that the given conjugates come from a polynomial, we should create the polynomial from the given factors.
The first factor is x - (a + √b).
The second factor is x - (a - √b).
The polynomial is
f(x) = [x - (a + √b)]*[x - (a - √b)]
= x² - x(a - √b) - x(a + √b) + (a + √b)(a - √b)
= x² - 2ax + x√b - x√b + a² - b
= x² - 2ax + a² - b
This is a quadratic polynomial, as expected.
If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.
x = (1/2) [ 2a +/- √(4a² - 4(a² - b)]
= a +/- (1/2)*√(4b)
= a +/- √b
x = a + √b, or x = a - √b, as expected.
Answer:
a - √b
Step-by-step explanation:
If you solve the quadratic equation x² - 2ax + a² - b = 0 with the quadratic formula, it should yield the pair of conjugate radical roots.x = (1/2) [ 2a +/- √(4a² - 4(a² - b)] = a +/- (1/2)*√(4b) = a +/- √bx = a + √b, or x = a - √b, as expected.
Where is the answer to the expression 4 − 8 located on a horizontal number line? 4 units to the left of 4
4 units to the right of 4
8 units to the left of 4
8 units to the right of 4
I need the answer asap whoever answers first and gets it right gets brainliest
Answers
A negative number is alwats at the left in a horizontal line.
Let's try to rapresent it.
-4 -3 -2 -1 0 +1 +2 +3 +4
So, you count from +4 to -4
Your answer is "8 units to the left of 4"
what's the Least common multiple for 2,6,8?
Answers
6= 2*3
8= 2*4
8= 2*2*2
The lcm of these three numbers equals 2*2*2*3*1. Notice how we only multiply 3 sets of 2. This is because 2 is a common factor between all 3 of the numbers.
2*2*2*3*1= 24
Final answer: 24
Find the area of the composite figure.Use 3.14 for pi.
Answers
area for the triangle section is 1/2 x b x h: 1/2 x 16 x 10 = 80 square m
area for half circle = 1/2 x 3.14 x 8^2 = 100.48 square m
100.48 + 80 = 180.48 square meters
Daniel and Sofia both solve this system of equations: y = -1.5x + 5.7 y = 0.5x + 0.3 Daniel's solution is (1.1, 2.4). Sofia's solution is (2.7, 1.65). They graph the equations to check their work. Based on the graph, whose solution is more likely to be correct?Daniel is more likely to be correct. The x-coordinate of the intersection is between 1 and 2 and the y-coordinate of the intersection is between 2 and 3. Sofia is more likely to be correct. The x-coordinate of the intersection is between 2 and 3 and the y-coordinate of the intersection is between 1 and 2. or niether
Answers
y = 0.5x + 0.3
-1.5x + 5.7 = 0.5x + 0.3
-1.5x - 0.5x = 0.3 - 5.7
-2x = - 5.4
x = -5.4/-2
x = 2.7
y = 0.5x + 0.3
y = 0.5(2.7) + 0.3
y = 1.35 + 0.3
y = 1.65
solution is (2.7, 1.65)
Sophia is more likely to be correct because the x coordinate is between 2 and 3 and the y coordinate is in between 1 and 2
Answer:
Sofia is more likely to be correct
=)
Step-by-step explanation:
Solve:
y^6 (y^5)
plz i put eleven idk why se says it's wrong :c
Answers
Ralph sold brownies for $0.27 a piece in order to earn money to buy baseball cards. If the cards cost $0.54 per pack, and if Ralph had no money left over after buying them, what is the least number of brownies he must have sold?
Answers
-cz+6z=tz+83 solve for z
Answers
6z - cz - tz = 83
z (6 - c - t) = 83
z = 83 / (6 - c - t)
hope that helps
Answer:
The value of the equation for z is [tex]z=\frac{83}{6-c-t}[/tex].
Step-by-step explanation:
Consider the provided equation.
[tex]-cz+6z=tz+83[/tex]
Subtract tz from both the sides.
[tex]-cz+6z-tz=tz-tz+83[/tex]
[tex]-cz+6z-tz=83[/tex]
Take z common.
[tex]z(-c+6-t)=83[/tex]
[tex]z(6-c-t)=83[/tex]
Divide 6-c-t from both the sides.
[tex]\frac{z(6-c-t)}{6-c-t}=\frac{83}{6-c-t}[/tex]
[tex]z=\frac{83}{6-c-t}[/tex]
Thus, the value of the equation for z is [tex]z=\frac{83}{6-c-t}[/tex].
Daisy works at an ice-cream parlor. She is paid $10 per hour for the first 8 hours. She works for x hours in a day and x is greater than 8, the expression giving her net earnings for the day is
A. x(80+1.5)
B. (x-8)1.5
C. 80+15 (x-8)
D. (8)(15)(x-8)
Answers
With that this is the solution step by step:
1) Number of hours worked: x
2) Rate for the first 8 hours: $10 per hour
2) Pay for the first 8 hours = $10 * 8 = $80
3) Number of hours worked over 8 hours = x - 8
4) Rate for the hours worked over 8: 1.5 times $10 per hour = $15 per hour
5) Pay for the hours worked over 8 = $15 (x - 8) = 15 (x - 8)
6) Total pay = 80 + 15 (x - 8)
That is the option C.
Answer: option C. 80 + 15(x - 8)
the answer is option C
need help, thank you!
2x+3y=5x−y
y=0
x=?
Answers
2x -5x = -y - 3y
-3x =-4y
X=4\3 y
Answer:
X=4\3
Step-by-step explanation:
Jennifer can clean her room in 2 hours, while John can clean the same room in 5 hours. How many hours would it take for them to clean the room together?
7
10
seven tenths
ten sevenths
I think the answer is tenth sevenths but im not sure! Please Help ASAP
Answers
Answer: ten sevenths
Step-by-step explanation:
Given: Time taken by Jennifer to clean her room [tex]t_1= 2 \text[ hours}[/tex]
Time taken by John to clean same room [tex]t_2= 5\text[ hours}[/tex]
If they work together to clean the room , then the total time taken by them is given by :-
[tex]\dfrac{1}{t}=\dfrac{1}{t_1}+\dfrac{1}{t_2}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{2}+\dfrac{1}{5}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{5+2}{10}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{7}{10}\\\\\Rightarrow\ t=\dfrac{10}{7}\text{ hours}[/tex]