Ecuación de la hipérbola con centro en (0;0), focos en abrir paréntesis 0 coma espacio menos raíz cuadrada de 28 cerrar paréntesis espacio y espacio abrir paréntesis 0 coma espacio raíz cuadrada de 28 cerrar paréntesis espacio ,eje conjugado = 2 raíz cuadrada de 3
Answer:
[tex]\frac{y^{2}}{25}-\frac{x^{2}}{3}=1[/tex]
Step-by-step explanation:
Para resolver este problema debemos tomar en cuenta los datos que nos dan y la ecuación de una hipérbola. Comencemos con los datos:
centro: (0,0)
focos: [tex](0,-\sqrt{28}),(0,\sqrt{28})[/tex]
eje conjugado = [tex]2\sqrt{3}[/tex]
por los focos podemos ver que la hipérbola se dirige hacia el eje y, por lo que debemos tomar la siguiente forma de la ecuación de la parábola:
[tex]\frac{y^{2}}{a^{2}}+\frac{x^{2}}{b^{2}}=1[/tex]
de los focos podemos obtener que:
[tex]c=\sqrt{28}[/tex]
y del eje conjugado podemos saber que al dividir la longitud del eje conjugado dentro de 2 obtenemos b, así que:
[tex]b=\sqrt{3}[/tex]
podemos utilizar la siguiente fórmula para obtener a:
[tex]c^{2}-a^{2}=b^{2}[/tex]
si despejamos a en la ecuación obtenemos lo siguiente:
[tex]a=\sqrt{c^{2}-b^{2}}[/tex]
ahora podemos sustituir los valores:
[tex]a=\sqrt{(\sqrt{28})^{2}-(\sqrt{3})^{2}}[/tex]
[tex]a=\sqrt{28-3}[/tex]
[tex]a=\sqrt{25}[/tex]
a=5
así que media vez conozcamos a, podemos sustituir los datos en la ecuación de la hipérbola así que obtenemos lo siguiente:
[tex]\frac{y^{2}}{a^{2}}+\frac{x^{2}}{b^{2}}=1[/tex]
[tex]\frac{y^{2}}{(5)^{2}}+\frac{x^{2}}{(\sqrt{3})^{2}}=1[/tex]
[tex]\frac{y^{2}}{25}+\frac{x^{2}}{3}=1[/tex]
si graficamos la hipérbola, queda como en el documento adjunto.
As displayed on a production possibilities curve, what will an increase in technology allow a society to do? a. Produce more, as long as the resources are also available. c. It will not affect society’s production. b. Produce less, because more resources are spent on developing technology. d. The society will spend more on the same level of production. Please select the best answer from the choices provided A
Answer:
a. Produce more, as long as the resources are also available
Step-by-step explanation:
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Ace
The correct answer is A) produce more, as long as the resources are also available.
As displayed on a production possibilities curve, an increase in technology will allow a society to produce more, as long as the resources are also available.
A production possibilities graph is a valid representation of the available ways an economy is able to use the resources. In this case, an increase in technology will allow a society to produce more, as long as the resources are also available means that as long there are enough resources in the market, technology in a country helps with the production of more things to be consumed or traded.
xét tính chẵn lẻ của hàm số : y = tanx + cotx
Answer:
Step-by-step explanation:
Madam Chong's mass is 72 kg. After participating in a fitness programme, her mass decreases at a rate of 3 kg per month. Find the minimum number of months that Madam Chong has to participate in the programme so that her mass becomes less than 52 kg. (Give your answer to the nearest whole number.)
Researchers want to see if playing with a specific toy increases the verbal abilities of young children. One group of children plays with the new toy for 4 hours a week for 4 weeks and is given a vocabulary test at the end of the experiment. The other group of matched pairs follows the same schedule, but these children play outside instead of with the toy. The children who play outside are the _____ group.
Answer:
Hence the children who play outside are the Control group.
Step-by-step explanation:
Researchers want to ascertain if twiddling with a selected toy increases the verbal abilities of young children. One group of youngsters plays with the new toy for 4 hours every week for 4 weeks and is given a vocabulary test at the top of the experiment. the opposite group of matched pairs follows an equivalent schedule, but these children play outside rather than with the toy. the children who play outside are the Control group.
Here the One group of children who plays with the toy is considered an experimental group.
how to find range from a distribution table.
Answer:
Range = highest value - lowest value
Explanation:
This is the required formula to find range from a distribution table.
The initial population of a town is 4200, and it grows with a doubling time of 10 years. What will the population be in 8 years?
Answer:
The population in 8 years will be of 7313.
Step-by-step explanation:
Population of a town:
The population of a town, after t years, with a doubling time of n years, is given by:
[tex]P(t) = P(0)(2)^{\frac{t}{n}}[/tex]
The initial population of a town is 4200, and it grows with a doubling time of 10 years.
This means that [tex]P(0) = 4200, n = 10[/tex]
So
[tex]P(t) = 4200(2)^{\frac{t}{10}}[/tex]
What will the population be in 8 years?
This is P(8). So
[tex]P(8) = 4200(2)^{\frac{8}{10}} = 4200(2)^{0.8} = 7313[/tex]
The population in 8 years will be of 7313.
Help pleas like please ASAP
Answer:
(x+9)(x+5)
Step-by-step explanation:
find 2 numbers that add to 14 and multiply to 45
please help me out (geometry)
Answer:
x = 15
Step-by-step explanation:
2x+10+4x+80=180
or, 2x+4x=180-80-10
or, 6x=90
or, x=15
Answered by GAUTHMATH
In trapezoid WXYZ, m∠ZYX=107°. Identify m∠ZWX.
Answer:
73 degrees.
Step-by-step explanation:
the inward angle at W is the outward angle at Y and therefore the complement of 107 degrees to 180.
180 - 107 = 73 degrees.
The measure of angle ZWX is 73 degrees.
What is a quadrilateral?Any closed figure made by 4 line segments joined end to end in series is called a quadrilateral.
We are given that the trapezoid WXYZ, m∠ZYX=107°.
We have been given an image of a trapezoid and we are asked to find the measure of angle ZWX .
We can see from our trapezoid that angle XYZ and angle WZY measures 90 degrees.
Since we know that trapezoid is a quadrilateral and sum of all angles of a quadrilateral equals
m∠ZYX + m∠ZWX = 180
m∠ZWX = 180 - 107
m∠ZWX = 73 degrees.
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ASAP PLEASE HELPPPPPPPPPPPPPPPPPP MEEEEEEEEEEEEEEE
Answer:
-2/5 is the answer
I hope this will help you
Answer:
-2/5
Step-by-step explanation:
Just add the top numerator together -4 + 2 = -2
I need help with this, I can’t figure out the answer…
Anyone good at Ks3 maths
Answer:
[tex]{ \tt{distance = speed \times time}} \\ { \tt{ = 56 \times 3 \frac{1}{2} }} \\ = { \tt{196 \: miles}}[/tex]
In a city of 26,000 population 5000 read English news paper, 12000 read Nepali La News paper and 1000 read both of these. What percent read neither English nor Ne newspaper.
Answer:
38.46%
Step-by-step explanation:
We are given;
Total population; n(S) = 26000
Number that read English news paper; n(E) = 5000
Number of people that read nepali; n(N) = 12000
Number that read both English and nepali; n(E n N) = 1000
Thus from probability laws, number that read either English or nepali is;
n(E u N) = n(N) + n(E) - n(N n E)
n(E u N) = 12000 + 5000 - 1000 = 16000
Thus;
number that read neither English nor nepali is;
n(E' u N') = n(S) - n(E u N)
n(E' u N') = 26000 - 16000 = 10000
Thus, the percentage is;
10000/26000 × 100% = 38.46%
A ladder that is 10 feet long leaning against a wall perpendicular to the ground. The point at which the ladder touches the walk is 8 feet above the ground. How far away is the base of the ladder from the bottom of the wall ?
Answer:
6 feet
Step-by-step explanation:
Gonna use the Pythagorean Theorem: a² + b² = c²
a² + 8² = 10²
a² + 64 = 100
Subtract both sides by 64
a² + 64 = 100
-64 -64
a² = 36
Square root both sides
√a² = √36
a = 6 = length between bottom of the wall to the base of the ladder
I NEED HELP WITH THIS PLEASE!!!!!
Answer:
nt ooooo
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Step-by-step explanation:
the longest side of a triangle is 80cm more than the second and 130cm more than the shortest side and its perimeter is 540cm. find its area
help help
Answer:
Area of triangle1/2b*h Now you can do
The area of the triangle is 9000 square centimeters
How to determine the area?Let the sides in order of length be represented as:
x, y and z.
So, we have:
z = 80 + y
z = 130 + x
P = 540
The perimeter is calculated as:
P = x + y + z
So, we have:
x + y + z =540
Substitute z = 130 + x
x + y + 130 + x =540
Evaluate the like terms
2x + y = 410
Substitute z = 130 + x in z = 80 + y
130 + x = 80 + y
Evaluate the like terms
x - y = -50
So, we have:
2x + y = 410
x - y = -50
Add both equations
3x = 360
Divide by 3
x = 120
Substitute x = 120 in z = 130 + x
z = 130 + 120
z = 250
Substitute z = 250 in z = 80 + y
250 = 80 + y
y = 170
So, we have:
x = 120
y = 170
z = 250
The area is then calculated as:
[tex]Area = \sqrt{s * (s -x) *(s - y) * (s -z)[/tex]
Where
s = P/2 = 540/2
s = 270
So, we have:
[tex]Area = \sqrt{270 * (270 -120) *(270 - 170) * (270 -250)[/tex]
Evaluate
Area = 9000
Hence, the area of the triangle is 9000 square centimeters
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Which function is represented by the graph
Answer: A
Screenshot of calculator
Which situation does the graph illustrate?
Answer:
eju 48, 23w6yuw43wdgn
Step-by-step explanation:
It is a good idea to check your solutions when using the quadratic formula?
Answer: Since the square root of a negative number is not a real number, then a negative radical will result in no real solution.
Step-by-step explanation:
i know it’s kinda all hard to see. i have many more questions like this and i can’t do graphs to save my life.. pls help !!
Answer: D
Step-by-step explanation:
Brooke and Lamont ran a half marathon Brooke finished in 1 hour 50 minutes Lamont finished in 100 minutes who had the faster time
Answer:
Brooke = 1 hr 50 min
Lamont = 100 min = 1 hr 40 min
Because 60 min = 1 hr
Lamont was faster
Hope this helped
An animal shelter takes in an average of 5 animals per day. The shelter must keep its total occupancy below 300. Currently, the shelter has 165 animals. If none of the animals get adopted, which inequality represents how many more days, x, the shelter can continue to take in animals without exceeding its occupancy limit?
Answer:
5x less than 300 - 165
Step-by-step explanation:
It will take 27 days to take in animals without exceeding its occupy limit.
What is algebraic expression ?An expression which is made up of variables and constants , along with algebraic operation (addition , subtraction etc ) is called Algebraic expression.
According to the question :
165 + (x) 5 = 300
5x = 135
x = 27
Hence , it will take 27 days to occupy the limit
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One of the legs of a right triangle measures 9 cm and its hypotenuse measures 16 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
13.2 cm
Step-by-step explanation:
using the Pythagorean theorem, we can find the length of the other leg, since this is a right triangle. The equation is a^2 + b^2 = c^2, A and B being the legs and C being the hypotenuse. Since we are finding the other leg, we can switch the equation around to find A/B instead. (A/B being the legs). so we get: B^2 = C^2 - A^2 ; then we simplify [tex]b=\sqrt{c^2-a^2}[/tex]
We plug in the numbers given:
[tex]b = \sqrt{16^2-9^2}\\b=\sqrt{256-81}\\b=\sqrt{175} \\b= 13.229[/tex]
rounded to nearest tenth: 13.2
The measure of the other leg in the right triangle is 13.22 cm.
What is a right triangle?A triangle with one angle measuring 90° is called a right triangle.
Given that, a right triangle has a leg measuring 9 cm and its hypotenuse is 16 cm longs, we need to find the other side,
So, using the Pythagoras theorem,
16² = 9² + x²
x = √256-81
x = √175
x = 13.22
Hence, the measure of the other leg in the right triangle is 13.22 cm.
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Help Please!!!
Find the volume of the sphere
Answer:
523.6
Step-by-step explanation:
Not sure how to explain •-•
Hope it helps c:
Answer: use formula pi r^3
3.14 × 5 x 5 x 5 x 4 ÷ 3
Step-by-step explanation:
Which statement is not correct?
options b is not correct
Answer:
B is right option
Step-by-step explanation
A reflex angle is an angle that measures greater than 180 degrees and less than 360 degrees.
Find the value of x rounded to the nearest tenth.
Answer:
The answer to the equation is C
Solve the equation 2sin x cos x = cos x, for 0° < x≤ 90°
Answer:
2sinx.Cosx=cosx
2sin90°.cos90°=cos90°
2×1.0=0
0=0
Please help right now (30 points if you’re interested) The table shows the ratio between the number of books ordered and their cost. 7,14 8,16 9,18. Find equivalent ratios when the number of books ordered is 1,2, and 3. Write them as ordered pairs in the form (x-coordinate, y-coordinate). Starting from the origin explain how to plot three equivalent ratios on a coordinate grid.
The equivalent ratios are: (1, 2), (2, 4), and (3, 6)
The graph can be plotted on a coordinate grid as shown in the diagram attached below.
Recall:
Ratio between two quantities, x and y, can be represented by the equation, y = kx, where k is the constant of proportionality.k = y/xLet x = number of books
y = cost (dollars)
Using any of the ordered pairs from the table, say, (7, 14), find k:
k = y/x = 14/7 = 2
Write the equation by plugging in the value of k into y = kx
y = 2x
Using the equation, y = 2x, find the equivalent ratios when x = 1, x = 2, and x = 3:
When x = 1:
y = 2(1) = 2 --> (1, 2)
When x = 2:
y = 2(2) = 4 ---> (2, 4)
When x = 3:
y = 2(3) = 6 ---> (3, 6)
The graph for the three equivalent ratios, (1, 2), (2, 4), and (3, 6) can be plotted on a coordinate grid as shown in the diagram attached below.
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Tonya and Leo each bought a cell phone at the same time. The trade-in values, in dollars, of the cell phones are modeled by the given functions, where x is the number of months that each person has owned the phone. Tonya's Phone Leo's Phone f(x) =490(0.88)x x g(x) 0 480 2 360 4 270 phone has the greater initial trade-in value. During the first four months, the trade-in value of Tonya's phone decreases at an average rate the trade-in value of Leo's phone.
Answer:
The answer is Tonya's phone had the greater initial trade-in value.
Leo's phone decreases at an average rate slower than the trade in value of Tonya's phone.
Step-by-step explanation:
Given
Tonya
[tex]f(x) = 490 * 0.88^x[/tex]
Leo
[tex]x \to g(x)[/tex]
[tex]0 \to 480[/tex]
[tex]2 \to 360[/tex]
[tex]4 \to 470[/tex]
Solving (a): The phone with greater initial value
The initial value is when x = 0. So, we have:
[tex]f(x) = 490 * 0.88^x[/tex]
[tex]f(0) = 490 * 0.88^0[/tex]
[tex]f(0) = 490 * 1[/tex]
[tex]f(0) = 490[/tex]
From Leo's table
[tex]g(0) = 480[/tex]
By comparison;
[tex]f(0) > g(0)[/tex]
i.e.
[tex]490 > 480[/tex]
So: Tonya's had the greater initial trade-in value
Solving (b): The phone with lesser rate
An exponential function is:
[tex]y = ab^x[/tex]
Where:
[tex]b \to rate[/tex]
For Tonya
[tex]b = 0.88[/tex]
For Leo, we have:
[tex](x_1,y_1) = (0,480)[/tex]
[tex](x_2,y_2) = (2,360)[/tex]
So, the equation becomes:
[tex]y = ab^x[/tex]
[tex]480 = ab^0[/tex] and [tex]360 = ab^2[/tex]
Solving [tex]480 = ab^0[/tex], we have:
[tex]480 = a * 1[/tex]
[tex]480 = a[/tex]
[tex]a= 480[/tex]
[tex]360 = ab^2[/tex] becomes
[tex]360 = 480 * b^2[/tex]
Divide both sides by 480
[tex]0.75 = b^2[/tex]
Take square roots
[tex]0.87 = b[/tex]
[tex]b=0.87[/tex] -- Leo's rate
By comparison; Leo's rate is slower i.e. 0.87 < 0.88