Consider the two points F(-9,0) and G(9,0) as the foci of an ellipse. The length of the major axis is 36. Give the equation of the ellipse.
Answers
well, one focus point at (9 , 0) and another at (-9 , 0) will mean the major axis runs over the x-axis, with a center at the origin, so the "c" distance will be 9 units, and since the major axis is 36 units, that means its "a" component or namely its half is half of 36 or 18 units, so
[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} a=18\\ h=0\\ k=0 \end{cases}\implies \cfrac{(x- 0)^2}{ 18^2}+\cfrac{(y- 0)^2}{ b^2}=1\qquad \textit{we also know that }C=9[/tex]
[tex]9=\sqrt{18^2 - b^2}\implies 9^2=18^2-b^2\implies 9^2+b^2=18^2\implies b^2=18^2-9^2 \\\\\\ b^2=243\hspace{5em}\cfrac{(x- 0)^2}{ 18^2}+\cfrac{(y- 0)^2}{ 243}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{324}+\cfrac{y^2}{243}=1 \end{array}}[/tex]
Check the picture below.
Related Questions
The note F# has a frequency of 1,480 hertz. The note B has a frequency of 988 hertz. Find the ratio of F# to B to two decimal places. Express the answer in integer-ratio form.
answer is a fraction.
Answers
The ratio of F# to B to two decimal places is 1.50:1.
What is ratio?A ratio is simply used to compare two things or numbers.
In this case, the note F# has a frequency of 1,480 hertz and the note B has a frequency of 988 hertz.
The ratio of F to B will be:
= 1480 / 988
= 1.50
The ratio is 1.50:1.
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Answer:
3/2
Step-by-step explanation:
A group of elementary school students designed a study to find a possible relationship between the number of students absent from school and the overall rate of flu infections in their town. Which of the following is a correct pairing of possible null and alternative hypotheses for this experiment?
Answers
The possible pair of null and alternative hypotheses for this experiment is "The null hypothesis is that the flu infection rate has no impact on the number of students absent from school.
The alternative hypothesis is that as the flu infection rate increases, the number of students absent from school also increases."
Hypotheses
Hypotheses refers the testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.
Given,
A group of elementary school students designed a study to find a possible relationship between the number of students absent from school and the overall rate of flu infections in their town.
Here we need to find the correct pairing of possible null and alternative hypotheses for this experiment.
Here the given situation is relationship between the number of students absent from school and the overall rate of flu infections in their town.
So, the null hypotheses of this relation is flu infection rate has no impact on the number of students absent from school
And the alternative hypotheses of the relation is defines that the flu infection rate increases, the number of students absent from school also increases.
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Answer:
Step-by-step explanation:
The null hypothesis is that the flu infection rate has no impact on the number of students absent from school.
The alternative hypothesis is that as the flu infection rate increases, the number of students absent from school also increases.
For each graph below, state whether it represents a function.
Answers
Answer:
graphs 2 and 4 are functions
Step-by-step explanation:
To know if a graph represents a function, draw multiple vertical (straight up and down) lines through the graph. If any of the vertical lines crosses the graph 2 or more times, it is NOT a function.
9.8 x 100 =
0.040 x 1,000 =
61 divide 10 =
8.909 x 100 =
Answers
Answer:
9.8 * 100 = 980
0.040 * 1000 = 40
61 / 10 = 6.1
8.909 * 100 = 890.9
Step-by-step explanation:
For d the question is asking after four months, the heat is turned off. The excess amount, electricity from the solar panels begins to build back up according to the function. E(d)=38d+500. How do you interpret the 38 in the 500 and this model, we’re doing our presents the number of days since the heat was turned off. How would I solve this?
Answers
From the equation E(d) = 38d + 500, The initial electricity is 500W and the build up is 38W per day
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
The standard equation of a straight line is:
y = mx + b
Where m is the rate of change and b is the y intercept
Let E represent the electricity from the solar panels after d days.
Since:
E(d) = 38d + 500
The y intercept is 500 and the slope is 38
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216. Разложите на множители, а затем вычислите значение выражения
a) a² + ab при а = 6,6, b = 3,4;
б) x2 - ху при х = 0,5, у = 2,5;
в) —5а² — 5ах при а = 4, x = -3
Answers
Answer:
Doesn't make a lot of sense. Can you be more specific.
Step-by-step explanation:
216. Factor and then calculate the value of the expression
a) a² + ab with a = 6.6, b = 3.4;
b) x2 - xu at x = 0.5, y = 2.5;
c) —5a² — 5ah at a = 4, x = -3
Answers
Answer:
a) 66, b) - 1, c) - 20Step-by-step explanation:
Solve as below
a) a² + ab with a = 6.6, b = 3.4;
a² + ab = a(a + b) = 6.6(6.6 + 3.4) = 6.6(10) = 66b) x² - xu at x = 0.5, y = 2.5;
x² - xu = x(x - u) = 0.5(0.5 - 2.5) = 0.5(- 2) = - 1c) -5a² - 5ah at a = 4, h = -3;
-5a² - 5ah = - 5a(a + h) = - 5(4)(4 - 3) = - 20(1) = - 20Answer:
a) 66b) -1 c) -20Step-by-step explanation:
a) a² + ab = ?
→ (6.6)² + (6.6 × 3.4)
→ 43.56 + 22.44
→ 66
So, the answer is 66.
b) x² - xu = ?
→ (0.5)² - (0.5 × 2.5)
→ 0.25 - 1.25
→ -1
So, the answer is -1.
c) -5a² - 5ah = ?
→ -5(4)² - 5(4 × -3)
→ (-5 × 16) - (5 × -12)
→ -80 + 60
→ -20
So, the answer is -20.
The formula W=0.86g^2-0.01g+5.9 models the weight, W, in ounces, for a cat who is fed g grams per day of a special food. According to the formula, how much will a cat weigh when it is fed 13 grams of the special food per day? Round to the nearest hundredth.
Answers
Weight of cat when 13 grams food is fed is 151.11 ounces.
Explain equationEquations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. LHS = RHS (left hand side = right hand side) appears in all mathematical equations. You can solve equations to determine an unknown variable's value, which corresponds to an unknown quantity.
Given, the formula for weight,
W = 0.86[tex]g^{2}[/tex] - 0.01g + 5.9
= 0.86[tex](13^{2} )[/tex] - 0.01*13 + 5.9
= 0.86*169 - 0.13 + 5.9
= 145.34 - 0.13 + 5.9
= 151.11 ounces
Therefore, the weight of the cat will be 151.11 ounces.
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The following data represent the number of people aged 25 to 64 years covered by health insurance (private or government) in 2018. Approximate the mean and standard deviation for age.
Age: 25-34 35-44 45-54 55-64
Number: 24.3 36.1 36.7 20.9
(Millions)
The mean age is:
The standard deviation is:
Answers
The mean age is equal to: 44.09.
The standard deviation is equal to: 10.07.
How to determine the mean age and standard deviation?First of all, we would determine the median of each class interval as follows:
Median 1 = (25 + 34)/2 = 29.5
Median 2 = (35 + 44)/2 = 39.5
Median 1 = (45 + 54)/2 = 49.5
Median 1 = (55 + 64)/2 = 59.5
Next, we would calculate the mean age by using this mathematical expression:
Mean age = ∑fx/∑f
Substituting the given parameters into the formula, we have;
Mean age = [(24.3 × 29.5) + (36.1 × 39.5) + (36.7 × 49.5) + (20.9 × 59.5)]/(24.3 + 36.1 + 36.7 + 20.9)
Mean age = [716.85 + 1,425.95 + 1,816.65 + 1,243.55]/118
Mean age = [5,203]/118
Mean age = 44.09.
Now, we can calculate the standard deviation as follows:
Standard deviation, S = √((∑f(xi - μ)²/∑f)
Standard deviation, S = √((24.3 × (29.5 - 44.09)² + (36.1 × (39.5 - 44.09)² + (36.7 × (49.5 - 44.09)² + (20.9 × (59.5 - 44.09)²)/(24.3 + 36.1 + 36.7 + 20.9))
Standard deviation, S = √((5172.70 + 760.56 + 1,074.14 + 4,963.08)/118)
Standard deviation, S = √(11,970.48/118)
Standard deviation, S = √101.5
Standard deviation, S = 10.07.
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The resistance of a thermistor, a device used to monitor the temperature inside an engine, changes with temperature. The resistance of the thermistor is given by R(t) = t3 + 5, where R is measured in ohms and t is the temperature in °C. What is the average rate of change of resistance per degree of temperature change between 0°C and 2°C?
A.
4 ohms/°C
B.
8.5 ohms/°C
C.
11 ohms/°C
D.
17 ohms/°C
Answer: In photo below
You're Welcome :)
Answers
The average rate of change of the resistance of the thermistor for each degree change in the temperature, when the temperatures changes from 0 °C and 2 °C is A. 4 ohms/°C
What is the average of a set of values?The average is calculated by adding the values in the dataset then dividing the result by the count of the numbers or values in the set. The average is also known as the arithmetic mean.
The function for finding the resistance of the thermistor is; R(t) = t³ + 5
The unit of the R = Ohms
The unit of t = Degrees Celsius, °C
The resistance of the thermistor when the temperature is t = 0 °C is found as follows;
R(0) = 0³ + 5 = 5
Therefore;
When the temperature is 0 °C the resistance of the thermistor is 5 Ohms
When the temperature is t = 2 °C, we have;
R(2) = 2³ + 5 = 13
The resistance of the thermistor at t = 2 °C is 13 Ohms
The average rate of change of a function, f(x), is found using the formula;
[tex]A(x) = \dfrac{f(x_2) - f(x_1) }{x_2-x_1}[/tex]
The average rate of change of the resistance per degree change in the temperature, between the temperature interval of 0 °C and 2 °C is therefore;
[tex]A(x) = \dfrac{R(2) - R(0)}{2 - 0}[/tex]
Which gives;
[tex]A(t) = \dfrac{13 -5}{2 - 0}= 4[/tex]
The average rate of change of the resistance of the thermistor between the temperatures of t = 0 °C and t = 2 °C is 4 Ohms/°C
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What is the equation of the line that passes through the point (-3,-8) and has a slope of 4?
Answers
Answer:
[tex]y-8=4(x+3)[/tex]
Step-by-step explanation:
The equation of the line passing through the point [tex](x_1, y_1)[/tex] and slope [tex]m[/tex] is [tex]y-y_1=m(x-x_1)[/tex].
f(x)=x^2-1, g(x)=x+2
Answers
The composite function ( f. g(x)) is x² + 4x + 3
What is a function?A function can be described mathematically as a rule, law or equation that explains, shows and elaborates the relationship between to variables.
The variables are known as;
The independent variableThe dependent variableFrom the information given, we have the functions as;
f(x)=x^2-1g(x)=x+2To determine the composite function ( f. g(x)), we have to substitute the value of g(x) as a function in the function f(x) as the variable 'x', we get;
( f. g(x)) = (x + 2)² - 1
Now, let's expand the square
( f. g(x)) = (x + 2) ( x+ 2) - 1
Expand the bracket
( f. g(x)) = x² + 2x + 2x + 4 - 1
Now, let's collect like terms, we get
( f. g(x)) = x² + 4x + 3
Thus, the function is x² + 4x + 3
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The complete question:
Find ( f. g(x)) if f(x)=x^2-1, g(x)=x+2
How many square inches are in a square mile?
Answers
Answer: 4.014e+9 square inches
24.) MULTIPLE FORMS Write the decimal 0.5 in two ways. One with a denominator of 10 and one
with a denominator of 100.
Answers
Answer:
A denominator of 10: 5/10
A denominator of 100: 50/100
00
Which could be the base shape of the cylinder?
Oline
O non-square rectangle
O circle
O square
Answers
Answer:
The answer is a D. a circle
The base shape of the cylinder can only be a circle.
What is Three dimensional shape?a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.
A cylinder is a three-dimensional shape that has two congruent parallel circular bases connected by a curved surface.
The shape of the base determines the shape of the cylinder. If the base is circular, then the cylinder is called a circular cylinder.
A non-square rectangle and a square are not circular, and thus cannot be the base shape of a cylinder.
Hence, the base shape of the cylinder can only be a circle.
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Some students were playing tag on a playground. The number of girls was less than twice the number of boys. If there were 7 girls, how many boys were playing tag? Write an equation and solve.
Answers
The number of boys were playing tag are 5.
What is equation?
Two expressions joined by an equal sign form a mathematical statement known as an equation. An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.
Given: Some students were playing tag on a playground. The number of girls was three less than twice the number of boys. If there were 7 girls.
Suppose the number of boys are x,
So, the number of girls are, 2x - 3.
There are 7 girls.
So, 2x - 3 = 7
2x = 10
x = 10/2
x = 5
Therefore, the number of boys were playing tag are 5.
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Eve and Patty swam fewer laps than Maureen. Patty swam more laps than Eve, and Maureen swam fewer laps than Raymond. Who swam the most laps?
Answers
Answer:
Raymond
Step-by-step explanation:
1 ) Eve and Patty swam fewer laps than Maureen so...
Eve and Patty < Maureen
2 ) Patty swam more laps than Eve...
Patty > Eve
3 ) Maureen swam fewer laps than Raymond...
Maureen < Raymond
4 ) We can eliminate Eve and Patty since they swam fewer laps than Maureen. The ones who are left are...
Maureen and Raymond
5 ) We know that Maureen swam fewer laps than Raymond so we can eliminate Maureen.
Raymond
6 ) This mean that the one who swam the most laps is...
Raymond
Hope this helps! :)
Use long division to divide.
(x5 + 2x12x² - 5x - 12) = (x² - 3)
Answers
The reminder of the equation using the long division method is 70X - 12.
long division method :
Four main steps to solving this problem:
Divide.Multiply.Subtract.Drop down the last digit.[tex]x^2 - 3$\overline{)x^5 + 24x^3- 5x - 12}$( x^3 + 25x\\\\[/tex]
x₅ + 3 x³
(-) (-)
25x³ - 5x - 12
25x³ - 75x
(-) (+)
70x - 12
here
divisor - (x² - 3)
dividend - (x⁵ + 2x12x² - 5x - 12)
quotient - (x³ +25x)
the given question is incomplete the correct question is
Use long division to divide.
(x⁵ + 2x12x² - 5x - 12) / (x² - 3)
The reminder of the equation using the long division method is 70X - 12.
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Graph the function rule. Tell whether the graph is continuous or discrete. The height h, in inches, of the juice in a 20-oz bottle depends on the amount of juice j, in ounces, that you drink. This situation is represented by the function rule h=8−0.4j.
Answers
Upon graphing of the function rule h = 8 - 0.4j, we see that the graph is continuous.
We are given the function as; h = 8 - 0.4j
Let h represent the height in inches on the y-axis and let j represent the amount of juice in ounces on the x-axis.
We are told that the height of the juice in a 20-oz bottle depends on the amount of juice. This means that j is an independent variable and h is dependent variable.
The function represents the height of juice after drinking j ounces of juice. Therefore as the juice is being drank, the height of the juice in bottle will change continuously. Therefore, the graph of our given function will be continuous because we can drink fractions of an ounce juice.
The equation of a line in slope-intercept form is given as;
y = mx + b
where;
m is Slope of line
b is y-intercept
If we rewrite our function slope-intercept form of equation, we will get;
h = -0.4j + 8
Thus;
Slope = -0.3
y-intercept = 8.
The graph is as plotted in the attached file
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Devontae claimed that the line y=-3/4x forms an angle of about 53.13° with the positive x-axis. Which statement proves his claim correct or incorrect?
a) Correct because arctan(4/-3) = -53.13
b) Correct because arccos(-3/4) = 53.13
c) Incorrect because arctan(-3/4) = -36.87
d) Incorrect because arccos(-3/4) = -138.59
Answers
The statement that proves the claim about the angle is incorrect is that;
c) Incorrect because arctan(-3/4) = -36.87
How to solve Trigonometric Ratios?The 6 main trigonometric ratios of a right angle triangle are;
Sine θ = length of the opposite leg / length of the hypotenuse
Cosine θ = length of the adjacent leg / length of the hypotenuse
Tangent θ = sine θ/cosine θ = opposite leg / adjacent leg.
cosecant θ = 1 / sine θ = hypotenuse / opposite leg
secant θ = 1 / cosine θ = hypotenuse / adjacent leg
cotangent θ= 1 tangent θ = adjacent leg / opposite leg.
Now, we are told that the angle formed is 53.13°. Since the options are either arctan or arccos, we will use them to verify the angles;
cos 53.13° = 0.6
tan 53.13° = 1.33
They are both positive and it means both x and y values are positive since we are told that it involves the positive x-axis.
Thus, y/x cannot be negative or -3/4 as given.
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You roll a fair six-sided die twice. Find the probability of rolling a 3 the first time and a number greater than 4 the second time.
Answers
The probability of rolling a 3 first time and a number greater than 4 thre second time is 1/18
What is probability?Probability is the likelihood that an event will happen. This can range from an event being impossible to some likelihood to being absolutely certain. In math terms, probability is on a scale from 0 to 1. Zero means the event is impossible, like rolling a seven on a die that only has digits from 1 to 6. One is an event that will happen, it is certain. An example of a certain event is tomorrow being Friday if today is Thursday. This is definitely going to happen.
The possible outcomes of a fair die are : 1, 2, 3, 4, 5, 6. which is 6 in all
the required outcome for obtaining a 3 = 3 which is 1 outcome
the required outcome for obtaining a number greater than 4 : 5, 6. which is 2 outcomes.
probability of getting 3 first time = 1/6
probability of getting a number greater than 4 = 2/6 ( lowest term = 1/3)
Probability of rolling a 3 first time and a number greater than 4 second time is = 1/6 x 1/3 = 1/18
In conclusion, probability of obtaining a 3 and a number greater than 4 is 1/18.
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math, pls help, will mark brainlest
Answers
Answer:
Step-by-step explanation:
3x + 3x equals 11x
lamp post tilts
toward the Sun at a 2° angle from
the vertical and casts a 25-foot shadow.
The angle from the tip of the shadow
to the top of the lamp post is 45°.
Find the length of the lamp post.
Answers
Answer:
the lamp of post is 24 of the same
The velocity function of a car is given by v(t) = -3t^2 + 18t + 9 m/s. Find the acceleration of the car three seconds before it comes to a stop. A. a = -6.46 m/s² B. a = -2.76 m/s² C. a = -0.46 m/s² D. a = 2.76 m/s²
Answers
The acceleration when the car comes to a full stop is 20.76 meters per square second.
How to find the acceleration?Here we have the velocity function:
v(t) = -3t^2 + 18t + 9
To find the acceleration we need to differentiate with respect to the variable t, so we will get the acceleration:
a(t) = 2*(-3)*t + 1*18
a(t) = - 6*t + 18
Now, the car will come to a stop when the velocity is equal to zero, so we need to solve:
-3t^2 + 18t + 9 = 0
Dividing all by -3 we get:
(-3t^2 + 18t + 9)/-3 = 0
t^2 - 6t - 3 = 0
The solutions are:
[tex]t = \frac{6 \pm \sqrt{(-6)^2 - 4*1*-3} }{2*1} \\\\t = \frac{6 \pm 6.92}{2}[/tex]
We only care for the positive solution:
t = (6 + 6.92)/2 = 6.46
The acceleration at that time is:
a(6.46) = - 6*6.46 + 18 = -20.76
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Samantha owes $25.50 and borrows another $20.00. She pays back $15.25 of her debt and then earns $45.00. Later, Samantha pays back $22.50 of her debt.
How much debt does she still have to pay back? Show your work.
Answers
6) Tomás está haciendo compras en el supermercado. Primero eligió
una bandeja con naranjas cuya etiqueta dice 1.350 g. ¿Cuántos
gramos más debe comprar si quiere llegar a 5 kg?
Answers
With the help of unitary method it can be found out that Tomás has to buy more 3650 grams of oranges if he wants to reach 5 kg.
It is given to us that -
Tomás first chose a tray with oranges whose label says 1,350 gram
We have to find out more grams of oranges that he should buy if he wants to reach 5 kilogram.
We know that
1 kilogram = 1000 grams
=> 1000 grams = 1 kilogram ----- (1)
By unitary method, we can find out the number of kilograms equivalent to 1350 grams of oranges.
From equation (1), we have
1000 grams = 1 kilogram
=> 1350 grams = (1/1000) * 1350
=> 1350 grams = 1.35 kilograms ----- (2)
Now, from equation (2), we can see that Tomás first chose 1,350 grams of oranges which is equal to 1.35 kilograms of oranges.
This implies that the more kilograms of oranges that Tomás has to buy to reach 5 kilograms is given by -
(5 - 1.35) kilograms
= 3.65 kilograms
From equation (1), we have
1 kilogram = 1000 grams
=> 3.65 kilograms = 3.65 * 1000 grams
=> 3.65 kilograms = 3650 grams.
Thus, by solving through unitary method we find out that Tomás has to buy more 3650 grams of oranges if he wants to reach 5 kg.
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Given m || n
find the value of x and y.
(6x+19)° (2y+1)⁰
(3x+8)°
m
n
Answers
A value for x is therefore represented by the first number in an ordered pair, and a value for y is represented by the second.The x- and y-coordinates are the names given to these values.
Find the value of x and y ?The Method of Elimination
To ensure that the two equations have the same leading coefficient, multiply each equation by a reasonable number in step one.
Step 2: Reverse the first equation and subtract the second one.
Step 3: Find y using this new equation.
Step 4: Change Equation 1 or Equation 2 above to y = 2 and then solve for x.
multiply the equation y = x - 6 by -6.
You will then get the equation: 6y = -6x + 36
The two equations will be:
6y = -6x + 36
y = 6x - 19
And you can see that if you add them, you will be able to eliminate x. answer is -6.
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Question 3 of 10
The blue segment below is a diameter of 0. What is the length of the radius
of the circle?
7.7
0
A. 15.4 units
B. 3.85 units
C. 11.55 units
D. 7.7 units
Answers
Answer:
I think B. 3.85 units
Step-by-step explanation:
A dairy farmer wants to mix a 45% protein supplement and a standard 20% protein ration to make 2000 pounds of a high-grade 35% protein ration. How many pounds of each should he use?
Answers
The farmer should use 1200 pounds of type 1 mixture and 800 pounds of type 2 mixture to satisfy the given conditions
From given information,
Type 1: 45 percent of protein in the supplement is x pounds
Type 2: 20 percent of the protein in the supplement is (2000 - x) pounds
Also Mixture A 35% of the protein in the supplement is 2000 pounds
According to the equation after removing the percentage sign we have
45x + 20(2000-x)= 35*2000
45x + 40000 - 20x = 70000
25x = 30000
x = 1200
Now for type 2 mixture we have
2000 - 1200 = 800 pounds
Therefore, the farmer should use 1200 pounds of type 1 mixture and 800 pounds of type 2 mixture to satisfy the given conditions
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The price of a sweater was reduced from $30 to $18. By what percentage was the price of the sweater reduced?
i need help
Answers
Explanation: you divide 18 from 30