Find an equation of the tangent line to the hyperbola x2 a2 − y2 b2 = 1 at the point (x0, y0).
The equation of the tangent line is [tex]y = \frac{b^{2} x_{0}x }{a^{2} y_{0} } - \frac{b^{2} x_{0}^{2} }{a^{2} y_{0} } + y_{0}[/tex]
To find the tangent to the hyperbola [tex]\frac{x^{2} }{a^{2} } - \frac{y^{2} }{b^{2} }[/tex] at (x₀, y₀), we differentiate the equation implicitly to find the equation of the tangent at (x₀, y₀).
So, [tex]\frac{d}{dx} (\frac{x^{2} }{a^{2} } - \frac{y^{2} }{b^{2} }) = \frac{d0}{dx}\\\frac{d}{dx} \frac{x^{2} }{a^{2} } - \frac{d}{dx}\frac{y^{2} }{b^{2} }= 0\\\frac{2x }{a^{2} } - \frac{dy}{dx}\frac{2y }{b^{2} } = 0\\\frac{2x }{a^{2} } = \frac{dy}{dx}\frac{2y }{b^{2} } \\\frac{dy}{dx} = \frac{b^{2}x }{a^{2}y }[/tex]
So, at (x₀, y₀)
[tex]\frac{dy}{dx} = \frac{b^{2} x_{0} }{a^{2} y_{0} }[/tex]
So, the equation of the tangent line is gotten from the standard equation of a line in point-slope form
So, [tex]\frac{y - y_{0} }{x - x_{0} } = \frac{b^{2} x_{0} }{a^{2} y_{0} } \\y - y_{0} = \frac{b^{2} x_{0} }{a^{2} y_{0} }(x - x_{0}) \\y = \frac{b^{2} x_{0} }{a^{2} y_{0} }(x - x_{0}) + y_{0} \\y = \frac{b^{2} x_{0}x }{a^{2} y_{0} } - \frac{b^{2} x_{0}^{2} }{a^{2} y_{0} } + y_{0}[/tex]
So, the equation of the tangent line is [tex]y = \frac{b^{2} x_{0}x }{a^{2} y_{0} } - \frac{b^{2} x_{0}^{2} }{a^{2} y_{0} } + y_{0}[/tex]
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What is the dependent quantity?
A) types of food I eat
B) not enough information
C) cholesterol levels
Answer?: I believe its C
No Explanation Because No
Answer: C is the answer
Step-by-step explanation:
A baseball team played 75 games and lost 20% of them. How many games did the team lose?
O 15
O 20
O 55
O 60
Answer: 15
Step-by-step explanation: 20% → .20
.20 x 75 = 15
The grocery store is having a sale on frozen vegetables. 3 bags are being sold for $10.35. At this rate, what is the cost of 7 bags?
Answer:
24.15
Step-by-step explanation:
10.35 x 2 = 20.7 But you still need 1 bag 1/3 of 10.35 = 3.45 Add all of them up = 24.15
What is the length of side s of the square shown below? 45° 6 30
A. 34
B. 6
C. 3
D. 6-2
E. 2
F. VE
Answer:
The correct answer should be D.
Step-by-step explanation:
-79=7w+3(4w-1) all steps please and quick
solve the system by elimination
x - y = -1
4x + 6y = -74
a) no solution
b) infinite number of solutions
9514 1404 393
Answer:
one solution: (x, y) = (-8, -7)
Step-by-step explanation:
We can add 6 times the first equation to the second equation in order to eliminate y.
6(x -y) +(4x +6y) = 6(-1) +(-74)
10x = -80
x = -8
y = x+1 = -7 . . . . . solve the first equation for y; substitute x
The one solution is (x, y) = (-8, -7).
solve pls brailiest!
Answer:
73,if you need explanation then let me know, always happy to help anyone! btw if you could give me brainliest then that would be great, i also undestand if not because im not the first to answer so dont be shy and hit theirs with brainliest if you want! :))
Step-by-step explanation:
(5x+4)-3x
Solve.
No scam.
Answer:
=2x+4
Step-by-step explanation:
Let's simplify step-by-step.
5x+4−3x
=5x+4+−3x
Combine Like Terms:
=5x+4+−3x
=(5x+−3x)+(4)
=2x+4
Answer:
2x+4
Step-by-step explanation:
Hope fully it is correct
Help please !!!!!!!!!!!
Answer:i have no Step-by-step explanation:
a
Find the domain and range for the function shown in the
graph given below.
Answer:
d{0 less than or equal to x less than or equal to 20, xer}
r{0 less than or equal to y less than or equal to -6,yer}
Step-by-step explanation:
The Domain and Range of the graph given is -
Domain ↔ [1, -6]
Range ↔ [- 21, 20]
We have a graph as shown in the figure.
We have to determine its domain and range.
What do you mean by domain and range of a function?For any function y = f(x), Domain is the set of all possible values of y that exists for different values of x. Range is the set of all values of x for which y exists.
According to question, we have -
From the graph it is clear that -
The values of y belong to the set - [1, -6]
and
The values of x belong to the set - [- 21, 20]
Therefore, according to the definition of domain and range -
Domain ↔ [1, -6]
Range ↔ [- 21, 20]
Hence, the Domain and Range of the graph given is -
Domain ↔ [1, -6]
Range ↔ [- 21, 20]
To solve more questions on finding the domain and range of functions, visit the link below -
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What is an acute- angled triangle?
A.) Has 3 acute angles
B.) Has 1 right angle
C.) Has one acute angle
D.) Has 1 obtuse angle
Answer:
c
Step-by-step explanation:
Find the equation of the linear function represented by the table
y 6 9 12 15
x 1 2 3 4
9514 1404 393
Answer:
y = 3x +3
Step-by-step explanation:
The slope of the line can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
Using the first two sets of table values, this is ...
m = (9 -6)/(2 -1) = 3/1 = 3
You can find the point-slope equation using the form ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -6 = 3(x -1) . . . . . using the first point in the table
Solving for y gives ...
y = 3x -3 +6 . . . eliminate parentheses, add 6
y = 3x +3
What are the measures for the nuber angles
1. 75
2. 105
3. 105
4. 75
6. 105
7. 105
8. 75
Is there a relationship between the distance and the sum? Is there a relationship between the distance and the difference? A 5-column table with 3 rows. Column 1 is labeled a with entries 1, 4, negative 6. Column 2 is labeled b with entries 2, negative 1, negative 3. Column 3 is labeled a + b with entries 3, 3, negative 9. Column 4 is labeled a minus b with entries negative 1, 5, negative 3. Column 5 is labeled Distance with entries 1 unit, 5 units, 3 units. Which describes the relationship between the distance and the difference? The distance is always the opposite of the difference. The distance is exactly the difference. The distance is the absolute value of the difference. The distance is not related to difference.
Answer:
The distance is the absolute value of the difference. aka c
Step-by-step explanation:
help me for brainliest
Write an equation in slope intercept form that goes through the point (5,-7) and is PARALLEL to the line y=-3x+8
Answer:
there is no line parallel to y = -3x + 8 that goes through (5, -7). this point falls on this line
Step-by-step explanation:
[tex]y = - 3x + 8[/tex]
[tex] - 7 = - 3(5) + b \\ - 7 = - 15 + b \\ b = 8[/tex]
The answer is
[tex]y = - 3x + 8[/tex]
solve pls brainliest
Help finding the missing length
Answer:
4x2-6x+6
Step-by-step explanation:
(9x2-2x) +(3x-5)+(m) =13x2-5x+1
(13x2-5x+1)-(9x2+x-5)=m
Find the product of 44.6 and 2.24.
(Show your work)
Answer:
46.84
Step-by-step explanation:
Add the decimals first to get .84 then add the real numbers to get 46.
trong dân số một bà 70 tuổi có khả băng SLE là 2% .Nếu ANA dương tính thì khả năng bị bệnh SLE là bao nhiêu
Answer:
từ khoảng 70 đến 90 phần trăm
1. The value of angle A is
50°. What is the value of
angle B?
Answer:
130º
Step-by-step explanation:
a line is 180º so if one angle is 50 then it's just 180-50
What graph represents a function with a growth factor of 5?
Answer:
The answer should be C!
Step-by-step explanation:
When you multiply the y value 0.04 and 5 it comes out as 0.02.
Write 0.00000000568 in proper scientific notation.
Answer:
568 to the negative power of 8
so. -8
568
three angles of a quadrilateral are 34°, 70° and 126°. find the measure of the fourth angle.
Answer:
130 will be correct answer
Step-by-step explanation:
The three angles are
34° 70° and 126°
we have to find fourth angle
let us consider fourth angle as X
The sum of quadrilateral is 360°.
So
34°+70°+126°+ x = 360°
130+X =360°
X = 360°-130°
X = 230°
Here we got the fourth angle
What is the value of y?
Y
Y
60
O A. 120°
B. 60°
C. 40°
O D. 30°
Answer:
B. 60°
Step-by-step explanation:
1. The measure of all angles in a triangle sum up to 180°. This means that y + y + 60 = 120.
2. (Solving)
Step 1: Simplify both sides of the equation.
[tex](y+y)+(60)=180[/tex] [tex]2y + 60 = 180[/tex]Step 2: Subtract 60 from both sides.
[tex]2y + 60 - 60 = 180 - 60[/tex] [tex]2y = 120[/tex]Step 3: Divide both sides by 2.
[tex]\frac{2y}{2}=\frac{120}{2}[/tex] [tex]y = 60[/tex]Step 4: Check if solution is correct.
[tex](60)+(60)+60 = 180[/tex] [tex]120 + 60 = 180[/tex] [tex]180 = 180[/tex]Therefore, the answer is B. 60°.
hi could someone explain this??
im thinking it is J=50(15)^t???
Answer:
J=15t+50
Step-by-step explanation:
The equation to represent this situation will be in the form J=mt+b where b is the starting value of love units, m represents the "love units" that are multiplied by the number of week, t is the number of weeks, and J represents Jack's love at that specific week.
The equation becomes: J=15t+50
To check, the equation should equal 50 when t=0, 65 when t=1, and 80 when t=2.
Checking t=0:
J=15(0)+50=0+50=50
Checking t=1:
J=15(1)+50=15+50=65
Checking t=2:
J=15(2)+50=30+50=80
The equation J=15t+50 does model the behavior of Jack's love at any week t based on the given data. Note that the equation used was based on slope intercept form (y=mx+b) due to the given data having a linear relationship.
Given that the function graphed is ƒ(x), what is ƒ(1)?
A) −2
B) −1
C) 1
D) 2
Answer: -2
Step-by-step explanation:
Which best describes the association between variables x and y
A rectangular cake pan has a volume of
234
cubic inches. If the length of the pan is
9
inches and the width is
13
inches, what is the height of the pan?
Step-by-step explanation:
volume of a rectangular pan = length of the pan × width of the pan × height of the pan
V=l.b.h
234=9.13.h
h=234/9×13
h= 2in.
hope this helps you.
Answer:
2 inches
Step-by-step explanation:
V= 234, L=9, W=13, H=?
V= LxBxH
234= 9x13xH
234= 117H
divide through by 117
234/117 = 117H/117
H= 2inches