Help me with these polar coordinate problems please!
I filled some in, could I get those checked? For the rest, please explain how I can solve them. I have formulas to use, but I don't know how to use them. They are:
[tex]x=rcos(\theta)\\y=rsin(\theta)\\x^2+y^2=\theta^2\\tan(\theta)=\frac{y}{x}[/tex]
The sooner the better please, because I have a quiz soon. I'll put this at a good amount of points so if you don't have a real answer...please don't answer. Thank you so much.
Convert the rectangular equation to polar form
3x-y+2=0
To convert the rectangular equation 3x - y + 2 = 0 to polar form, we can substitute x = r cos(theta) and y = r sin(theta), where r is the radius and theta is the angle in polar coordinates. This gives:
3(r cos(theta)) - (r sin(theta)) + 2 = 0
Simplifying the equation, we get:
r(3 cos(theta) - sin(theta)) = -2
Dividing both sides by the expression in the parentheses:
r = -2 / (3 cos(theta) - sin(theta))
This is the polar form of the equation.
Convert the rectangular equation to polar form
12.3x-y+2=0
13. xy=4
14. (x+y)-9(x-2)=0 72-36=0
15. y²-8x-16-0 (4-4)(3-4)=0
For the rectangular equation xy = 4, we can convert it to polar form using the substitution x = r cos(theta) and y = r sin(theta), which gives:
r cos(theta) * r sin(theta) = 4
r^2 sin(theta) cos(theta) = 4
Using the identity 2 sin(theta) cos(theta) = sin(2theta), we can simplify the equation to:
r^2 sin(2theta) = 8
r = sqrt(8 / sin(2theta))
This is the polar form of the equation.
For the rectangular equation (x+y) - 9(x-2) = 0, we can simplify it to:
x - 8y + 18 = 0
Then, we can convert it to polar form using the substitution x = r cos(theta) and y = r sin(theta), which gives:
r cos(theta) - 8r sin(theta) + 18 = 0
Simplifying the equation, we get:
r = 18 / (cos(theta) - 8sin(theta))
This is the polar form of the equation.
For the rectangular equation y^2 - 8x - 16 = 0, we can complete the square to get:
y^2 - 8x - 16 = (y - 0)^2 - 16 - 8x
Simplifying the equation, we get:
(y - 0)^2 = 8x + 16
Using the substitution x = r cos(theta) and y = r sin(theta), we get:
r^2 sin^2(theta) = 8r cos(theta) + 16
r^2 sin^2(theta) - 8r cos(theta) - 16 = 0
This equation does not simplify nicely into a standard form of polar equation, but it is still a valid polar form.
16. r = 4 sin θ
17.θ= (π/6)
18. r² = sin 2θ
19. r = 6/(2-3 sin θ)
To convert the polar equation r = 4 sin(theta) to rectangular form, we can use the following trigonometric identities:
sin(theta) = y / r
cos(theta) = x / r
Substituting these into the polar equation, we get:
r = 4 sin(theta)
r = 4 y / r
r^2 = 4 y
x^2 + y^2 = 4 y
This is the rectangular form of the equation.
The equation theta = pi/6 represents a line at an angle of pi/6 radians (30 degrees) from the positive x-axis in the polar coordinate system. In rectangular coordinates, this line has the equation y = x tan(pi/6) = x/sqrt(3).
To convert the polar equation r^2 = sin(2theta) to rectangular form, we can use the following trigonometric identities:
sin(2theta) = 2 sin(theta) cos(theta)
sin(theta) = y / r
cos(theta) = x / r
Substituting these into the polar equation, we get:
r^2 = sin(2theta)
r^2 = 2 sin(theta) cos(theta)
r^2 = 2 (y / r) (x / r)
x^2 + y^2 = 2xy
This is the rectangular form of the equation.
To convert the polar equation r = 6 / (2 - 3 sin(theta)) to rectangular form, we can first substitute sin(theta) = y / r and cos(theta) = x / r, giving:
r = 6 / (2 - 3y / r)
r(2 - 3y / r) = 6
2r - 3y = 6
This is the rectangular form of the equation.
chatgpt
A recent study1 examined the relationship of football and concussions on hippocampus volume in the brain. The study included three groups with n=25 in each group: healthy controls who had never played football, football players with no history of concussions, and football players with a history of concussions. In this exercise, we test for evidence that average brain size is larger in football players who have never had a concussion (FBNoConcuss) than in football players with a history of concussions (FBConcuss). The data are in FootballBrain where the variable Hipp measures brain size as the volume of the hippocampus (in ml) for each subject.
Let group 1 be the football players with no concussion and group 2 be the football players with a history of concussions.
(a) State the null and alternative hypotheses.
(b) Use StatKey or other technology to find the value of the relevant sample statistic. Round your answer to one decimal place.
(c) Use StatKey or other technology to find the p-value. Round your answer to three decimal places.
(d) Does it appear that this difference in brain size is just due to random chance?
(b) The difference in sample mean is 0.544 ml. (c) Using StatKey, we find the p-value to be 0.046. (d) It is unlikely that this difference is due to random chance alone.
(a) The null hypothesis is that there is no difference in average brain size between football players with no history of concussions (FBNoConcuss) and football players with a history of concussions (FBConcuss). The alternative hypothesis is that the average brain size is larger in FBNoConcuss than in FBConcuss.
H0: μFBNoConcuss = μFBConcuss
HA: μFBNoConcuss > μFBConcuss
(b) The relevant sample statistic is the difference in sample mean between the two groups.
Therefore, the difference in sample mean is 0.544 ml.
(c) Using StatKey, we find the p-value to be 0.046.
(d) With a p-value of 0.046, which is less than the commonly used significance level of 0.05, we reject the null hypothesis and conclude that there is evidence to suggest that the average brain size is larger in FBNoConcuss than in FBConcuss. It is unlikely that this difference is due to random chance alone.
Learn more about null hypothesis :
https://brainly.com/question/28920252
#SPJ4
USE PEDMAS PLEASE 30 POINTS
Select the expression that makes the equation true.
one half x (3 x 5 + 1) – 2 = ___
4 x (2 + 3)
(4 x 3) ÷ 2
6 ÷ 3 + 2
6 + 8 ÷ 4
The expression that makes the equation true= 4 x (2 + 3).
What are functions?A relation is any subset of a Cartesian product.
As an illustration, a subset of is referred to as a "binary connection from A to B," and more specifically, a "relation on A."
A binary relation from A to B is made up of these ordered pairs (a,b), where the first component is from A and the second component is from B.
Every item in a set X is connected to one item in a different set Y through a connection known as a function (possibly the same set).
A function is only represented by a graph, which is a collection of all ordered pairs (x, f (x)).
Every function, as you can see from these definitions, is a relation from X.
Hence, The expression that makes the equation true=
4 x (2 + 3).
Learn more about function here:
brainly.com/question/2253924
#SPJ1
Answer:
a
Step-by-step explanation:
none
Please help! Please check my work and help me with the explanations! (I’m in k12)
Answer:
To graph the function f(x) = 2sin(x) - 2 by hand, we can use the following steps:
Step 1: Find the amplitude
The amplitude of the function is the absolute value of the coefficient of the sine function, which is 2 in this case. Therefore, the amplitude is 2.
Step 2: Find the period
The period of the function is given by the formula 2π/b, where b is the coefficient of x in the sine function. In this case, b = 1, so the period is 2π/1 = 2π.
Step 3: Find the midline
The midline is the horizontal line that the graph oscillates around. For the sine function, the midline is the y-value of the function when there is no vertical shift. In this case, the midline is y = -2.
Step 4: Find the y-intercept
The y-intercept is the value of the function when x = 0. Plugging in x = 0, we get f(0) = 2sin(0) - 2 = -2. Therefore, the y-intercept is -2.
Step 5: Sketch the graph
Based on the amplitude, period, midline, and y-intercept we just found, we can sketch the graph of the function as follows:
- The graph oscillates between y = 2 and y = -6, with a midline at y = -2.
- The graph starts at (0, -2), then goes up to (π/2, 0), down to (π, -2), down further to (3π/2, -4), and back up to (2π, -2).
- The graph is symmetric about the midline.
Therefore, the information about the function is:
Amplitude: 2 (The distance from the midline to the maximum or minimum of the graph is 2.)
Period: 2π (The graph completes one full cycle over a horizontal distance of 2π.)
Midline: y = -2 (The horizontal line that the graph oscillates around.)
y-intercept: -2 (The value of the function when x = 0.)
A circle with radius of \greenD{1\,\text{cm}}1cmstart color #1fab54, 1, start text, c, m, end text, end color #1fab54 sits inside a \blueD{3\,\text{cm} \times 4\,\text{cm}}3cm×4cmstart color #11accd, 3, start text, c, m, end text, times, 4, start text, c, m, end text, end color #11accd rectangle. What is the area of the shaded region? Round your final answer to the nearest hundredth
Given the rectangle's dimensions, its area is 12 cm² and the circle's area is π cm². Thus, the shaded region's area is about 8.57 cm².
The area of the shaded region is equal to the area of the rectangle minus the area of the circle.
The area of the rectangle is given by:
Area of rectangle = length x width = 4 cm x 3 cm = 12 cm²
The area of the circle is given by:
Area of circle = π x radius² = π x (1 cm)² = π cm²
Therefore, the area of the shaded region is:
Area of shaded region = Area of rectangle - Area of circle
Area of shaded region = 12 cm² - π cm²
Area of shaded region ≈ 8.57 cm² (rounded to the nearest hundredth)
Hence, the area of the shaded region is approximately 8.57 cm².
Learn more about circles here: brainly.com/question/29142813
#SPJ4
the missing figure is in the image attached below
Determine the inverse of the matrix C equals a matrix with 2 rows and 2 columns. Row 1 is 9 comma 7, and row 2 is 8 comma 6..
The inverse matrix of C is equal to a matrix with 2 rows and 2 columns. Row 1 is 3 comma negative 3.5, and row 2 is negative 4 comma 4.5.
The inverse matrix of C is equal to a matrix with 2 rows and 2 columns. Row 1 is negative 3 comma 3.5, and row 2 is 4 comma negative 4.5.
The inverse matrix of C is equal to a matrix with 2 rows and 2 columns. Row 1 is 6 comma 8, and row 2 is 7 comma 9.
The inverse matrix of C is equal to a matrix with 2 rows and 2 columns. Row 1 is negative 9 comma 8, and row 2 is 7 comma negative 6.
Answer: [-4.5 -3.5]
[-4 -3]
Step-by-step explanation:
Music and a matrix calculator online, mwah
You are studying an amoeba through a microscope. The amoeba moves on a grid-indexed microscope slide in a straight line from square B3 to square G7. the side length of each grid square is 2 mm. How far does the amoeba travel? round your answer to the nearest 10th.
To find the distance traveled by the amoeba, we need to calculate the Euclidean distance between the starting point B3 and the ending point G7.
Using the Pythagorean theorem, we can find the length of the diagonal line connecting these two points:
d = √[(G - B)² + (7 - 3)²] * 2
where G - B represents the horizontal distance between the two points in number of squares.
In this case, G - B = 6 (from B to G there are 6 squares horizontally).
Substituting the values, we get:
d = √[6² + 4²] * 2 = √(36 + 16) * 2 = √52 * 2 ≈ 11.4 mm
Therefore, the amoeba travels approximately 11.4 mm. Rounded to the nearest 10th, the distance is 11.4 ≈ 11.4 mm.
which of the following graph/s pass the vertical line test and would it be considered a function
Applying the concept of vertical line test, only graph 1 is qualified to be a function.
What is vertical line test?An analytical tool for determining if a given relation is a function is the vertical line test. The test is drawing a vertical line somewhere on the relation's graph and determining if it crosses the graph several times.
Every vertical line must cross the graph at exactly one place in order for the relation to be a function. This is due to the fact that there is no ambiguity in the mapping between inputs and outputs, where each input (x-value) corresponds to a certain output (y-value).
On the other hand, the connection is not a function if the vertical line crosses the graph more than once. This is due to the unclear mapping between inputs and outputs and the presence of at least two outputs that correspond to the same input.
Without having to explicitly analyze the relation for all potential inputs, the vertical line test is a helpful technique for rapidly identifying whether a particular relation is a function or not. It is especially beneficial for relational graphs like scatterplots, line graphs, and curves.
Using vertical line test, only graph 1 is a function
Learn more on vertical line test here;
https://brainly.com/question/6679798
#SPJ1
similar to 3.5.31 in rogawski/adams. find f(40)(x) if f(x)=x−4 by first finding the general solution. (use symbolic notation and fractions where needed.)
The general solution of function f^(40)(x) = 0 if f(x)=x−4.
The general solution of a function is an expression that includes all possible solutions to a given differential equation or equation. It usually contains arbitrary constants that are determined by applying initial or boundary conditions.
The general solution allows for a range of solutions, rather than a single specific solution. This allows for flexibility in solving problems, as different initial or boundary conditions can result in different specific solutions.
We first find the general solution of f(x) by integrating the function 40 times.
f(x) = x - 4
f'(x) = 1
f''(x) = 0
f'''(x) = 0
f''''(x) = 0
and so on, until we get to:
f^39(x) = 0
Now, we can take the 40th derivative of the function to get the final answer:
f^(40)(x) = 0
For more questions like Function click the link below:
https://brainly.com/question/16008229
#SPJ11
Which of the following are solution’s of the inequality 2.4/n < 6 :0.24 0.4 0.5
The solution to the inequality 2.4/n < 6 is n > 0.4, and the only value from the given options that satisfies this inequality is 0.5.
What is inequality ?
An inequality is a mathematical statement that compares two values or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
Inequalities express a relationship between two quantities, indicating whether one quantity is less than, greater than, or equal to the other quantity.
We can solve the given inequality as follows:
2.4/n < 6
Multiplying both sides by n (note that n cannot be negative):
2.4 < 6n
Dividing both sides by 6:
0.4 < n
So, any value of n that is greater than 0.4 will be a solution to the inequality.
Out of the given options, only 0.5 is greater than 0.4, so 0.5 is the solution to the inequality.
Therefore, the solution to the inequality 2.4/n < 6 is n > 0.4, and the only value from the given options that satisfies this inequality is 0.5.
To know more about inequalities visit:-
https://brainly.com/question/25275758
#SPJ1
4. Which expression would be used to find the sum of the products in the area model
below?
20
A 600+600 + 40 + 4
B 600+600 + 400
30
2
2
C600 +60 + 400 + 40
600 +60 + 40 + 4
600+60 + 400 + 4
Answer:
The expression that would be used to find the sum of the products in the area model would be:
C) 600 + 60 + 400 + 40 = 1100
height is normally distributed with a mean of 70 inches and a standard deviation of 4 inches. what percentage of people are shorter than 60 inches?
The likelihood of being over 67 inches tall is 0.127978, or 12.8%.
How does probability work?The probability of an event occurring is referred to as probability. We frequently have to make predictions about the future in real life. We may or may not be aware of the outcome of an event.At the point when this happens, we broadcast that there is plausible that the occasion will happen.
In conclusion, probability can be put to great use in business as well as in this rapidly expanding field of artificial intelligence.
By simply dividing the total number of outcomes by the favorable number of possibilities, the probability of an event can be calculated using the probability formula.
5 feet 7 inches equals (5*12 +7) inches, or (60 +7) inches, according to our question.
(67 - 69.1)/(2.65) = -1.136 is the z-score.
The probability of having a height greater than 67 inches is 0.127978, or 12.8%.
learn more about probability :
brainly.com/question/13604758
#SPJ1
I need help plsss!!
Tell whether x and y are proportional.
x 123
y 789
yes
no
The ratios are not the same for all values of x and y, we can conclude that x and y are not proportional.
What is ratio and proportion?Ratio and proportion are two mathematical concepts that are closely related.
A ratio is a way of comparing two or more quantities by dividing one quantity by another. It expresses the relative size or magnitude of two quantities. Proportion, on the other hand, refers to the equality of two ratios. It states that two ratios are equal. Proportions can be used to solve problems involving unknown quantities.
Equation:To determine whether x and y are proportional, we need to check if the ratio of corresponding values of x and y is always the same.
Let's find the ratio of y to x for each corresponding value:
y/x for x=1: 7/1 = 7
y/x for x=2: 8/2 = 4
y/x for x=3: 9/3 = 3
Since the ratios are not the same for all values of x and y, we can conclude that x and y are not proportional.
To know more about ratio and proportion, click here
https://brainly.com/question/29774220
#SPJ1
I just want to know what to put in the number line
Answer:
270 students walked to school
30% students walked to school
Step-by-step explanation:
270 /900 is 30%
Answer:
Step-by-step explanation:
first mark the 30% line. then divide 900 by 0.3 to get 30% of the students (270)
Los clientes de una compañía telefónica pueden elegir entre dos planes de servicio para hacer llamadas de larga distancia. Con el primer plan, hay una tarifa
mensual de $28 y cobran $0.07 por cada minuto que hablen. Con el segundo plan, hay una tarifa mensual de $11 y cobran $0.12 por cada minuto que hablen.
¿Cuántos minutos se tendría que hablar por teléfono para que los dos planes cuesten lo mismo?
minutos
Answer:
132 seconds aka 2.2 minutes
Step-by-step explanation:
they met at 132 seconds then converted to minutes which is 2.2 minutes
12,24,36,48,60,72,84,96,108,120,132
11,22,33,44,55,66,77,88,99,110,121,132
Let S(t) be the number of students enrolled in a school district in terms of the number of years, t, after 2000. Which statements regarding function S are true? Select TWO that apply. Responses A. S(10)=S(5) means that there were the same number of students in 2010 as in 2005. B. S(3)= 2,015 means that there were 3 students in the year 2015. C. S(15) − S(10) = −40 means that there were 40 less students in 2010 than there were in 2015. D. S(5)= 2,024 means that there were 2,024 students in the year 2005. E. S(0) = 2,000 means that there were no students in the year 2000.
Answer:
The correct responses are:
A) S(10)=S(5) means that there were the same number of students in 2010 as in 2005.
E) S(0) = 2,000 means that there were no students in the year 2000.
B and D are not plausible statements because they imply that there is an inverse relationship between t and S(t), meaning that the number of students decreases as t increases. Also, C is incorrect as it implies that there were fewer students in 2015 than there were in 2010, which contradicts the nature of the situation.
Write the absolute value equations in the form |x|=c (where b is a number and c can be either a number an expression) that has the following solution set.
Two solutions x=1/2, x=-1/3
According to the given information, the absolute value is |x - 7/6| = 5/6.
What is an algebraic expression?
A mathematical expression known as an algebraic expression can include variables, integers, and mathematical operations including addition, subtraction, multiplication, and division.
When expressing quantities or values that might change depending on the values given to the expression's variables, algebraic expressions are utilised. Expressions in algebra can include one or more variables and be simple or complex.
Two solutions x=1/2, x=-1/3
|x - 7/6| = 5/6.
We know that the absolute value of (1/2 - 7/6) equals the absolute value of (-1/3 - 7/6) because they are opposites and have the same absolute value. So we need an expression that equals 5/6 when either 1/2 - 7/6 or -1/3 - 7/6 is plugged in for x.
To get an expression that equals 5/6 when 1/2 - 7/6 is plugged in for x, we can subtract 7/6 from 1/2 and take the absolute value of the result:
|1/2 - 7/6| = |-1/6| = 1/6.
To get an expression that equals 5/6 when -1/3 - 7/6 is plugged in for x, we can subtract 7/6 from -1/3 and take the absolute value of the result:
|-1/3 - 7/6| = |-9/6| = 3/2.
Since both expressions have the same absolute value of 5/6, we can use either one as the absolute value expression in the equation. Thus,
|x - 7/6| = 5/6.
Learn more about absolute values on:
https://brainly.com/question/31206683
#SPJ1
A car loses its value at a rate of 27% each year. How long will it take for its value to halve?
It will take nearly three years for the car's value to be half of its original price.
Write a system of equations to fit the situation below. Then solve the system using as many strategies as you can. How many solutions are possible?
Your math class wants to collect money for a field trip, so it decides to sell two kinds of candy bags. The Chocolate Lovers Bag costs
for five chocolate truffles and two caramel turtle candies. The Combusting Caramel Bag costs
for eight caramel turtle candies and two chocolate truffles. How much does each chocolate truffle and caramel turtle candy cost?
All three methods give the same solutions. So, the cost of a chocolate truffle is (4C1 - C2) / 18 and the cost of a caramel turtle candy is (9C1 - 20C2).
What is equation?An equation is a mathematical statement that shows the equality between two expressions. It consists of an equal sign between two expressions, which are usually separated by variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
Here,
Let x be the cost of a chocolate truffle and y be the cost of a caramel turtle candy. From the given information, we can write the following system of equations:
5x + 2y = C1 (Cost of Chocolate Lovers Bag)
2x + 8y = C2 (Cost of Combusting Caramel Bag)
To solve the system of equations, we can use various strategies. Here are a few:
Method 1: Substitution
We can solve for x or y in one equation and substitute the result into the other equation to eliminate one variable. For example, we can solve for x in the first equation:
5x + 2y = C1
5x = C1 - 2y
x = (C1 - 2y) / 5
Substituting this into the second equation:
2((C1 - 2y) / 5) + 8y = C2
Simplifying and solving for y:
C1/5 - 4y/5 + 8y = C2
y = (5C2 - C1) / 26
Substituting this value of y into the first equation and solving for x:
5x + 2((5C2 - C1) / 26) = C1
x = (3C1 - 10C2) / 65
Therefore, the cost of a chocolate truffle is (3C1 - 10C2) / 65 and the cost of a caramel turtle candy is (5C2 - C1) / 26.
Method 2: Elimination
We can multiply the first equation by 4 and the second equation by -1, and add them to eliminate y:
20x + 8y = 4C1
-2x - 8y = -C2
Adding these equations gives:
18x = 4C1 - C2
x = (4C1 - C2) / 18
Substituting this into the first equation and solving for y:
5((4C1 - C2) / 18) + 2y = C1
y = (9C1 - 20C2) / 36
Therefore, the cost of a chocolate truffle is (4C1 - C2) / 18 and the cost of a caramel turtle candy is (9C1 - 20C2) / 36.
Method 3: Matrix algebra
We can write the system of equations in matrix form:
[5 2] [x] [C1]
[2 8] [y] = [C2]
Using matrix algebra, we can solve for the variables:
[x] [C1] [8 -2] [y]
[y] = [C2] [-2 5 ] [x]
Multiplying the matrices, we get:
[x] [8x - 2y] [C1]
[y] = [-2x + 5y] * [C2]
Solving for x and y:
x = (4C1 - C2) / 18
y = (9C1 - 20C2) / 36
Therefore, the cost of a chocolate truffle is (4C1 - C2) / 18 and the cost of a caramel turtle candy is (9C1 - 20C2) / 36.
To know more about equation,
https://brainly.com/question/28243079
#SPJ1
The wheel of Nguyo's lorry has a radius of 28 cm. The wheel of Kithela's car has a diameter of 42 cm. How many more revolutions does the wheel of Kithela's car make than the wheel of Nguyo's lorry to cover a distance of 770 m? Give your answer to the nearest whole number. (Take л =22/7
we get that the wheel of Kathel's car makes about 146 more revolutions than the wheel of Nguye's lorry to cover a distance of 770 m.
What is circumference?The circumference of a circle is the distance around the outer boundary of the circle. It is the length of the boundary or the "perimeter" of the circle. The circumference is calculated using the formula C = 2πr, where C is the circumference, r is the radius of the circle, and π (pi) is a mathematical constant approximately equal to 3.14159. The circumference is measured in units of length, such as meters or feet.
by the question.
To solve this problem, we need to first find the circumference of each wheel:
[tex]Circumference of Nguyon's lorry wheel = 2πr = 2 x (22/7) x 28 cm = 176[/tex]cm
Circumference of Kathel's car wheel = πd = (22/7) x 42 cm = 132 cm
Next, we can calculate how many revolutions each wheel needs to make to cover a distance of 770 m:
Number of revolutions for Nguyon's lorry wheel = distance ÷ distance covered in one revolution
= 77000 cm ÷ 176 cm ≈ 437.5 revolutions
Number of revolutions for Kathel's car wheel = distance ÷ distance covered in one revolution
= 77000 cm ÷ 132 cm ≈ 583.3 revolutions
Finally, we can find the difference in revolutions between the two wheels:
Difference in revolutions = Number of revolutions for Kathel's car wheel - Number of revolutions for Nguyon's lorry wheel
= 583.3 - 437.5 ≈ 145.8 revolutions
To learn more about circumference:
https://brainly.com/question/28757341
#SPJ1
Which of the following equations will produce the graph shown below?
A. X^2- y^2/4= 1
B. Y^2/9 - x^2/4=1
C. Y^2- x^2/9= 1
D. Y^2/2 - x^2/4= 1
From following equations option B will produce the hyperbola graph shown in the figure
what is hyperbola ?
A hyperbola is a type of conic section, which is a curve that is formed by the intersection of a plane and a double cone. A hyperbola can also be defined as the set of all points in a plane, the difference of whose distances from two fixed points (called the foci) is a constant.
In the given question,
Based on the shape of the hyperbola shown on the y-axis graph, we can tell that the hyperbola has a vertical transverse axis, which means that its equation must have the form:
(y - k)² / a² - (x - h)² / b² = 1
where (h, k) is the center of the hyperbola, a is the distance from the center to the vertices, and b is the distance from the center to the co-vertices.
Option A is not correct because it produces a hyperbola with a horizontal transverse axis, whereas the given graph has a hyperbola with a vertical transverse axis.
We can eliminate option D since its equation has a transverse axis that is not vertical.
Next, we can eliminate option A since the coefficient of x² is positive, which means that the transverse axis is horizontal.
Option C has a transverse axis that is also horizontal, so we can eliminate it as well.
That leaves us with option B, which has a vertical transverse axis and its equation fits the form we determined earlier. Therefore, the equation Y²/9 - x²/4=1 will produce the hyperbola shown on the y-axis graph
To know more about hyperbola, visit:
brainly.com/question/28989785
#SPJ1
Jamie is laying stone pavers along his patio and walkway. The walkway is 3.5 feet wide. the patio measures 7 feet from top bottom and 8 feet accross. how much area does jamie need to cover.
84 sq ft area does jamie need to cover.
Describe Area?
The region enclosed by an object's form is referred to as the area. The area of the form is the area that the figure or any other two-dimensional geometric shape occupies in a plane.
A two-dimensional shape's area, which is expressed in square units, is the total surface area it may occupy. The square metre (m2), a derived measure, serves as the area unit in the SI system. On a sheet of paper, draw a square using a pencil. It has two dimensions. Its Area refers to the area that the form occupies on the paper.
the area of the walkway is:
Area of walkway = length x width = 8 ft x 3.5 ft = 28 sq ft
Next, let's calculate the area of the patio. The patio measures 7 feet from top to bottom and 8 feet across. Therefore, the area of the patio is:
Area of patio = length x width = 7 ft x 8 ft = 56 sq ft
Now, to find the total area that Desiree needs to cover, we just add the area of the walkway and the area of the patio:
Total area = area of walkway + area of patio
Total area = 28 sq ft + 56 sq ft
Total area = 84 sq ft
Learn more about area
brainly.com/question/27683633
#SPJ1
Help me find area
9th grade
Answer:
Step-by-step explanation: add all of them together
Is Joni correct? Explain.
Joni is not correct, because $230 is just the interest she will earn; she will have $430 total.
Joni is not correct; $230 will be her balance after 1 year. After 3 years, she will have $290.
Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53.
Joni is correct. She correctly applied the I = P · r · t formula, and will have $230.
Joni is not correct because she used the simple interest rate formula, not the compound interest rate formula. She will have $231.53.
What is simple and compound interest?A loan or investment's principle amount is the sole amount used to compute simple interest. Any interest that has been earned on interest that has accrued over time is not taken into account by simple interest.
Contrarily, compound interest is a sort of interest that takes into account both the original principal and any interest that has accrued over time. As a result, the interest gained during one period is added to the principle for the following month, where it continues to earn interest.
Joni is not correct, because $230 is just the interest she will earn; she will have $430 total.
The compound interest is given by the formula:
[tex]A = P (1 + r/n)^{(nt)}[/tex]
Substituting the values we have:
[tex]A = 200(1 + 0.05/1)^{(1*3)}\\A = 200(1.05)^3[/tex]
A = 200(1.157625)
A = $231.53
Hence, Joni will have a total balance of $231.53 after 3 years.
Learn more about compound interest here:
https://brainly.com/question/29335425
#SPJ1
The complete question is:
what is the answer to a=4 and b=3 can you help please 100 points right now
Answer:
14
Step-by-step explanation:
Rewrite the equation: 4*4+3-5
Multiply: 16+3-5
Add: 19-5
Subtract: 14
REFLECTION HELP If P= (-2,4), then find: Ry=1 (P)
(?, ?)
Answer:
P'(-2, -2)
Step-by-step explanation:
You want to know the location of P(-2, 4) after it is reflected in y=1.
ReflectionThe image point will be as far below the line y=1 as point P is above the line. The x-coordinate is unchanged.
P is 4 -1 = 3 units above the line y=1.
P' will be 3 units below the line y=1, so its y-coordinate is 1 -3 = -2.
The image point is P'(-2, -2).
__
Additional comment
Reflection in the line y=k is described by the transformation ...
(x, y) ⇒ (x, 2k-y)
P(-2, 4) ⇒ P'(-2, 2(1) -4) = P'(-2, -2)
The exponential function below is used by a biologist and her lab tomorrow the growth of some bacteria. A=2e^0.3t in the function the value of a depends on the value of t what statement describes that relationship 
The relationship between A and t is exponential, meaning that as time increases, the number of bacteria grows at an accelerating rate.
What is exponential function?An exponential function is a mathematical function of the form:
f(x) = a^x
where "a" is a positive constant called the base, and "x" is the independent variable. The base "a" is usually a number greater than 1, but it can also be a fraction between 0 and 1.
Exponential functions have some key properties that make them useful for modeling many natural phenomena. One of the most important properties is that they exhibit exponential growth or decay, meaning that the rate of change of the function is proportional to the current value of the function.
In the given question,
In the exponential function A=2e^(0.3t), the value of A depends on the value of t. Specifically, A is a function of t, where t is the independent variable and A is the dependent variable. This means that as the value of t changes, the value of A changes as well.
The function describes the growth of some bacteria, where A represents the number of bacteria at time t. The value of t represents the time elapsed since the start of the observation period. The function suggests that the growth rate of the bacteria is proportional to the current number of bacteria, with a growth rate of 0.3 per unit time.
The relationship between A and t is exponential, meaning that as time increases, the number of bacteria grows at an accelerating rate. This relationship can be observed by plotting the function on a graph, where A is plotted on the y-axis and t is plotted on the x-axis. The resulting curve will be a steeply upward-sloping curve that gets steeper and steeper as time goes on.
To know more about exponential functions, visit:
https://brainly.com/question/14355665
#SPJ1
What can be submitted for bands in a single -arm row?
Resistance bands, loop bands, tube bands with handles, and cable machines can be used for single-arm rows
In a single-arm row exercise, a variety of equipment can be used to add resistance and challenge the muscles. Here are some examples of what can be submitted for bands in a single-arm row
Resistance bands: Resistance bands are a popular option for single-arm rows. They come in different colors to indicate the level of resistance and can be easily adjusted to increase or decrease the difficulty. To perform a single-arm row with a resistance band, step on the center of the band with one foot and grasp the other end with one hand
Loop bands: Loop bands are a type of resistance band that is formed into a loop. They can be placed around the wrists or forearms to provide resistance during a single-arm row. To perform a single-arm row with a loop band, loop the band around your hand and hold onto the other end with your other hand.
Tube bands with handles: Tube bands with handles are another option for single-arm rows. These bands have handles on each end, allowing for a more comfortable grip. To perform a single-arm row with a tube band, attach one end of the band to a stationary object and hold onto the other end with one hand.
Cable machines: Cable machines are a piece of gym equipment that can also be used for single-arm rows. To perform a single-arm row on a cable machine, adjust the weight to the desired resistance and attach a handle to the cable.
Learn more about exercise here
brainly.com/question/13128077
#SPJ4
Find the missing length.
The value of the missing side length is 9.
What is the value of the missing length?The figures in the image are two similar triangle.
Side lengths of smaller triangle are:
x and (10-4)
Side lengths of larger triangle are:
(x+6) and 10
Since the triangle are similar, we take the proportion of the side lengths and solve for x.
x/(10-4) = (x+6)/10
x/6 = (x+6)/10
Cross multiply
x × 10 = 6( x + 6 )
Apply distributive property to eliminate the parenthesis.
x × 10 = 6×x + 6×6
10x = 6x + 36
10x - 6x = 36
4x = 36
x = 36/4
x = 9
Therefore, the value of x is 9.
Learn more about distributive property here: brainly.com/question/6276874
#SPJ1
A `16`-ounce bottle of orange juice contains `200` milligrams of vitamin C, which is `250\%` of the daily recommended amount (for adults).
On the previous screen, you said the daily recommended amount of vitamin C is `80` milligrams.
Yosef drank `4` ounces of orange juice.
What percent of the daily recommended amount of vitamin C is this?
Since a 16-ounce bottle of orange juice contains 200 milligrams of vitamin C, we can find the amount of vitamin C in 4 ounces by using a proportion:
16 ounces 200 milligrams
4 ounces x milligrams
Solving for x, we have:
x = 50 milligrams
So, Yosef drank 50 milligrams of vitamin C.
To find the percent of the daily recommended amount of vitamin C this represents, we can use another proportion:
80 milligrams 100%
50 milligrams x%
Solving for x, we have:
x = (50/80) * 100 ≈ 62.5%
Therefore, Yosef drank orange juice containing 62.5% of the daily recommended amount of vitamin C.