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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A photographer made a 5-inch by 8-inch print of a photo. He then made a 10-inch by 16-inch print of the same photo.
Which scale factor was used to create the larger photo from the smaller photo?
Can you help please.?
Answer:
2.33yd or 2 1/3yd
Step-by-step explanation:
7/3=2.33
Write an algebraic expression to represent the coast of m gallons of gassoline if each gallon coast $1.45
Answer:
$1.45m
Step-by-step explanation:
State the slope for the equation.
y=5x+8
Enter you answer in the box.
Slope: m=
Answer:
Step-by-step explanation:
The y-intercept of the equation is -8.
You can test this by making X = 0 and solving algebraically. Similarly, if you make y = 0, you can solve the X value. This means X = 8/5
Co-ordinates (8/5, -8)
a school has 400 feet of fencing to build a set of 3 athletic fields as shown below. What dimensions should they use to build the largest possible athletic complex. Include appropriate units with your answer.
The area of a shape is the amount of space it occupies.
The dimensions to build the largest possible athletic complex is 100 by 50 feet
Assume the length of the fence is y.
So, we have:
[tex]\mathbf{Area = xy}[/tex]
[tex]\mathbf{Perimeter = 2y + 4x}[/tex]
Substitute 400 for perimeter
[tex]\mathbf{2y + 4x = 400}[/tex]
Divide through by 2
[tex]\mathbf{y + 2x = 200}[/tex]
Make y the subject
[tex]\mathbf{y = 200 -2x}[/tex]
Substitute [tex]\mathbf{y = 200 -2x}[/tex] in [tex]\mathbf{Area = xy}[/tex]
[tex]\mathbf{Area =x(200 - 2x)}[/tex]
[tex]\mathbf{Area =200x - 2x^2}[/tex]
Differentiate
[tex]\mathbf{A' =200 - 4x}[/tex]
Set to 0
[tex]\mathbf{200 - 4x = 0}[/tex]
Collect like terms
[tex]\mathbf{4x = 200}[/tex]
Divide both sides by 4
[tex]\mathbf{x = 50}[/tex]
Recall that: [tex]\mathbf{y = 200 -2x}[/tex]
So, we have:
[tex]\mathbf{y = 200 - 2 \times 50}[/tex]
[tex]\mathbf{y = 200 - 100}[/tex]
[tex]\mathbf{y = 100}[/tex]
Hence, the dimensions to build the largest possible athletic complex is 100 by 50 feet
Read more about areas and perimeters at:
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a stock market fell 25 points the following day it dropped another 12 points what was the total change in the stock market after two days
Answer: its either c or b
Step-by-step explanation:
What is answer to 2 + 3m =
You can't really do anything with it cause it's fully simplified
Answer:
Nothing you can do because it is already simplified. So yea
Step-by-step explanation:
Hi i need help with this !
Answer:
4y+8x
Step-by-step explanation:
well, because that was the only one that did not have a line on desmos.
increase 600 by 8⅓ percent
Answer:
650
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
What is the unit rate of 124 pages and 2 hours
Answer:
62 pages per hour.
Step-by-step explanation:
Divide 124 ÷ 2.
Find the value of x. 1/2 - 15 = 2/5x - 7
Answer:
(Hope this helps can I pls have brainlist (crown)
Step-by-step explanation:
In pic
(Credit: Symbolab )
x = 80
Needs to show work.
Find the X intercept and the Y intercept for 2x-6y=12
Answer:
x: (6,0)
y: (0,-2)
Step-by-step explanation:
To find the x-intercept, substitute in 0 for y and solve for x . To find the y intercept, substitute in 0 for x and solve for y .
Ex -
X : 2x -6(0)=12
2x=12
2 cancels out with 2
12/2 = 6
Y: 2(0 )- 6y =12
-6y=12
negative 6 times negative 6 cancels
12/-6 = -2
Answer:
See Below
Step-by-step explanation:
Given: 2x-6y=12
Plug 0 in the equation for y:
y is zero
2x-6(0)=12
2x=12
The x-intercept: (6,0)
Plug 0 in the equation for x:
x is zero
2(0)-6y=12
−6y=12
The y-intercept: (0,−2)
A 2-column table with 9 rows titled December Temperatures. Column 1 is labeled Day with entries 1, 2, 3, 4, 5, 6, 7, 8, 9. Column 2 is labeled Temperature (degrees Fahrenheit) with entries 33, 34, 42, 36, 39, 36, 39, 40, 44.
What is the interquartile range for the data set?
The answer is 6
Answer:
Step-by-step explanation:
I really need points but good luck with your question
what is rhe vertex of the graph of the function f(x)=x²+6x+9
the nth term of a sequence is n(n-8)÷√n+3
find the 1st and 6th terms
Answer:
-4 and -2✓6+3
Step-by-step explanation:
use pemdas
1(1-8)÷✓1 + 3
-7÷1+3
-4
6(6-8)÷✓6+3
-12÷✓6+3
multiply fraction by ✓6 on bottom and top to get rid of square root on bottom
-12✓6÷6+3
divide -12 by 6 and put radical next to it
-2✓6+3
Show all work to multiply quantity 6 plus the square root of negative 64 end quantity times quantity 3 minus the square root of negative 16 end quantity
Answer: 50
Step-by-step explanation:
[6+√-64] × 3-√-16
(6+8i)(3-4i)
6(3-4i)+8i(3-4i)
18-24i+24i+32
18+32=50
the answer is 50Answer:
fifty
Step-by-step explanation:
fifty
If y varies directly with x which equation describes x = 72 and y = 36?
Answer:
k = 1/2
Step-by-step explanation:
direct variation equation is y = kx where 'k' is the constant of variation
substitute 36 for 'y' and 72 for 'x' to get:
36 = 72k
solve for 'k' to get:
k = 36/72 or k = 1/2
No one answered the palm tree question so I will put this question up for 15 points. Please answer now it’s due!
Answer:
15 feet
Step-by-step explanation:
Answer:
15 feet is the answer ok
Pls answer the question in the photo
Answer:
correct answer to the problem is x= -9
Joe answered correctly.
Answer: nick
Step-by-step explanation: subtract 6 from both sides to get 0 on one side and then divide both sides by 2 to get x on its own
Which equation represents a line which is parallel to the line 3y−2x=−24?
Answer:
Any equation of the line with slope 2/3.
Parallel lines have identical slope.
Step-by-step explanation:
3y - 2x = - 24
3y = 2x - 24
y = 2/3x - 8
Students were asked to find an equivalent value of the expression 13 divided by 19/100 which could a student use?
Answer:
68.4210526316
you first divide 19/100 and then you divide the out put 13/ 0.19
Step-by-step explanation:
Find the mass of 250 ml of water. The density of water is 1 g/ml.
D= Density
M=
Volume - 10ml
What is the Mass?
V=
Mass - 70
Density
Alaalam
Answer:
250g
Step-by-step explanation :
250ml x 250g/ml = 250 g
To get the mass (in grams), you need to divide the ml's off and get the g alone.
can anyone heelp me pls
Answer:
lotion 3,. suspension 2, capsule 1 , I think
i rlly need help help me out pls
Answer:
San francisco
Step-by-step explanation:
once you divide the distance by time then multiply the answer by the longest amount of time (aka 4)
San francisco = 2556
Minot = 1826
Phoenix = 2252
James has $10 less than three times the amount Amy has. Which expression represents James' amount if Amy has d dollars?
Answer:
james has 3d-10
Step-by-step explanation:
Amy has d dollars
james has 10 less than 3 times Amy's amount
so the answer will be 3d - 10
hope it helps : )
The expression that represents James' amount is 3d - 10. Then the correct option is A.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
A sentence-to-equation translation is a process of turning a given statement into an expression or equation.
James has $10 less than Amy, who has three times as much money.
Let d be the amount Amy has. Then the expression is given as,
⇒ 3d - 10
The expression that represents James' amount is 3d - 10. Then the correct option is A.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ5
The missing options are given below.
a) 3d - 10
b) 10 - 3d
c) 3d - 30
d) 30 - 3d
Erin ran 5 km in 25 minutes. What is her speed in km per minute? (Answer as a decimal)
Answer:
what what what what what what what what
Which graph represents the function f(x)=0.5x+4?
Which graph represents the function f(x)=−2x−1?
Answer:
Step-by-step explanation:
1.)The 4th picture will be the correct one.
Step-by-step explanation:
The first picture shows the graph of f(x) and in the options there are pictures of graph of g(x) = f(x) -1
So, it is clear from the equation of the functions that the graph of f(x) and g(x) will be similar but the the y value in g(x) will be 1 less than the y value in f(x) corresponding to a certain x value.
So, the graph will translate down by 1 unit.
Therefore, the 4th picture will be the correct one.
2.)-(2^x) - 1 will have a y-intercept of -1-1 = -2, a horizontal asymptote of y=-1, and will be decreasing everywhere. The third selection is the graph that has these characteristics.
Answer:
graph 4
Step-by-step explanation: because I love you <3 ;)
solve both pls brainliest
Answer:
x= 4.66
v-9= 63
Step-by-step explanation:
Hope this helps! :)
*Victor was 72 btw*
In the rectangle below, AE = 2x+5, CE=5x-13, and mZECD=28°.
Find BE and m ZEBC.
А
WO
B
E
B
B
m ZEB
D
С
Answer:
https://www.portnet.org/cms/lib6/NY01001023/Centricity/Domain/290/Scanned-image.pdf
Step-by-step explanation:
...
What is the slope of the line?
Answer:
-3
Step-by-step explanation:
we take two points to find slope m
lets take ( 1, 4) and ( 2, 1)
then m=(1-4)/(2-1)
m=(-3)/(1)
m= -3