Find a polar equation of the conic with its focus at the pole.
Conic: Parabola
Vertex or Vertices: (1, π/2)
Answers
The polar equation of the parabola with focus at the pole and vertex at (1,π/2) is r = (1+cos(θ))/4 sin²(θ/2).
Since the focus of the parabola is at the pole (r=0), we know that the directrix will be a horizontal line through the focus.
The vertex is at (1,π/2) which tells us that the axis of symmetry of the parabola is the line θ = π/2.
Therefore, the directrix is the line y = -d, where d is the distance from the vertex to the focus. We can find d using the formula d = 1/4p where p is the distance from the vertex to the directrix.
Since the vertex is (1,π/2) and the axis of symmetry is θ = π/2, the equation of the axis of symmetry can be written as r cos(θ - π/2) = 1.
At the vertex, r = 1/cos(π/2 - π/2) = 1. So, the distance from the vertex to the axis of symmetry is 1. Therefore, p = 1 and d = 1/4.
Since the directrix is a horizontal line, we can express it in polar coordinates as θ = -π/2. So, the polar equation of the directrix is r sin(θ + π/2) = r cos(θ) = -1/4.
Since the focus is at the pole, the distance from any point on the parabola to the focus is simply r. The distance from any point on the parabola to the directrix is r cos(θ) + 1/4.
By definition, a parabola has the property that the distance from any point on the parabola to the focus is equal to the distance from that point to the directrix.
Therefore, we have the equation:
r = r cos(θ) + 1/4
Simplifying this equation gives:
r = 1/(1-cos(θ))/4
Multiplying both the numerator and denominator by (1+cos(θ)) gives:
r = (1+cos(θ))/4 sin²(θ/2)
So the polar equation of the parabola with focus at the pole and vertex at (1,π/2) is r = (1+cos(θ))/4 sin²(θ/2).
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Related Questions
The Rhythm Record Shop orders sixty-minute cassette tapes at $1.49 and CDs at $4.98. A total of 451
items were ordered and the total amount of the invoice is $1240.86. How many of each item were
ordered?
Answers
The number of sixty-minute cassette tapes ordered is 288 and the number of CDs ordered is 163.
What are the linear equations that represent this question?1.49a + 4.98b = $1240.86 equation 1
a + b = 451 equation 2
Where:
a = number of sixty-minute cassette tapes ordered b = number of CDs orderedHow many CDs were ordered?Multiply equation 2 by 1,49
1.49a + 1.49b = 671.99 equation 3
Subtract equation 3 from equation 1
568.87 = 3.49b
Divide both sides of the equation by 3.49
568.87 / 3.49
b = 163
How many sixty-minute cassette tapes were ordered ?Subract 163 deom 451
451- 163 = 288
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Angel deposits $51,400 in a savings account that pays 2.3% interest, compounded monthly.
A) What is the account balance after one year?
b)How much did Angel make in interest during that one year?
c)What is the account balance after five years?
d)How much did Angel make in interest during the five years?
Answers
Answer:
a) $65,586.40
b) $14,186.40
c) $122,332
d) $70,932
Diana works in a building that is 130 feet tall. She is outside, looking up at the building at an angle of 37° from her feet to the top of the building. If Diana walks forward and her angle looking to the top of the building changes to 40°, how much closer is she to the building? Round the answer to the nearest tenth of a foot. 10.3 ft 17.6 ft 30.2 ft 97.2 ft
Answers
Answer: 17.6
Step-by-step explanation:
The answer to the nearest tenth B. 17.6 ft
What is an instance of word problems?
Word issues commonly encompass mathematical modeling questions, where information and facts about a positive device are given and a scholar is needed to develop a version. for instance: Jane had $5.00, then spent $2.00. How lots does she have now?
How can we resolve word problems?A proven step-by-step approach for solving word problems is sincerely quite simple.
Draw a photograph.suppose “What do I want to locate?”list what's given.find the important thing words.resolve.check your work.Learn more about Word problems at https://brainly.com/question/13818690
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Need help thank you very much
Answers
Answer:
8×8×8×8×8= 32,768
10×10×10= 1,000
Answer:
8x8x8x8x8=32768
Step-by-step explanation:
10x10x10=1000
Solve for x
3x - 8= 7x +4
Answers
Answer:
x=-3
Step-by-step explanation:
PLEASE HELP ASAP
will mark brainliest
Answers
Answer:
7
Step-by-step explanation:
7-7=0 and this cannot happen in the denominator
Answer:
Step-by-step explanation:
7 cannot as 7-7=0 and 0 cant be in denominator
0 works
-7 works
4 works
i think
A high school athlete runs 1.00 ✕ 102 m in 13.65 s.
What is the velocity in m/s
What is the velocity in km/h?
Answers
answe:
102/13.65= 7.47m/s
then multoply by 3600 to get per hour
26.9 km/h
What is the equation of this line?
A: y=-2x
B: y = ½x
C: y = -½x
D: y = 2x
Answers
Answer:
D
Step-by-step explanation:
when x=1, y should = 2
2(1)=2
so y=2x is correct
let p=0.579 compute Q
let q=0.871 compute p.
Answers
In probabilities, variables p and q are often used as complements of another.
The value of q is 0.421The value of p is 0.129The relationship between variables p and q is:
\(\mathbf{p+ q = 1}\)
So, we have:
(a) p = 0.579
Substitute 0.579 for p in \(\mathbf{p+ q = 1}\)
\(\mathbf{0.579 + q = 1}\)
Make q the subject
\(\mathbf{q = 1 - 0.579}\)
\(\mathbf{q = 0.421}\)
The value of q is 0.421
(b) q = 0.871
Substitute 0.871 for q in \(\mathbf{p+ q = 1}\)
\(\mathbf{p + 0.871 = 1}\)
Make p the subject
\(\mathbf{p = 1 - 0.871}\)
\(\mathbf{p = 0.129}\)
The value of p is 0.129
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yea... pls help me pls!
Answers
Answer:
960
Step-by-step explanation:
12x10x16=1920
1920/2=960
Ethan is watering his plants. He starts with a watering can filled with 32 ounces of water, and he pours 3.5 ounces onto each plant. When Ethan finishes watering his plants, he has 14.5 ounces of water left. How many plants does he have? Write and solve an equation to find the answer.
Answers
The number of plants Ethan has are 5.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let x be the number of plants Ethan has.
Ethan uses 3.5 ounces of water for each plant, so he will use a total of 3.5p ounces of water.
If he starts with 32 ounces of water and ends up with 14.5 ounces
Total of 32 - 14.5 = 17.5 ounces of water.
As given the amount of water used is equal to the amount of water per plant times the number of plants:
3.5x = 17.5
Divide both sides by 3.5
x=5
Hence, , Ethan has 5 plants.
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How do you think life on Earth would be different without the evolution of angiosperms? Provide two examples, each with an explanation. {BRAINLIEST ON THE LINE}
Answers
Therefore , the solution of the given problem of unitary method comes out to be the development of humans and other life forms would have been different without angiosperms.
An unitary method is what?To accomplish the objective, one may use this widely used ease, already existing variables, or any significant components from the initial Bishop customizable question. If that's the case, another opportunity to interact with the item will come up. If not, every essential component that influences how well evidence of an equation functions will be lost.
Here,
Ecological Changes: Angiosperms are essential components of many Earth species' food chains and ecosystems.
Flowering plants provide sustenance, shelter, and breeding grounds for a variety of insects and animals.
For instance, many herbivorous animals rely on flowering plants as their main source of sustenance, and bees and butterflies use the nectar from flowers as a source of energy.
Angiosperms play a major role in human economic and cultural life. Angiosperms make up a large portion of our food crops, including grains, veggies, fruits, and nuts.
In conclusion, the evolution of angiosperms has profoundly influenced human culture and civilization, as well as the ecology and evolution of life on Earth.
The development of humans and other life forms would have been different without angiosperms.
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Assume the distribution of IQ scores for adults can be modeled with a normal distribution with a mean score of 100 points and a standard deviation of 10 points. 30% of adults will have an IQ score higher than what value?
Answers
Step-by-step explanation:
Use z-score table to find the z-score that corresponds to .7000 ( 70%)
approx .525 s.d. above the mean
.525 * 10 = 5.25 points above 100 = 105.25
Given that $k$ is a positive integer less than 6, how many values can $k$ take on such that $3x \equiv k \pmod{6}$ has no solutions in $x$
Answers
Supposing the value of x to be an integer, the values of k that donot
satisfy the given equation 3x = k mod 6 are 1,2,4,5.
What is an integer?An integer, which can comprise both positive and negative integers, including zero, is a number without a decimal or fractional portion.
What is the difference between integers and whole numbers?Integers are a set of numbers that include both positive and negative numbers, as well as zero. Whole numbers, on the other hand, only include the set of non-negative numbers starting from 0 (i.e., 0, 1, 2, 3, 4, ...). In other words, whole numbers are a subset of integers.
If 3x = k mod 6 has no solutions in x, then k must not be divisible by 3. The positive integers less than 6 that are not divisible by 3 are 1, 2, 4, and 5. Therefore, k can take on 4 values: 1, 2, 4, and 5.
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I need help, i don't understand
Answers
Answer:
Step-by-step explanation:
the sum of the angles is 360 degrees
you have 3 angles equal to 91
91*3=273
360-273=87
87/3=29
the angle g, or d, is 29
Bob and Anna are planning to meet for lunch at Sally's Restaurant, but they forgot to schedule a time. Bob and Anna are each going to randomly choose from either 1\text{ p. M. }1 p. M. 1, start text, space, p, point, m, point, end text, 2\text{ p. M. }2 p. M. 2, start text, space, p, point, m, point, end text, 3\text{ p. M. }3 p. M. 3, start text, space, p, point, m, point, end text, or 4\text{ p. M. }4 p. M. 4, start text, space, p, point, m, point, end text to show up at Sally's Restaurant. They must both choose exactly the same time in order to meet. Bob has a "buy one entree, get one entree free" coupon that he can only use if he meets up with Anna. If he successfully meets with Anna, Bob's lunch will cost him \$5$5dollar sign, 5. If they do not meet, Bob's lunch will cost him \$10$10dollar sign, 10. What is the expected cost of Bob's lunch?
Answers
The expected cost of Bob's lunch is $9.69, rounded to the nearest cent.
To figure out the probability of Bob and Anna successfully meeting up, we need to use a unitary method. The probability of Bob choosing a specific time is 1/4, and the probability of Anna choosing the same time is also 1/4. Since they both need to choose the same time, we can multiply their individual probabilities to find the probability of them meeting up:
1/4 x 1/4 = 1/16
This means that the probability of Bob and Anna successfully meeting up is 1/16 or 0.0625.
Now we can use this probability to find the expected cost of Bob's lunch. If Bob and Anna meet up, Bob will get a discount on his lunch and pay $5. If they don't meet up, he'll have to pay the full price of $10. So the expected cost of Bob's lunch is:
(Probability of meeting up x Cost if they meet) + (Probability of not meeting up x Cost if they don't meet)
(1/16 x $5) + (15/16 x $10) = $0.3125 + $9.375 = $9.69
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40000$ consumer loan will be paid in monthly equal installment over
2years monthly payments , if the interest rate is 15.8% what will
be the amount?
Explain the answer in details
Answers
A consumer loan of $40,000 with a 15.8% interest rate will require monthly payments over a period of 2 years. The total amount to be paid, including both principal and interest, will be approximately $45,380.
To calculate the monthly payments, we need to determine the total amount to be paid over the loan period, including the principal amount and the interest. The formula used for calculating equal monthly installments is:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Principal amount
r = Monthly interest rate
n = Number of monthly payments
In this case, the principal amount (P) is $40,000, the interest rate (r) is 15.8% per year, and the loan duration (n) is 2 years (24 months).
First, we convert the annual interest rate to a monthly rate by dividing it by 12: 15.8% / 12 = 0.0132.
Next, we substitute the values into the formula:
M = 40,000 * (0.0132 * (1 + 0.0132)^24) / ((1 + 0.0132)^24 - 1)
Calculating this formula gives us the monthly payment (M) of approximately $1,907.42.
To find the total amount to be paid, we multiply the monthly payment by the number of payments: $1,907.42 * 24 = $45,778.08. However, this includes both the principal and the interest. Subtracting the principal amount ($40,000) gives us the total interest paid: $45,778.08 - $40,000 = $5,778.08.
Therefore, the total amount to be paid, including both principal and interest, will be approximately $45,778.08.
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4. A triangle with vertices A(1,2), B(3,5), and C(5,-4) is reflected across the y-axis. Provide the transformed coordinates of the
triangle. Show all work.
Answers
a. An exciting endeavor, 50 archaeology students volunteer for the expedition although only 20 are needed. How many ways can the lead researchers pick 20 students from the 50 eager candidates? b. From the 20 selected students, aside from the excavation process, 4 special tasks are available for the students to work on. Task 1 requires 3 students, task 2 requires 8, task 3 requires 5 and task 4 requires 4. No student can take on more than 1 task. How many different outcomes are there to fill all 4 tasks?
Answers
Through Binomial Coefficient, there is 3,491,888,400 different outcomes to fill all 4 tasks from the 20 selected students.
What is Binomial Coefficient?
In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem.
a. To determine the number of ways the lead researchers can pick 20 students from the 50 eager candidates, we can use the concept of combinations. The number of ways to choose 20 students from a group of 50 can be calculated using the binomial coefficient.
The number of ways to choose 20 students from a group of 50 is given by:
C(50, 20) = 50! / (20! * (50-20)!)
Using the formula for combinations, we can calculate the value:
C(50, 20) = 50! / (20! * 30!)
Calculating this value, we find:
C(50, 20) =471,292,122,4*\(10^{13}\)
Therefore, there is 471,292,122,4*\(10^{13}\) ways for the lead researchers to pick 20 students from the 50 eager candidates.
b. To determine the different outcomes to fill all 4 tasks from the 20 selected students, we need to consider the number of ways to assign students to each task.
Task 1 requires 3 students, task 2 requires 8 students, task 3 requires 5 students, and task 4 requires 4 students. Since no student can take on more than one task, we can calculate the number of ways to assign students to each task separately.
For Task 1: We need to choose 3 students from the 20 selected students. This can be calculated as
C(20, 3) = 20! / (3! * (20-3)!)
C(20, 3) =20! / (3! * 17!)
C(20, 3) =1140
For Task 2: We need to choose 8 students from the remaining 17 students (after assigning students to Task 1). This can be calculated as C(17, 8) = 17! / (8! * (17-8)!)
C(17, 8) = 17! / (8! * 9!)
C(17, 8) = 24310
For Task 3: We need to choose 5 students from the remaining 9 students (after assigning students to Tasks 1 and 2). This can be calculated as
C(9, 5) = 9! / (5! * (9-5)!)
C(9, 5) = 9! / (5! * 4!)
C(9, 5) = 126
For Task 4: We need to choose 4 students from the remaining 4 students (after assigning students to Tasks 1, 2, and 3). This can be calculated as C(4, 4) = 4! / (4! * (4-4)!)
C(4, 4) = 4! / (4! *0!)
C(4, 4) =1
To calculate the total number of different outcomes, we multiply the number of ways for each task together:
Total number of outcomes = C(20, 3) * C(17, 8) * C(9, 5) * C(4, 4)
Calculating this expression, we find:
Total number of outcomes=1140* 24310*126*1 =3,491,888,400
Therefore, there is 3,491,888,400 different outcomes to fill all 4 tasks from the 20 selected students.
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Janiya has a shoebox with a volume of 609 cubic inches. The length of the shoebox is 14.5 inches and the width is 7 inches. What is the height of the shoebox? Group of answer choices
Answers
Answer:
6 inches
Step-by-step explanation:
Hi there!
\(V=lwh\) where l is the length, w is the width and h is the height of a rectangular prism
Plug in the volume (609), length (14.5) and width (7)
\(609=(14.5)(7)h\\609=(101.5)h\)
Divide both sides by 101.5 to isolate h
\(\frac{609}{101.5} =\frac{101.5h}{101.5} \\6=h\)
Therefore, the height of the shoebox is 6 inches.
I hope this helps!
−3 2/7−(−5/7) plz help me
Answers
Answer:
-2 or -14/7 (they're the same)
Step-by-step explanation:
Write it out: \(-3\frac{2}{7} - (-\frac{5}{7})\) Simplify. It should now look like this: \(-3\frac{2}{7} + \frac{5}{7}\) Turn -3 2/7 into an improper fraction. It should now look like this: -19/7Add: \(-\frac{19}{7} + \frac{5}{7} = -\frac{14}{7} = -2\)I hope this helps!
Answer:
- 2 ⁴/₇Step-by-step explanation:
-3 ²/₇ - ( - ⁵/₇)
- 23 / 7 + 5 / 7
_ 23 + 5
7
_ 18
7
- 2 ⁴/₇
Fill in the blank with an appropriate word, phrase, or symbol(s). The number of regions created when constructing a Venn diagram with three overlapping sets is The number of regions created when constructing a Venn diagram with three overlapping sets is 8 3 6
Answers
The number of regions created when constructing a Venn diagram with three overlapping sets is 8.
In a Venn diagram, each set is represented by a circle, and the overlapping regions represent the elements that belong to multiple sets.
When three sets overlap, there are different combinations of elements that can be present in each region.
For three sets, the number of regions can be calculated using the formula:
Number of Regions = 2^(Number of Sets)
In this case, since we have three sets, the formula becomes:
Number of Regions = 2^3 = 8
So, when constructing a Venn diagram with three overlapping sets, there will be a total of 8 regions formed.
Each region represents a unique combination of elements belonging to different sets.
These regions help visualize the relationships and intersections between the sets, providing a graphical representation of set theory concepts and aiding in analyzing data that falls into multiple categories.
Therefore, the correct answer is 8.
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indica los monomios semejantes en cada uno de las siguientes series: por favor ayudenmen aaaaaaa D':
Answers
Answer:
Do you have this in english so that I can help :)
Step-by-step explanation:
LOOK OMG :0
Jennifer is a wedding planner. She set up six chairs at each table for the reception. If t represents the number of tables, which of the following expressions represents the total number of chairs that she set up?
A. 6 + t
B. t + 6
C. 6t
D. t - 6 ( hurry fo meh)
Answers
For every table that is present there are 6 chairs at the table
Answer:
C is the correct answer
Someone help please, i cant solve this one :|
Answers
Answer:
i think its B
Step-by-step explanation:
Answer:
A. y = 45.25x + 10
Step-by-step explanation:
We can use the points (3, 145.75) and (5, 236.25) to solve.
Find the slope using the formula [ y2-y1/x2-x1 ].
236.25-145.75/5-3
90.5/2
45.25
Find the y-intercept using the formula for slope-intercept form [ y = mx + b ]
y = 45.25x + b
145.75 = 45.25(3) + b
145.75 = 135.75 + b
10 = b
Put everything we solved for into the formula above.
y = 45.25x + 10
Best of Luck!
Evaluate the expression when x= -3.
x2-5x-8
Answers
Step-by-step explanation:
x²-5x-8When x=-3, then
(-3)²-5×(-3)-89+15-824-816Answer:
\( {x}^{2} - 5x - 8 \\ x = - 3 \\ {( - 3)}^{2} - 3 \times - 5 - 8 \\ 9 + 15 - 8 \\ 24 - 8 \\ = 16 \\ thank \: you\)
Point S is on line segment \overline{RT}
RT
. Given RS=4x-10,RS=4x−10, ST=2x-10,ST=2x−10, and RT=4x-4,RT=4x−4, determine the numerical length of \overline{RS}.
RS
.
Answers
The length of overline RS is 22
Line: In geometry, a line is a straight one-dimensional figure with no thickness that extends in both directions indefinitely.
Line Segment: A line segment has two defined endpoints.
According to the question
RS = 4x − 10
ST=2x−10
RT=4x−4
From the question above:
Point S lies on |RT|
So, RT = RS + ST
Substituting the values for each in the above equation to solve for x
4x - 4 = 4x - 10 + 2x - 10 --- collecting like terms
4x - 4 = 4x + 2x - 10 - 10
4x - 4 = 6x - 20--- again collecting like terms
6x - 4x = 20 - 4
2x = 16 --- dividing throughout by 2
2x/2 = 16/2
x = 8
Since, RS = 4x − 10
RS = 4*8 - 10
RS = 32 - 10
RS = 22
Hence, the numerical length of RS is calculated as 22
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When an organization with a functional structure diversifies into related product-markets, it generally a. develops a worldwide product-division structure. b. maintains its functional structure. c. develops a divisional structure. d. develops a matrix structure.
Answers
When an organization with a functional structure diversifies into related product-markets, it generally maintains its functional structure.
In a functional structure, the organization is organized based on specialized functions such as marketing, finance, operations, and human resources. Each function operates independently, and decisions are made within each functional unit. When diversifying into related product-markets, the organization can leverage its existing functional expertise to support the new product lines or markets.
Maintaining the functional structure allows the organization to retain the benefits of specialization and efficiency within each function. It also enables the organization to capitalize on the existing knowledge, skills, and resources of each functional area, ensuring a smoother transition into new product-markets.
This approach minimizes disruption and allows the organization to effectively manage the integration of new product lines while maintaining focus on core competencies. By leveraging the existing functional structure, the organization can adapt and respond to the specific requirements of each product-market while maximizing operational efficiency.
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I will award 30 points to anyone that can solve this. If i fail i have to retake
Answers
Answer: it’s all in the pictures hope this helps!!:)
Step-by-step explanation:
Answer:
x=-4, y=1
Step-by-step explanation:
T is a point inside parallelogram ABCD. The area of ΔTAB = 11, the area of ΔTBC = 4, and the area of ΔTCD = 6. Find the area of ΔTAC.
Answers
wrong question
the ∆TAC is not the triangle