Suppose you have two hyperbolas that are the same except that the transverse axis and conjugate axis are switched. How does switching the axes affect the equations of the asymptotes for the two hyperbolas? Why?
Answers
assuming both hyperbolas at centered at the origin, the values for the numerator and denominator will switch, so that the slope of one is the reciprocal of the other's slope.
Final answer:
Switching the axes of two hyperbolas affects the equations of the asymptotes.
Explanation:
When the transverse axis and conjugate axis are switched in two hyperbolas, it affects the equations of the asymptotes. The equations of the asymptotes are determined by the ratio of the coefficients of x² and y² in the hyperbola equation. When the axes are switched, this ratio changes, resulting in different equations for the asymptotes.
For example, let's consider two hyperbolas with equations:
1) 8x² + 10xy - 3y² - 2x - 4y - 2 = 0
2) 8y² + 10xy - 3x² - 2x - 4y - 2 = 0
In the first hyperbola, the ratio of the coefficients of x² and y² is 8/(-3), which determines the equation of the asymptotes. In the second hyperbola, the ratio is (-3)/8, leading to different equations for the asymptotes.
Related Questions
Anyone help please!!!!
Answers
cos(α-B)-cos(α+B) = 2 sinα sinβ
Left hand side = cos(α - B)-cos(α + B)
= cosα cosβ + sinα sinB - (cosα cosB - sinα sinβ)
= cosα cosβ + sinα sinB - cosα cosB + sinα sinβ)
= sinα sinβ + sinα sinβ
= 2 sinα sinβ
= Right Hand side
cos(a-B)-cos(a+B)
cosucosv - sinusinv = cos(u+v)
cosucosv + sinusinv = cos(u-v)
cos(a-B)-cos(a+ B) = cosa cosB + sina sinB - (cosa cosB - sina sinB)= cosa cosB + sina sinB - cosacosB + sinb sinB= 2 sina sinB
dy/dx = y/x^2
dy/y = dx/x^2
ln y * ln c = -1/x
cy = e^(-1/x)
y = ce^(-1/x)
Answers
dy/y = dx/(x^2)
int[dy/y] = int[dx/(x^2)] ... apply integral to both sides
ln(|y|) = (-1/x) + C
|y| = e^{(-1/x) + C}
|y| = e^C*e^(-1/x)
|y| = C*e^(-1/x)
y = C*e^(-1/x)
So you have the correct answer. Nice job.
------------------------------------------------
Check:
y = C*e^(-1/x)
dy/dx = d/dx[C*e^(-1/x)]
dy/dx = d/dx[-1/x]*C*e^(-1/x)
dy/dx = (1/(x^2))*C*e^(-1/x)
is the expression for the left hand side (LHS)
y/(x^2) = [C*e^(-1/x)]/(x^2)
y/(x^2) = (1/(x^2))*C*e^(-1/x)
is the expression for the right hand side (RHS)
Since LHS = RHS, this confirms the solution for dy/dx = y/(x^2)
A gallon of Moo Milk costs \$5.12$5.12dollar sign, 5, point, 12. What is the price, in dollars, of an 888 ounce glass of Moo Milk? There are 128128128 ounces in 111 gallon.
Answers
A gallon of Moo Milk costs $5.12 What is the price, in dollars, of an 8 ounce glass of Moo Milk? There are 128 ounces in 1 gallon.
Solution:
Cost of 1 gallon of Moo Milk = $ 5.12
1 gallon = 128 ounces, so we can write:
Cost of 128 ounces of Moo Milk = $ 5.12
Cost of 1 ounce of Moo Milk = $ 5.12/128 = $ 0.04
Cost of 8 ounces of Moo Milk = $ 0.04 x 8 = $ 0.32
Thus, 8 ounces of Moo Milk will cost $ 0.32
Answer:
0.32
Step-by-step explanation:
The ration of gallons to cost is 1:$5.12
We want to know the ratio of ounce to cost.
We need to convert gallons to ounces.
There are 128 ounces in 1 gallon.
So, if one Moo Milk costs $5.12, then 128 ounces also cost $5.12
The ratio of ounces to cost is 128:$5.12
Now, we can find an equivalent ratio to find the cost for 1 ounce.
Then we can multiply by 8 to find the cost of 8 ounces
Ounces ---------> Cost
128 ------------> 5.12 (Both divided by 128)
1 -------------> 0.04 (Both times 8)
8 ------------> 0.32
An 8 ounce of Moo Milk costs $0.32
WILL GIVE BRAINLIEST IF YOU HAVE THE REST OF THE ANSWERS
Answers
I completed this a few months ago but don't remember the rest of the answers. Message me and I'll be able to find them for you, but anyway, I'm positive the answer is A.
Proof:
A=(123-55)/2=34
Solve for x: 12(x-7)+3(2x+2)=50x-62
Answers
Hope this helps
This is because
12 (-1/2 - 7) + 3 (2 x -1/2 + 2) = 50x - 62
12 x -7.5 + 3 x 1 = -25 - 62
-87 = -87
Which box plot represents the data?
30, 35, 25, 5, 5, 25, 40, 45, 50, 10, 15, 40
Answers
Explain how the difference of a fraction or a rational number and its additive inverse is equal to zero.
Answers
Hope This Helped =3
12 POINTS
Simplify i38.
i
−1
−i
1
Answers
Note that i^38 = i^32 * I^4 * I^2.
Note that i^0, i^4, i^8, etc., all equal 1. Therefore,
i^38 = (1)(1)i^2 = 1*(-1) = -1 (answer)
Answer:
-1
Step-by-step explanation:
I got this correct on my quiz
i^38 = -1
How many terms are in the arithmetic sequence 6, 2, −2, …, −102?
Hint: an = a1 + d(n − 1), where a1 is the first term and d is the common difference
27
28
29
30
Answers
6, 2, −2, …, −102
will evaluated as follows:
the explicit formula is:
an=a1+d(n-1)
a1=first term
d=common difference
n=number of terms
thus from the question:
a1=6
d=2-6=-4
an=-102
plugging the values in the expression we get:
-102=6-4(n-1)
solving for n we shall have:
-102-6=-4(n-1)
-108=-4(n-1)
27=n-1
thus
n=27+1
n=28
Answer: 28 terms
Final answer:
Calculate the number of terms in the arithmetic sequence 6, 2, -2, ..., -102 using the provided formula to find it is 28.
Explanation:
In mathematics, an Arithmetic Progression (AP) is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference, denoted by d.
Arithmetic sequence: 6, 2, -2, ..., -102
Formula: an = a1 + d(n - 1)
Identify a1 = 6 and an = -102Calculate d = an - a1 = -102 - 6 = -108Substitute the values into the formula and solve for n to find the number of termsTherefore, the number of terms in the arithmetic sequence is 28.
please verify my probability answer!!!
Answers
The probability that the second student likes to play baseball:[tex]P(B)=\dfrac{15}{24}=\dfrac{5}{8}[/tex]
Together:
[tex]P(A)\cdot P(B)=\dfrac{2}{5}\cdot\dfrac{5}{8}=\dfrac{1}{4}[/tex]
Answer:
1/4
Step-by-step explanation:
Hope this helped :)
GIVING AWAY 50 POINTS TO WHOEVER SHOWS LEGIT WORK!
The lengths of the sides of three squares are s, s + 1, and s + 2. If their total area is 365 cm squared (^2), find their total perimeter.
Answers
S+1 = one length square 2
S+2= one length square 3
Our equation would be
S^2+(S+1)^2+(S+2)^2=365
Idk if it would be called distribute but.. distribute
S^2+S^2+2S+1+S^2+4S+4=365
Add like terms
3S^2+6S-360=0
Divide everything. By 3
S^2+2S-120=0
Factor
(S-10)(S+12)=0
The two solutions are:
S-10=0
S=10
S+12=0
S=-12
Since a length can’t be a negative the only possible solution would be 10
Since a perimeter is all lengths added together we can multiply the length by four to get the perimeter
Square 1
10*4=40
Perimeter is 40cm
Square 2
S+1 =11
11*4=44
Perimeter is 44cm
Square 3
S+2=12
12*4=48
Perimeter is 48cm
Add all the perimeters together to get the total perimeter:
Total perimeter:
40+44+48=132
The total perimeter is 132cm
I hope this helps. Sorry if I messed up anything on here it was kinda hard to keep track of everything. Feel free to ask if you need anything cleared up :)
what equations is equivalent to y = log x
Answers
"log" standing alone actually means "logarithm to the base 10."
Thus, y = log x <=> y = log x
10
y
Stated another way (inverse functions), x = 10
A lucky integer is a positive integer which is divisible by the sum of its digits. what is the least positive multiple of 9 that is not a lucky integer?
Answers
It is not divisible by 18. Before that they are all added up to 9.
two angles are drawn below. the measure of angle x is 90
a. 20
b. 60
c. 100
d. 120
Answers
So the answer is B) 60
Beacuse that that is an acute angle and acute is less then 90
What is the area of a square
Answers
For example, if a square's length is 4cm, then you can assume the width is going to be 4cm. Finding area, you multiply 4 and 4 to get 16, and the unit of measurement (cm) and square it (^2). Thus meaning this answer would be 16cm^2.
I hope this helps!
Assuming a truck container holds 24 cases, how many cases would 6 truck containers hold?
Answers
6 truck will hold 144 containers in total
) a pair of fair dice is rolled. what is the probability that the sum of the top faces is a number 10 or greater?
Answers
the probability is 16.7%
Hope this helps.
In which type of quadrilateral are consecutive sides congruent?
Select the best answer from the choices provided.
trapezoid
parallelogram
square
rectangle
Answers
Final answer:
A square is the quadrilateral with congruent consecutive sides. It is an equilateral rectangle and a special type of parallelogram with equal-length sides and right angles.
Explanation:
The type of quadrilateral in which consecutive sides are congruent is a square. A square is a special type of parallelogram where all sides are equal in length and all angles are right angles. When considering a square as a rectangle (which technically it is), its diagonals (which are equal in length) bisect one another at right angles, suggesting the property of being an equilateral rectangle. Furthermore, in a larger context, if we treat the sides of any parallelogram symmetrically, such as in a notation [PQRS], the order can change to [QRSP], [QPSR], and [PRQS] without affecting its properties, which aligns with the symmetric nature of a square's sides.
The sum of the squares of two consecutive positive even integers is 100. find the two integers
Answers
6^2= 36
8^2=64
36+64=100
Let's denote the two consecutive positive even integers as x and x+2.
We know their squares sum up to 100, represented mathematically as:
x^2 + (x + 2)^2 = 100.
Expanding this equation, we get:
x^2 + x^2 + 4x + 4 = 100.
Combining like terms gives us:
2x^2 + 4x - 96 = 0.
This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 2, b = 4, and c = -96.
We can solve this quadratic equation for x using the quadratic formula:
x = [-b ± sqrt(b^2 - 4ac)] / 2a.
Substituting a, b, and c into this formula, we find that:
x = [-4 ± sqrt((4)^2 - 4*2*-96)] / 2*2,
x = [-4 ± sqrt(16 + 768)] / 4,
x = [-4 ± sqrt(784)] / 4,
x = [-4 ± 28] / 4.
So the solutions are x = (28 - 4) / 4 = 6 and x = (-28 - 4) / 4 = -8.
Since we are looking for positive even integers, we discard the negative solution.
Therefore, the two consecutive positive even integers are 6 and 6 + 2 = 8.
Can someone answer this question for me as well.
The equation tan-1 (9.4/8.2) = x can be used to find the measure of angle LKJ. What is the measure of angler LKJ? Round to the nearest whole degree.
*KL = 7.7 cm, LJ = 8.9 cm*
Answers
tan(x) = 9.4/8.2
x = (tan^-1)(9.4/8.2)
Simplifying gives:
x = (tan^-1)(1.146)
x = 48.9 degrees.
This is approximately equal to 49 degrees.
What is the maximum volume of a square pyramid that can fit inside a cube with a side length of 18 cm?
a. 5,832 cm
b. 2,916 cm
c. 1,944 cm
d. 972 cm
Find the volume of the cylinder in terms of Pie. The diagrams are not drawn to scale.
a. 52.8 m
b. 58.08 m
c.127.78 m
d. 29.04 m
Answers
we know that
[volume of a square pyramid]=(1/3)*b²*h
where
b is the length side of the square base-----> 18 cm (is equal to the length side of cube)
h is the height---------> 18 cm (is equal to the length side of cube)
[volume of a square pyramid]=(1/3)*18²*18----> 1944 cm³
the answer Part 1) is
c. 1,944 cm³
Part 2) Find the volume of the cylinder in terms of Pie. The diagrams are not drawn to scale.
volume of a cylinder=pi*r²*h
for r=2.2 m
h=12 m
volume of a cylinder=pi*2.2²*12-----> volume=58.08*pi m³
the answer Part 2) is
58.08*pi m³
During a radio contest, $50 is added to the prize money each time a caller answers the contest question incorrectly. if the first caller has a chance to win $100, which equation finds the amount the 10th caller receives, if the 10th is the first to answer the question correctly?
Answers
1. You have that $50 is added to the prize money each time a caller answers the contest question incorrectly and the first caller has a chance to win $100.
2. Therefore, the amount the 10th caller receives, if the this caller answers the question correctly, is:
x: the amount the 10th caller receives.
y: the number of caller
x=100+50(y-1)
As y=10 (the 10th caller), you have:
x=100+50(10-1)
x=100+50(9)
x=100+450
x=$550
Answer:
a is correct on edege
Step-by-step explanation:
Is 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 a number?
Answers
The points F(3, 5) and G(0, –4) are the endpoints of the graphed line segment. What are the coordinates of the point P on the line segment such that P is the length of the line segment from G?
Answers
The points F(3, 5) and G(0, –4) are the endpoints of the graphed line segment. Hence the required coordinate point is (9/4, 11/4).
What is the coordinate of the point which divides a line segment in a specified ratio?Suppose that there is a line segment [tex]\overline{AB}[/tex] such that a point P(x,y) lying on that line segment [tex]\overline{AB}[/tex] divides the line segment [tex]\overline{AB}[/tex] in m:n, then, the coordinates of the point P is given by:
[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)[/tex]
where we have:
the coordinate of A is[tex](x_1, y_1)[/tex]
and the coordinate of B is [tex](x_2, y_2)[/tex]
The coordinate point between two points P and G divided between ratios a and b is expressed as;
[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)[/tex]
Given the coordinate points F(3, 5) and G(0, –4) divided within the ratio 1:3
[tex](x,y) = \left( \dfrac{mx_2 + nx_1}{m+n} , \dfrac{my_2 + ny_1}{m+n} \right)\\\\(x,y) = \left( \dfrac{1(0) + 3(3)}{1+3} , \dfrac{1(-4)+ 3(5)}{1+3} \right)\\\\(x,y) = \left( \dfrac{9}{4} , \dfrac{11}{4} \right)[/tex]
Hence the required coordinate point is (9/4, 11/4).
Learn more about a point dividing a line segment in a ratio here:
https://brainly.com/question/14186383
#SPJ2
1. In an auditorium, there are 21 seats in the first row and 26 seats in the second row. The number of seats in a row continues to increase by 5 with each additional row.
(a) Write an iterative (explicit) rule to model the sequence formed by the number of seats in each row. Show your work.
(b) Use the rule to determine how many seats are in row 15. Show your work.
2. Rhonda started a business. Her business made $40,000 in profits the first year. Her annual profits have increased by an average of 6% each year since then.
(a) Write an iterative rule to model the sequence formed by the profits of Rhonda’s business each year.
(b) Use the rule to determine what the annual profits of Rhonda’s business can be predicted to be 20 years from the start of her business. Round your answer to the nearest dollar. Do not round until the end. Show your work.
3. The sequence 3, 12, 48, 192, … shows the number of pushups Kendall did each week, starting with her first week of exercising.
(a) What is the recursive rule for the sequence?
(b) What is the iterative rule for the sequence?
Answers
[tex]s_n=s_{n-1}+5[/tex]
Since [tex]s_1=21[/tex], we have
[tex]s_2=s_1+5[/tex]
[tex]s_3=s_2+5=s_1+2\cdot5[/tex]
[tex]s_4=s_3+5=s_1+3\cdot5[/tex]
[tex]\cdots[/tex]
[tex]s_n=s_{n-1}+5=\cdots=s_1+(n-1)\cdot5[/tex]
So the explicit rule for the sequence [tex]s_n[/tex] is
[tex]s_n=21+5(n-1)\implies s_n=5n+16[/tex]
In the 15th row, the number of seats is
[tex]s_{15}=5(15)+16=91[/tex]
2. Let [tex]p_n[/tex] be the amount of profit in the [tex]n[/tex]-th year. If the profits increase by 6% each year, we would have
[tex]p_2=p_1+0.06p_1=1.06p_1[/tex]
[tex]p_3=1.06p_2=1.06^2p_1[/tex]
[tex]p_4=1.06p_3=1.06^3p_1[/tex]
[tex]\cdots[/tex]
[tex]p_n=1.06p_{n-1}=\cdots=1.06^{n-1}p_1[/tex]
with [tex]p_1=40,000[/tex].
The second part of the question is somewhat vague - are we supposed to find the profits in the 20th year alone? the total profits in the first 20 years? I'll assume the first case, in which we would have a profit of
[tex]p_{20}=1.06^{19}\cdot40,000\approx121,024[/tex]
3. Now let [tex]p_n[/tex] denote the number of pushups done in the [tex]n[/tex]-th week. Since [tex]3\cdot4=12[/tex], [tex]12\cdot4=48[/tex], and [tex]48\cdot4=192[/tex], it looks like we can expect the number of pushups to quadruple per week. So,
[tex]p_n=4p_{n-1}[/tex]
starting with [tex]p_1=3[/tex].
We can apply the same reason as in (2) to find the explicit rule for the sequence, which you'd find to be
[tex]p_n=4^{n-1}p_1\implies p_n=4^{n-1}\cdot3[/tex]
Answer:
i will look but i think she was right
Step-by-step explanation:
A card is drawn from a standard deck of cards. Determine whether the events are mutually exclusive or inclusive. Then, find the probability.
P(a red card or a queen)
a.
inclusive, 15/26
c.
inclusive, 7/13
b.
mutually exclusive, 15/26
d.
mutually exclusive, 7/13
Answers
The two events are inclusive because they can both happen at the same time.
This means we find the probability using
P(A or B) = P(A) + P(B) - P(A and B)
P(r or Q) = P(r) + P(Q) - P(r and Q)
There are 26 red cards out of 52 cards.
There are 4 queens out of 52 cards.
There are 2 red queens out of 52.
26/52+4/52-2/52 = 28/52 = 7/13
The events are mutually inclusive and the required probability is p(getting a red or a queen) is 28/52 = 7/13
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here A card is drawn from a standard deck of cards. Now There are some events that can impact each other or that are overlapping. They have one or more outcomes in common. When events have outcomes in common, they are said to be overlapping events, also known as mutually inclusive events. Thus this event is defenitely inclusive.
Now the probability that a red card or a queen is =( 26 red cards + 2 black queens ) /52
= 28/52
=7/13
Hence, The events are mutually inclusive and the required probability is p(getting a red or a queen) is 28/52 = 7/13
Learn more about probability here:
https://brainly.com/question/30034780
#SPJ2
Bricklayers use the formula N = 7LH to estimate the number of bricks N needed to build a wall of height H and length L. What is the height of a wall that is 30 feet long and that requires 2,310 bricks to build? a. 12 ft c. 11 ft b. 10 ft d. 20 ft
Answers
N = 7LH
Clearing H we have:
H = N / (7L)
Substituting the values we have:
H = 2310 / (7 (30))
Rewriting we have:
H = 2310/210
H = 11 feet
Answer:
the height of a wall that is 30 feet long and that requires 2,310 bricks to build is:
c. 11 ft
What does a residual value of 1.3 mean when referring to the line of best fit of data set?
-a data point is 1.3 units above the line of best fit
-a data point is 1.3 units below the line of best fit
-the line of best fit has a slope of -1.3
-the line of best fit has a slope of 1.3
Answers
A residual value of 1.3, when referring to the line of best fit of a data set, means that,
⇒ a data point is 1.3 units above the line of best fit.
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
To find a residual value of 1.3 mean when referring to the line of best fit of data set.
Since, A residual is defined as the difference between the observed value of a dependent variable and the predicted value of that variable using the regression equation.
Hence, In this case, the residual value of 1.3 indicates that the observed value of the dependent variable is 1.3 units above the predicted value, or the line of best fit.
Thus,
A residual value of 1.3, when referring to the line of best fit of a data set, means that,
⇒ a data point is 1.3 units above the line of best fit.
Learn more about the equation of line visit:
https://brainly.com/question/18831322
#SPJ5
PLease dont answer if you dont know...
Use the Law of Sines to find side "b" of the triangle.
Answers
side a / sin (angle A) = side b / sin(Angle B)
Side a is opposite angle A, so from the picture we know side a = 50, angle A is 58 degrees and angle B is 48 degrees.
replace those values in the formula we get:
50 / sin(58) = b/ sin(48)
so now we can cross multiply the 2 fractions to get:
50 * sin(48) = b*sin(58)
to get b by itself, divide both sides by sin(58) to get:
b = (50*sin(48)) / sin(58)
b = 43.82
You may need to round the answer as needed.
the supplement of angle t is 4 times the measure of angle t
Answers
one angle = t
the other angle = 4 x t or 4t
so we now have t + 4t = 180
4 + 4t = 5t
so we have 5t = 180
divide both sides by 5:
t = 180 /5
t = 36
so angle t = 36 degrees
the other angle = 4 x 36 = 144 degrees