write a polar equation of a conic with the focus at the origin and the given data.hyperbola, eccentricity 3.5, directrix y
Answers
Complete Question is;
Write a polar equation of a conic with the focus at the origin and the given data. hyperbola, eccentricity 3.5, directrix y =2
Answer:
r = 14/(2 + 7(sinθ))
Step-by-step explanation:
We are given;
Eccentricity;e = 3.5
Directrix; y = 2
This means that d = 2
We are told that the focus is at the origin, so since the directrix is at y = 2,then the part of the hyperbola that is closest to this focus will open downwards and the equation is given by;
r = ed/(1 + e•sinθ)
Plugging in the relevant values, we have;
r = (3.5 × 2)/(1 + 3.5(sinθ))
r = 7/(1 + 3.5(sinθ))
To make every figure a whole number, let's multiply numerator and denominator by 2 to give;
r = 14/(2 + 7(sinθ))
Related Questions
A loan is being paid off by payments of 1,000, 2,000, ..., 10,000 at the end of years 1, 2, ..., 10.
The effective annual interest rate is 18%.
Determine the amount of interest in the 7th payment.
Answers
Therefore, the interest portion of the seventh payment is:7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7 - 7,000.
We have the following payments and their corresponding times of payment:At the end of year 1: $1,000At the end of year 2: $2,000At the end of year 3: $3,000At the end of year 4: $4,000At the end of year 5: $5,000At the end of year 6: $6,000At the end of year 7: $7,000
At the end of year 8: $8,000At the end of year 9: $9,000At the end of year 10: $10,000The present value of these payments is:PMT x [(1 - (1 + r)-n) / r]where PMT is the payment, r is the interest rate per year, and n is the number of years till payment.
For the first payment (end of year 1), the present value is:1,000 x [(1 - (1 + r)-1) / r]which equals
1,000 x (1 - 1 / (1 + r)) / r = 1,000 x ((1 + r - 1) / r) = 1,000
For the second payment (end of year 2), the present value is:2,000 x [(1 - (1 + r)-2) / r]which equals 2,000 x (1 - 1 / (1 + r)2) / r = 2,000 x ((1 + r - 1 / (1 + r)2) / r) = 2,000 x (1 + r) / r2
For the seventh payment (end of year 7), the present value is:
7,000 x [(1 - (1 + r)-7) / r]
which equals
7,000 x (1 - 1 / (1 + r)7) / r = 7,000 x ((1 + r - 1 / (1 + r)7) / r) = 7,000 x (1 + r + r2 + r3 + r4 + r5 + r6) / r7
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Which verbal translation is correct for the given expression. Check all that apply.
Answers
Answer:
the product of 3 and b
Step-by-step explanation:
i hope i read the question right. the expression was at the edge of the photo
yeah we never really say 3 multiplied by b
and 3×b cant be the sum or cube of b either
so its the last option
Work out the angle of X
Answers
Answer:
x = 99
Step-by-step explanation:
Since x is on a straight line the adjacent angle and x must equal 180. We will call this adjacent angle B. The angle to the right of B also is on a straight line.
So,
180 - 123 = the inside angle Simplify
57
The addition of a triangles interior angles equals 180
180 = 42 + 57 + B Move variables to one side
180 - (42 + 57) = B Simplify
81 = B
Now we can solve for X
180 - 81 = x Simplify
99
write a while loop to read integers from input until -1 is read. for each integer read before -1, add the integer to vector numbervect. ex: if the input is 1 6 5 3 -1, then the output is: 1 6 5 3
Answers
As per the concept of vector, the while loop for integers is written below.
The term vector refers a quantity or phenomenon that has two independent properties: magnitude and direction.
Here we need to write the a quantity or phenomenon that has two independent properties: magnitude and direction.
While we looking into the given question, we have know that,
Here the input is 1 6 5 3 -1, then
the output is: 1 6 5 3
Then the function for the given statement is written as,
while ((char1 = getchar()) != '-1')
{
if (char1 == ' ')
sp_ct1++;
else if (char1 == '\n')
nl_ct1++;
else
other1++;
}
Therefore, the above function is used to read integers from input until -1 is read.
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Order the values from least to greatest
-2.1,|5|,|4|,8, -7/12=
Answers
Step-by-step explanation:
-7/12 -2.1, 4, 5, 8
I couldn't read it well but I think this is what you meant.
some adults and children are watching a musical there are n children there are 25 fewer adults
Answers
According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99
A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.
B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.
To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.
Note: The given question is incomplete. The complete question is:
Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.
A) find the number of adults in terms of 'N'.
B) if there are 124 children how many adults are there?
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Which of the following would MOST LIKELY cause an increase in the Gross Domestic Product (GDP) of a country?Sofia is running the Challenge of Champions obstacle race at her summer camp. She runs 3/4
of a mile, but then she twists her ankle while going up the Mounds of Doom. Sofia still has1/2
of a mile left to run, so she drops out of the race.
Which equation can you use to find the total distance d of the race?
Answers
The equation that can be used to find the total distance d of the race, using the fraction of the time Sofia runs is; d - 1/2 = 3/4
What is a fraction?
A proper fraction is a represents of a part of a whole, using two numbers a numerator divided by a denominator.
The gross domestic product (GDP) of a country is most likely increased by the amount the government spends and the amount of inventories of the firms in the country.
The fraction of a mile distance Sofia runs before twisting her ankle = 3/4 of a mile
The distance Sofia has left to run = 1/2 of a mile
The equation that can be used to find the the total distance d of the race can be found as follows;
d = 3/4 + 1/2
Therefore; d - 1/2 = 3/4
The equation that can be used to find the total distance of the race is the option, obtained from the options in a similar question; d - 1/2 = 3/4
The possible question options, obtained from a similar question on the internet are;
d + 3/4 = 1/2d + 1/2 = 3/4(1/2)·d = 3/4d - 1/2 = 3/4Learn more on fractions here: https://brainly.com/question/30802046
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statement if p then not q this is different statement than the one give in the notes
Answers
Solution:
Given:
The conditional statement;
\(\begin{gathered} \text{If p, then not q} \\ p\rightarrow\text{ \textasciitilde{}q} \end{gathered}\)A converse statement is a result of reversing its two constituent statements.
\(\begin{gathered} \text{Conditional statement-If p, then not q} \\ \text{Converse statement-If not q, then p} \end{gathered}\)Therefore, the converse statement is: If not q, then p
The inverse statement assumes the opposite of each of the original statements.
\(\begin{gathered} \text{Conditional statement-If p, then not q} \\ I\text{nverse statement-If not p, then q} \end{gathered}\)Therefore, the inverse statement is: If not p, then q
To get the contrapositive statement, we interchange the conclusion of the inverse statement.
\(\begin{gathered} \text{Conditional statement-If p, then not q} \\ I\text{nverse statement-If not p, then q} \\ \\ \text{Hence, the contrapositive statement is gotten by reversing the conclusion of the inverse statement.} \\ \text{Contrapositive statement-If q, then not p} \end{gathered}\)
Therefore, the contrapositive statement is: If q, then not p
There are 100 performers in a dance recital. The ratio of men to women is 4 : 6. How many performers in the dance recital were men?
Answers
Answer:
40 men
Step-by-step explanation:
100 performers so the total men and women = 100
4 + 6 = 10
100/10 = 10
so 4(10) = 40
Use a definite integral to find the area of the region between the given curve and the x-axis on the interval [0, b].y= 2x^2.
Answers
Given :
Given a curve , \(y=2x^2\) .
To Find :
The area of the region between the given curve and the x-axis on the interval [0, b] .
Solution :
Now , area under the curve is given by :
\(A=\int\limits^b_0 {2x^2} \, dx \\\\A= |_0^b(\dfrac{2}{3}x^{(2+1)})\\\\A=\dfrac{2b^3}{3}\)
( Integration of \(x^2\) is \(\dfrac{x^3}{3}\) )
Therefore , the region between the given curve and the x-axis on the interval [0, b] is \(\dfrac{2b^3}{3}\) .
Hence , this is the required solution .
9
8
a
+
4
8
a
−
5
8
8
9
a+
8
4
a−
8
5
A
138a−58
8
13
a−
8
5
B
58a−58
8
5
a−
8
5
C
811a+14
11
8
a+
4
1
D
78a+85
8
7
a+
5
8
Answers
A particular fruit's weights are normally distributed, with a mean of 406 grams and a standard deviation of 27 grams.The heaviest 14% of fruits weigh more than how many grams?Give your answer to the nearest gram.
Answers
Given
mean of 406 grams and a standard deviation of 27 grams.
Find
The heaviest 14% of fruits weigh more than how many grams?
Explanation
given
mean = 406 gms
standard deviation = 27 gms
using standard normal table ,
\(\begin{gathered} P(Z>z)=14\% \\ 1-P(Zso , \(\begin{gathered} x=z\times\sigma+\mu \\ x=1.08\times27+406 \\ x=435.16 \end{gathered}\)Final Answer
Therefore , The heaviest 14% of fruits weigh more than 435.16 gms
Which of the following graphs could represent a quartic function?
A.
B.
D.
A. Graph A
Ο Ο Ο
B. Graph B
C. Graph C
D. Graph D
Answers
Answer:
D
Step-by-step explanation:
a quartic function is a polynomial of the 4th degree. that means that in the function expression the highest exponent of a term of x is 4.
y = ax⁴ + bx³ + cx² + dx + e
with a not 0.
the degree of a polynomial expression defines also how many zeroes (x values that create y = 0, that means points where the graph intersects the x-axis) there are.
a function has as many zeroes as the degree of the polynomial.
so, we are looking for potentially 4 zeroes.
the only graph that fulfills that is D.
the left "touch" of the graph on the x-axis counts for 2 (but equal) zeroes.
you can always test by virtually shifting the graph up or down and see, what are the max. x-axis intersections you can create.
if shifting D down a little bit you see, that this left "touch" turns into 2 intersections.
the same would apply for a "bend" or turn in the graph that does not even touch the x-axis.
if the original graph has not enough real x-axis intersections, it means that the remaining zeroes are then "imaginary" complex numbers (based on the sqrt(-1) = i).
a polynomial of the nth degree, must have n zeroes.
as a consequence it must have n-1 turns (even if the corresponding curve segments don't intersect with the x-axis in the real number space).
Answer:graph d
Step-by-step explanation:
just took the test
NO LINKS!! Find the areas of these composite figures
Answers
A) Area of triangle = 1/2 x 6 x 12 = 36
Area of semi circle = 1/2 x PI x 6^2 = 56.52
Total area = 36 + 56.52 = 92.52 square inches
B) Area of triangle = 1/2 x 10 x 12 = 60
Area of rectangle = 20 x 10 = 200
Total area = 200 + 60 = 260 square inches
Answer:
a) 92.5 in² (nearest tenth)
b) 260 m²
Step-by-step explanation:
Formulas
\(\textsf{Area of a rectangle}=\textsf{width} \times \textsf{length}\)
\(\textsf{Area of a triangle}=\dfrac12 \times \sf base \times height\)
\(\textsf{Area of a semicircle}=\dfrac12 \pi r^2 \quad \textsf{(where r is the radius)}\)
\(\textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}\)
Part (a)
This figure comprises:
an isosceles triangle (with base of 12 in and height of 6 in)a semicircle (with radius of 6 in)Total Area:
= area of triangle + area of semicircle
\(\sf = \dfrac{1}{2} \cdot 12 \cdot 6+\dfrac{1}{2} \pi (6)^2\)
\(\sf = 36 + 18 \pi\)
\(\sf = 92.5 \:\: in^2 \:(nearest\:tenth)\)
Part (b)
This figure comprises:
an isosceles triangle (with base of 10 m and height of 12 m)a rectangle (with width of 10 m and length of 20 m)Total Area:
= area of triangle + area of rectangle
\(\sf = \dfrac{1}{2} \cdot 10 \cdot 12+10 \cdot 20\)
\(\sf = 60+200\)
\(\sf = 260 \:\: m^2\)
which grows at the fastest rate for increasing values of x
\(f(x)=4*2^x\\h(x)=9x^2+25\\\\g(x)=15x+6\)
Answers
The function that grows at the fastest rate for increasing values of x is f(x) = 4×2ˣ.
We can see this by comparing the growth rates of the three functions for larger and larger values of x.
As x gets larger, the exponential function f(x) grows much faster than the other two functions, which are both polynomial functions.
if we plug in x = 10, we get:
f(10) = 4×2¹⁰ = 4×1024 = 4096
h(10) = 9×10² + 25 = 925
g(10) = 15×10 + 6 = 156
As we can see, f(10) is much larger than h(10) and g(10), indicating that f(x) grows at a much faster rate than the other two functions.
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You've been saving $8.50 each week to buy a bicycle from your local bike store. The bike originally cost $210, but is on sale for 25% off. So far, you have saved $120 for your purchase. How many more weeks must you save up to have enough money to buy the bike?
Answers
Answer:
5 weeks
Step-by-step explanation:
First, you must calculate what 25% off from $210 is. Since 100 - 25% = 75%, the price of the bike is 75% of $210.
\(\frac{x}{210}=\frac{75}{100}\)
\(100 * x = 75 * 210\)
\(100x = 15750\)
x = $157.50
Then, make an equation that represents the money needed to save up for the bike.
y = mx + b
bike's price = (money earned each week)(number of weeks) + money saved
157.5 = 8.50x + 120
157.5 - 120 = 8.50x + 120 - 120
37.5/8.5 = 8.5x/8.5
x = 4.4117
You need to round 4.4 to 5 because number of weeks must be whole numbers
Two cylinders, a and b, each started with different amounts of water. The graph shows how the height of the water changed as the volume of water increased in each cylinder. Match the graphs of a and b to Cylinders P and Q. Explain your reasoning. height in centimeters b volume in milliliters P
Answers
To match the graphs of cylinders a and b to cylinders P and Q, we need to analyze the relationship between the height of the water and the volume of water in each cylinder.
Cylinder P would correspond to graph b, while Cylinder Q would correspond to graph a.
The reasoning behind this is as follows:
Cylinder P, corresponding to graph b, shows a steeper increase in height with increasing volume. This indicates that the water level rises quickly as more volume is added, suggesting that the cylinder has a smaller cross-sectional area. Since height is directly proportional to volume for a cylinder, a smaller cross-sectional area would result in a higher rise in height for the same volume of water.
Cylinder Q, corresponding to graph a, shows a slower increase in height with increasing volume. This implies that the water level rises more gradually as more volume is added, indicating a larger cross-sectional area. A larger cross-sectional area would result in a smaller increase in height for the same volume of water.
In summary, the steeper graph b matches Cylinder P with a smaller cross-sectional area, while the gentler graph a matches Cylinder Q with a larger cross-sectional area.
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write and equation for the nth term of the geometric sequence for 2,8,32,128
then find a6 round to the nearest tenth if necessary.
Answers
The sixth term of the geometric sequence is 2048.
The given geometric sequence is 2, 8, 32, 128. We can observe that each term is obtained by multiplying the previous term by 4. Therefore, the common ratio (r) of the sequence is 4.
The formula for the nth term (an) of a geometric sequence is given by:
an = a1 * r^(n-1)
where a1 is the first term and r is the common ratio.
For this sequence, a1 = 2 and r = 4. Plugging in these values into the formula, we get:
an = 2 * 4^(n-1)
To find a6, we substitute n = 6 into the formula:
a6 = 2 * 4^(6-1)
= 2 * 4^5
= 2 * 1024
= 2048
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The Probable question may be:
Write an equation for the nth term of the geometric sequence 2, 8, 32, 128,
Then find a6. Round to the nearest tenth if necessary.
a = 5×4 X
a1 = n-1 X
snfnannfmskfmskfkwkwmfne
Answers
Answer:
45 degrees
Step-by-step explanation:
DBC: 180 - 135
DBC: 45 degrees
Hope that helps!
Graph the solution to the inequality |2x + 2) > 6.
Answers
The solution to the inequality is all the values of x that are either greater than 2 or less than -4. The required graph of inequality is given below.
What is Inequality :In mathematics, an inequality is a statement that compares two values, often using the symbols "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to).
Inequality graphs show the region of the coordinate plane that satisfies an inequality. The graph of inequality can be determined in a similar way to the graph of an equation, but with some additional steps.
Here we have
The inequality |2x + 2| > 6
To graph the solution to the inequality |2x + 2| > 6,
we can start by rewriting the inequality as two separate inequalities without the absolute value:
2x + 2 > 6 or 2x + 2 < -6
Simplifying these inequalities, we get:
2x > 4 or 2x < -8
x > 2 or x < -4
Therefore,
The solution to the inequality is all the values of x that are either greater than 2 or less than -4. The required graph of inequality is given below.
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Solve the inequality for x and identify the graph of its solution.
|x+2|<2
Choose the answer that gives both the correct solution and the correct graph.
Answers
The option C is correct.
In the given statement is:
Solve the inequality for x and identify the graph of its solution.
|x+2|<2
Here, The question is :
|x+2|<2
The modulus sign means that the absolute value of x + 2 is less than 2. This means that
-2 < x + 2 < 2
This is what is called double inequality. We must treat it as two separate inequalities.
From the left we get -2 < x + 2 and by subtract 2 to both sides we obtain
-4 < x.
On the right we have x + 2 < 2 , and by subtract 2 to both sides we get,
x < 0
We can write these solutions together as :
-4 < x < 0
and this range of values of x is illustrated on the number line see the image :
Hence, The option C is correct.
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let $x$ be a real number selected uniformly at random between 100 and 200. if $\lfloor \sqrt{x} \rfloor
Answers
The value of \($\lfloor \sqrt{X} \rfloor$\) can be any number between 10 and 13, since 14 is not an integer.
Let x be the random variable denoting the real number selected uniformly at random between 100 and 200.
The square root of \($X$, $\sqrt{X}$,\) will be a real number between 10 and 14. The floor function, \($\lfloor \sqrt{X} \rfloor$\) will take the integer less than or equal to\($\sqrt{X}$.\)This means that the value of \($\lfloor \sqrt{X} \rfloor$\) can be any number between 10 and 13, since 14 is not an integer.
For example, if \($X = 150$\), then \($\sqrt{X} = 12.25$\), so \($\lfloor \sqrt{X} \rfloor = 12$\)
In summary, for any real number selected uniformly at random between 100 and 200, the value of\($\lfloor \sqrt{X} \rfloor$\) is any number between 10 and 13.
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What is the slope of the line
Answers
Answer:
The slope is 2/3
Step-by-step explanation:
Take the line from the point it is touching then go up 2 and right 3 which is 2/3 and if the patter repeats then that's how you know its right.
Write an Integer for the situation,
300 feet below sea level
A -300
B 600
C -600
D 300
Answers
Below means negative
Answer: A. -300
Step-by-step explanation: I hope this helps!
What number belongs in the box to make the equation true? 2 7 3 5
Answers
what is 14 divided by 2/7 in simplest from
Answers
Answer:
98/2
Step-by-step explanation:
The numbers in 14 divided by 2/7 are labeled below:
14 = whole number
2 = numerator
7 = denominator
To make it a fraction form answer, you multiply the whole number by the denominator and make the result the new numerator. The old numerator becomes the new denominator:
14 x 7
2
=
98
2
Thus, the answer to 14 divided by 2/7 in fraction form is:
98
2
To make the answer to 14 divided by 2/7 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:
98 / 2 = 49
The answer is rounded to the nearest two decimal points if necessary.
98/2 can be simplified to 49/1.
49/1 is an improper fraction and should be written as 49.
the simplest form of 14 divided by 2/7 is 49.
To divide 14 by 2/7, we can convert the division operation into multiplication by taking the reciprocal (flipping) of the divisor. The reciprocal of 2/7 is 7/2. So, we have 14 multiplied by 7/2.
To simplify this further, we can cancel common factors between the numerator of 14 and the denominator of 2. Both 14 and 2 share a common factor of 2. Dividing both by 2, we get 7 and 1 respectively.
Therefore, the division 14 divided by 2/7 simplifies to 7 multiplied by 7/1, which equals 49. Thus, the simplest form of 14 divided by 2/7 is 49.
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The book fait fundraises $250 per day for the school make a table and equation
Answers
The equation that represents the total fund raised in x days is y = 250x
How to make a table and equation?The statement is given as:
The book fait fundraises $250 per day for the school
Let the number of days be x and the total amount be y.
So, we have
y = 250x
The table of value is then represented as:
x y
0 0
1 250
2 500
3 750
4 100
Hence, the equation that represents the total fund raised in x days is y = 250x
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Which percent is equivalent to 2 5/6?
Answers
Answer: 283.3333333% (283.3%)
Step-by-step explanation:
First, lets turn 2 5/6 into and improper fraction. It becomes 17/6.
Now, we divide 17/6
17/6 = 2.833333333
Now, to turn it into a percent, we multiply it by 100, or move the decimal point 2 places to the right. That gives us 283.3333333% (283.3%)
Hope this helps!
The sector of a circle has an area of 104pi/9
square inches and a central angle with measure 65 degree
. What is the radius of the circle, in inches?
Answers
Answer:
Given:
Area of the sector (A) = 104π/9 square inches
Central angle (θ) = 65 degrees
The formula for the area of a sector of a circle is:
A = (θ/360) * π * r^2
We can rearrange this formula to solve for the radius (r):
r^2 = (A * 360) / (θ * π)
Plugging in the given values:
r^2 = (104π/9 * 360) / (65 * π)
r^2 = (104 * 40) / 9
r^2 = 4160 / 9
r^2 ≈ 462.22
Taking the square root of both sides:
r ≈ √462.22
r ≈ 21.49
Therefore, the radius of the circle is approximately 21.49 inches.
Answer: 8 inches
Step-by-step explanation:
carpet is sold in square yards how much carpet would a person need to buy for a rectangle that has dimensions of 10 yards by 18 feet
Answers
A person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
How to determine the amount of carpet needed for a rectangular room?
To determine the amount of carpet needed for a rectangular room, you need to convert the measurements to the same unit of measurement. Since the carpet is sold in square yards, we need to convert the dimensions of the room to yards.
The length of the room is given in yards, so we don't need to make any conversions for that dimension. However, the width of the room is given in feet, so we need to convert it to yards by dividing by 3 (since there are 3 feet in a yard),
18 feet ÷ 3 feet/yard = 6 yards
So the dimensions of the room in yards are 10 yards by 6 yards.
To find the total area of the room, we need to multiply the length and width,
10 yards × 6 yards = 60 square yards
Therefore, a person would need to buy 60 square yards of carpet for a rectangular room with dimensions of 10 yards by 18 feet.
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