We need to differentiate this with respect to x to see if we can find an expression for the derivative of y at various points. That will be the slope of the tangent to the curve. Then we want to see where that derivative might be infinite -- i.e., where the tangent is vertical.
It's not written as a function, but it can still be differentiated using the chain rule:
x2 + xy + y2 = 3
(2x) + (x dy/dx + y dx/dx) + (2y dy/dx) = 0
(I used parentheses to show the differentiation of each term in the original equation.)
2x + x dy/dx + y + 2y dy/dx = 0
2x + y = -x dy/dx - 2y dy/dx
2x + y = dy/dx (-x -2y)
-(2x + y)/(x + 2y) = dy/dx
We have the derivative of y, but it's defined partly in terms of y itself. That's OK. Let's go on...
So where would the slope be infinite? That would happen when x + 2y = 0, or y = -x/2
Let's plug that in for y in the original equation to find points where that's the case.
x2 + xy + y2 = 3
x2 + x(-x/2) + (-x/2)2 = 3
x2 - x2/2 + x2/4 = 3
3x2 / 4 = 3
x2 = 4
x = ±2
So we have two x values where the tangent might be vertical. Let's plug them into the equation and see what the y values are. First x = 2...
x2 + xy + y2 = 3
4 + 2y + y2 = 3
y2 + 2y + 1 = 0
(y + 1)2 = 0
y = -1
So at the point (2, -1) the tangent is vertical.
Now try x = -2...
x2 + xy + y2 = 3
4 - 2y + y2 = 3
y2 - 2y + 1 =0
(y - 1)2 = 0
y = 1
So at the point (-2, 1) the tangent is vertical.
Find the
17th
term of the arithmetic sequence whose common difference is d=5 and whose first term is a1 = 1.
The [tex]17th[/tex] term of the arithmetic sequence is [tex]81[/tex]
An arithmetic sequence is a sequence of numbers produced by adding a fixed number, called the common difference, to a term in the sequence to get the next term of the sequence.
The formula for calculating the [tex]nth[/tex] term of a sequence is
[tex]a_n=a_1+(n-1)d[/tex]
where
[tex]a_n=\text{the nth term}\\a_1=\text{the first term}\\d=\text{the common difference}[/tex]
from the question
[tex]n=17\\d=5\\a_1=1[/tex]
from this information, we can calculate the [tex]17th[/tex] term of the sequence thus
[tex]a_n=a_1+(n-1)d\\a_{17}=1+(17-1)\times5\\=81[/tex]
so, [tex]a_n=81[/tex]
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Write the equation of the line in slope-intercept form that passes through (-3, -5) and (0, 4).
Answer:
y = 3x + 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, - 5 ) and (x₂, y₂ ) = (0, 4 )
m = [tex]\frac{4-(-5)}{0-(-3)}[/tex] = [tex]\frac{4+5}{0+3}[/tex] = [tex]\frac{9}{3}[/tex] = 3
The line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = 3x + 4 ← equation of line
What is the median of these numbers 9, 10, 6, 5, 6
Answer:
6.
Step-by-step explanation:
First you put the numbers in order, 5, 6, 6, 9, 10 then you find the number in the middle, which in this case is 6.
What is the slope of the line with the equation: y+6=24-2x
pleeaseeee
Answer:
The slope is -2
Step-by-step explanation:
y+6=24-2x
y=18-2x
y=-2x+18
Answer:
Slope = -2
Step-by-step explanation:
Changing this problem (y+6=24-2x) to Slope Intercept form turns it into y=-2x+18.
the formula is written as y=mx+b m=slope b=y-intercept and x & y being a certain number that is unknown . Therefore, the slope of the equation y=-2x+18 will be
m=-2/1 rise/run
Find the product
(-2) (7)
Answer:
-14
Step-by-step explanation:
Remember that a negative times a positive is negative:
(-2)(7) = -(2)(7) = -14
"The square root of two times a number subtract five is equal to ten."
It would be √2 x n - 5 = 10.
What type of number is 12/3?
Choose all answers that apply:
A) Whole number
B) Integer
C) Rational
D) Irrational
Pls help it’s for a test
Answer: All except Irrational
Step-by-step explanation:
12/3 = 4, 4 is an integer, a whole number, and it is rational.
hey i really need help its 11:32 where I am and this assignments due at 12:00
please!!!!
Answer:
3: 67 5:200% 6: 50% 7: 32 8) 20
Step-by-step explanation:
To train for an upcoming marathon, Susie plans to run 2 miles per day the first week and then increase the daily distance by a half a mile each of the following weeks.
There are many ways to approach this problem.
Week Miles
1 2
2 2.5
3 3
4 3.5
5 4
6 4.5
Write an equation to represent the nth term of the sequence.
Answer:
f(x)= .5x + 2
Step-by-step explanation:
Now this is not to complicated
first the constant is 2
after each day she gains .5 miles
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation to represent the nth term of the sequence is y=0.5x+2.
What is the equation of a line?A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
Let the distance travelled by Susie in any week,x be represented by y.
Given that Susie will run 2 miles in the initial or in the first week. Therefore, the distance for the initial work week will be,
Initial distance = y-intercept = c = 2
Further, if the daily distance is increased by half a mile each of the following weeks. Therefore, the slope of the equation is the change in the distance, therefore, we can write,
Slope, m = Change in the distance = 0.5
Now, if the equation represents the nth term of the sequence, then we can write,
y = mx + c
y = 0.5x + 2
Hence, the equation to represent the nth term of the sequence is y=0.5x+2.
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A tank is 5 metre long 3 metre wide and 1 m high. how many litre of water can it hold?
Answer:
15,000 liters
Step-by-step explanation:
First, find the volume in meters. 5*3*1=15 meters
1 meter = 1000 liters
(x15)
15 meters = 15000 liters
Hope this helped :D
mr. jessup and mr allen i ready mathematics pages 77 and 78
Pls help me it’s due at 12:00
Step-by-step explanation:
# easy learning
good luck and god Blees
If my friend answers this question under 5 seconds he's a god
x = 9
Scale size is 3 so multiply all terms in ABC by 3.
PLEASE HELP ASAP What is the m and b for this graph??
Answer:
m = - 1 and b = - 1
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 2) and (x₂, y₂ ) = (2, - 3) ← 2 points on the line
m = [tex]\frac{-3-2}{2-(-3)}[/tex] = [tex]\frac{-5}{2+3}[/tex] = [tex]\frac{-5}{5}[/tex] = - 1
b is the y- intercept, that is where the graph crosses the y- axis.
line crosses the y- axis at (0, - 1 ) ⇒ b = - 1
its graphing linear inequalities
if u can help that would be nice
Answer:
y>_ 5/3x+3 is the answer.
Step-by-step explanation:
The graph of the function has slope of 1 and y-intercept of -6.
Answer:
y=1x-6
Step-by-step explanation:
y=mx+c
c = -6
m = 1
therefore
y= mx+c
y = 1x-6
(3,6) in a 180 degree rotation
Answer:
(-3,6)
Step-by-step explanation:
There's a formula for this, but it's just reflecting it across the y-axis.
Hope this helped! :)
Name an angle adjacent to FGI
JGI
HGJ
DGE
HGE
Answer:<JGI
Explanation:
Any angle with the letter H can not be as it is on the opposite side. Leaving you with <JGI and <DGE. <DGE is beside angles DGF and angle EGH
Hope this helps.
The adjacent angle of the angle ∠FGI will be ∠JGI. Then the correct option is A.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
An angle is a structure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located.
Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.
From the figure, the contiguous point of the point ∠FGI will be ∠JGI. Then the right choice is A.
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Simplify.
8^15÷8^−3
Enter your answer as a number to a power, using the ^ symbol to indicate exponents. For example, to enter 4253, type it like this: 42^53
PLEASE THIS HAS TAKEN ME AN ENTIRE DAY I HAVE NO IDEA HOW TO DO THIS
Answer:
[tex]8^{18}[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex]a^{m}[/tex] ÷ [tex]a^{n}[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]8^{15}[/tex] ÷ [tex]8^{-3}[/tex]
= [tex]8^{(15-(-3))}[/tex]
= [tex]8^{(15+3)}[/tex]
= [tex]8^{18}[/tex]
The simplified form is 8^18
What are Exponents?The exponent of a number shows how many times the number is multiplied by itself. For example, 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times. Here, 2 is called the "base" and 4 is called the "exponent" or "power." In general, xn means that x is multiplied by itself for n times.
Properties of ExponentsThe properties of exponents or laws of exponents are used to solve problems involving exponents. These properties are also considered as major exponents rules to be followed while solving exponents. The properties of exponents are mentioned below.
Law of Product: am × an = am+nLaw of Quotient: am/an = am-nLaw of Zero Exponent: a0 = 1Law of Negative Exponent: a-m = 1/amLaw of Power of a Power: (am)n = amnLaw of Power of a Product: (ab)m = ambmLaw of Power of a Quotient: (a/b)m = am/bmGiven:
8^15÷8^−3
Using
a^m / a^n = a^( m-n)
So,
8^15÷8^−3
=8^(15-(−3))
=8^(15 +3)
=8^18
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heather is a hairdresser and her customers pay $5 to reserve an appointment time and $12 for every hour heather works on their hair style.as back to school special she offers to lower her price per hour by $5 what equation represents the total amount paid to heather,y,after x hours of hair styling
Answer:
y = 5 + 7x
Step-by-step explanation:
So 5 is going to be a constant factor. So Y is gonna equal 5 plus something. 12 dollars for every hour is 12x and there is a 5 dollar discount. 12-5 = 7 and so it is 7 dollars per hour.
So the total cost Y equal the constant 5 and 7x
Y = 5 + 7x
Charnise uses 3 gal. red paint to 5 gal. white paint to make pink paint. She
needs 24 gal. of pink paint. How many gallons of red paint will she need?
The method into creating pink paint is mixing 3 gallons of red paint and 5 gallons of white paint together. This mixture only creates 8 gallons of paint and she needs 16 more. List the factors of 16:
1, 2, 4, 8, and 16
We notice that 8 can be factored out of 16 and becomes:
16 / 8 = 2
If we multiply the sample by 3 (the one already counted plus the two extra), we can discover how much paint is needed. Multiply everything by 3:
3 x 3 = 9
5 x 3 = 15
So in this case, 15 gallons of white paint and 9 gallons of red paint are need and combine for 24 gallons in total.
The x-intercept of the graph of f(x)= 3 log (x+5)-2 is
Answer:
26
Step-by-step explanation:
do the math
HELP ME GUYS PLEASE!!! :)
Answer:
(10,-2)
Step-by-step explanation:
You can see that the first equation has already given as x-isolated equation aka x = 10.
With this, you can substitute x = 10 in the second equation 3x+5y = 20 then solve for y.
3(10)+5y=20
30+5y=20
Subtract both sides by 30.
5y=-10
Divide both sides by 5.
y=-2
So from x = 10 and y = -2, we can write as (10,-2) in coordinate form.
Answer:
(10,-2)
Step-by-step explanation:
since they already give u x, u can just sub it into the other equation
3(10)+5y=20
30+5y=20
5y=20-30
5y=-10
y=-2
Can someone please
Help me with this graph
Answer:
graph the slope and the -2
Step-by-step explanation:
first, plot a point at (0,-2) because of the -2 as the y intercept
then, start graphing ur slope
ur next points should be
(2,-1), (4,0) (6,1) and so on
2. A group of 40 subjects was divided into two groups with one group given an energy drink and one group
given water. The subjects were then given a spelling test and
the mean number of words correctly spelled was
recorded for each member of the two groups. This experiment was designed this way to quantify which of the
following types of variability?
(1) natural
(3) induced
(2) sampling
(4) measurement
The design of the experiment was done to quantify induced variability.
What is induced variability?
Induced variability is when a variable that is not naturally present in the experiment is introduced into the experiment in order to test the response of respondents to the variable introduced. The artificial variable that was introduced into the experiment was energy drinks.
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what is -7/9 x -2/3 in simplest form
Answer:
heres my fake account and name
Step-by-step explanation:
How much warmer is 82 than -40?
Pls help
Answer:
122 degrees
Step-by-step explanation:
Take the warmer temperature and subtract the colder temperature
82 - (-40)
82+40
122
The difference is 122
Solve the following inequality.
20 < 8
Answer:
x > 12/7
x > 1 5/7
Step-by-step explanation:
7x + 8 > 20
Subtract 8 from each side
7x+8-8 > 20-8
7x > 12
Divide each side by 7
7x/7 > 12/7
x > 12/7
Changing to a mixed number
x > 1 5/7
WILL GIVE BRAINLY,5 STARS,AND THANKS
Answer: Yes, he does.
Step-by-step explanation:
55 x 12 = 600 Also can I see the answers for the question
If the Plane moves at 253km southwest and the wind blows from 60' south east.
Calculate the Age of the Pilot.