Answer:
B) L(x) = -x + 2
Step-by-step explanation:
To find the tangent at (1,1), we differentiate x² - ln(x/y) = 1 with resect to x.
So, x² - ln(x/y) = 1
x² - (lnx - lny) = 1
x² - lnx + lny = 1
differentiating both sides with respect to x, we have
d{x² - lnx + lny]/dx = d1/dx
dx²/dx - dlnx/dx + dlny]/dx = d1/dx
2x - 1/x + 1/y(dy/dx) = 0
1/y(dy/dx) = 1/x - 2x
dy/dx = y(1/x - 2x)
dy/dx evaluated at (1,1) is
dy/dx = y(1/x - 2x)
= (1)(1/1 - 2(1))
= 1 - 2
= -1
This is the gradient of the tangent line.
To find the equation of the tangent line, we use (y - y')/(x - x') = m where y' = 1, x' = 1 and m = gradient of line = dy/dx = - 1
(y - y')/(x - x') = m
(y - y')/(x - x') = dy/dx
(y - 1)/(x - 1) = -1
cross-multiplying,
y - 1 = -1(x - 1)
expanding the bracket, we have
y - 1 = -x + 1
adding + 1 to both sides, we have
y -1 + 1 = -x + 1 + 1
y = -x + 2
So, L(x) = -x + 2
what is true about the solution to the system of inequalities shown? y < 1/3x -1
y<1/3x-3
Answer:
Step-by-step explanation:
All values that satisfy y ≤ (1/3)x - 3 are solution
which number liin shows -5x+10>-15
A. -10 to 1
B. 5 to 10
C. 1 to 10
D. -10 to 5
A tour guide climbs a mountain. When he reaches the top he is 356 ft above sea level. Therewhile, a deep sea diver descends to a depth of -24 ft. What is the vertical distance between the two people?
Answer:
b
Step-by-step explanation:
Geometry problem plz help?
Step-by-step explanation:
let eqn be y = mx + b.
m = (9 - 1)/(2 - 4) = -4
sub (4, 1):
1 = -4(4) + b
b = 17
therefore, it's y = -4x + 17
Topic: coordinate geometry
If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!
It is estimated that there are 828 motor vehicles in the US it is estimated that there are 828 Motor vehicles in the US for every 1,000 people. If the number of
motor vehicles in the US is 260 million, then what is its population to the nearest million?
A) 215 million B) 314 million C) 315 million D) 475 million PLZ HELP I NEED THIS QUESTION ANSWERED QUICKLY!!!!
Answer:
314 million
Step-by-step explanation:
Given that :
Number of motor vehicle in the U.S for every 1000 people = 828
If the number of motor vehicle in the United States = 260 million
Then,
Let x = number of people Given number of vehicles = 260,000,000
1000 people = 828 vehicles
x = 260,000,000
828x = (260,000,000 * 1000)
828x = 260,000,000,000
x = 314009661. 835
x = 314 million (approx)
The factors from least to greatest are
Answer:
wheres the picture?
Step-by-step explanation:
im ready but i dont know the problem
Simplify (5(2x^2 y^3 )^2)/(2x^3 y^4 )^3 PLease show work
Answer:
5*4 x^4 y^6 /8 x^9 y^12
20 /8 x^5 y^6
5/2 x^5 y^6
Step-by-step explanation:
Find all the missing elements. NEED HELP PLZZZZ
Answer:
B=42°C=98°c=10.7 unitsStep-by-step explanation:
Given
Angle A = Ф = 40°a=8b=7We know that trigonometric ratio as
sin Ф = opposite/hypotenusecos Ф = adjacent/hypotenusetan Ф = opposite/adjacentas
sin A = sin 40 = opposite/hypotenuse
From the diagram, it is clear that the opposite of angle A is a=8 and the hypotenuse is 'c'.
also the angle
sin A = sin 40 = opposite/hypotenuse = a/c = 8/c
sin 40 = 8/c
c = 8/sin 40
c = 8/0.745
c = 10.7
so the value of c will be: 10.7 units
so
tan B = opposite/adjacent
= b/a
= 0.9
[tex]B=\tan ^{-1}\left(0.9\right)[/tex]
[tex]=42^{\circ \:}[/tex]
Therefore, the value of B = [tex]42^{\circ \:}[/tex]
As the sum of the angles of triangle ABC is 180.
i.e.
A+B+C = 180
(40)° + (42)° + C = 180°
C = 180° - 40° - 42°
= 98°
Therefore, the value of C = 98°
Hence,
B=42°C=98°c=10.7 unitsplease help I'm actually crying! Find A and B if the graph of Ax + By = 7 passes through (2,1) and is parallel to the graph of 2x - 7y = 3.
Look at the Pictures:
What is the purpose of having a Institutional Review Boards?
Answer:
This group review serves an important role in the protection of the rights and welfare of human research subjects. The purpose of IRB review is to assure, both in advance and by periodic review, that appropriate steps are taken to protect the rights and welfare of humans participating as subjects in the research
Greta uses 2oz of pasta to make 2/3 of a serving of pasta.How many oz of pasta are there per serving
Answer:
3oz of pasta per serving
Step-by-step explanation:
Given parameters:
Number of oz of pastas used = 2oz
Quantity of serving = [tex]\frac{2}{3}[/tex]
Unknown:
Number of oz of pasta per serving = ?
Solution:
To solve this rate problem use;
Number of oz of pasta per serving = [tex]\frac{number of oz of pasta}{number of serving}[/tex]
Number of oz of pasta per serving = [tex]\frac{2}{\frac{2}{3} }[/tex] = 2 x [tex]\frac{3}{2}[/tex] = 3oz of pasta per serving
A large cooler full of water is being drained. The relationship between the amount of water in the cooler in liters and the number of minutes the cooler is draining is shown
the provided graph. What is the meaning of the intercept in this situation?
Answer:
The cooler is empty after 15 minutes.
Step-by-step explanation:
(-8,7), m=5
Y-7=5(x+8)
Answer:
The line of the equation is:
[tex]y-7=5\left(x+8\right)[/tex]
Step-by-step explanation:
Given
m=5point (-8, 7)As the point-slope form is given by
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope
substituting the values m=5 and the point (-8, 7)
[tex]y-7=5\left(x-\left(-8\right)\right)[/tex]
[tex]\mathrm{Apply\:rule}\:-\left(-a\right)=a[/tex]
[tex]y-7=5\left(x+8\right)[/tex]
Therefore, the line of the equation is:
[tex]y-7=5\left(x+8\right)[/tex]
Which of the following is 5/9 closest to? a 1/2 b 0 c 1
Answer: do you have a picture of the assignment?
Step-by-step explanation:
What is the equation of the line that passes through the point (5, 4) and has a slope
of 4/5
Answer:
Every point on a horizontal line has the same y-value. Use the y-value of the point to find the equation of the horizontal line.
y=4
what is the domain of this scatter plot?
Answer:
this answer should be green
A function has the function rule y = x - 7. If the input is 4, what is the output?
A. 3
B. -3
C. 11
D. -11
Answer:
The awnser is B. -3
Step-by-step explanation:
4-7=-3
x-7= y
What are the steps in order to correctly solve the equation
4x1/3 + 9 = 25
and what is the correct answer?
Answer:
X=12
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Answer:
x=12
Step-by-step explanation:
step one is multiplying rest is in pic mark as brainliest
Express the number 3,440,000 in Scientific Notation.
Answer:
3.44 * 10^6
Step-by-step explanation:
3,440,000
3.44 * 10^6
Answer: It would be 3.44 × 10^6.
Plz help me plz I need answer and explanation plz
plz answer me the due date within 10 minute plz answer me
9514 1404 393
Answer:
A = {put, the, cake, in, basket}
B = {is, the, cake, in, basket}
C = {no, the, cake, in, basket}
D = { }
Step-by-step explanation:
A = (A -B) ∪ (A∩B) ∪ (A∩C}
A = {put} ∪ {the, cake, in, basket} ∪ {the, cake, in, basket}
A = {put, the, cake, in, basket}
__
B = (B -A) ∪ (B -C) ∪ (B∩A) ∪ (B∩C)
B = {is} ∪ {is} ∪ {the, cake, in, basket} ∪ {the, cake, in, basket}
B = {is, the, cake, in, basket}
__
C = (C -B) ∪ (C∩A) ∪ (C∩B)
C = {no} ∪ {the, cake, in, basket} ∪ {the, cake, in, basket}
C = {no, the, cake, in, basket}
__
D = { } . . . . not defined anywhere
Joe says there is a total of 40 students. Do you agree with Joe? Why or Why not?
Answer:
Step-by-step explanation:
Well the question you should be asking first is....what is part a? Because if you put that picture up i could mostly help sooo
Which expression has a negative value?
O 2+ 12
O (-3)(-8)
O 10-(-18)
0-35-5
Answer:
-35-5 has a negative value
Step-by-step explanation:
-35 - 5 = -40
If this helps can I get brainliest? Thanks
Which numbers are solutions of h2+4=8h−3?
A. 1
B. 3
C. 5
D. 7
it asks which 2 are correct, please help.
Not sure but I think its b and d
Consecutive interior angles are
Answer:
When two lines are crossed by another line (called the Transversal): The pairs of angles on one side of the transversal but inside the two lines are called Consecutive Interior Angles.
Answer:
When two lines are crossed by another line (called the Transversal): The pairs of angles on one side of the transversal but inside the two lines are called Consecutive Interior Angles.
Step-by-step explanation:
Use the provided information to write the standard form equation of the parabola.
Opens up or down, and passes through (8,0), (13,-5), and (12,0)
Answer:
f(x) = -x² + 20x - 96Step-by-step explanation:
Parabola f(x) = ax² + bx + c passing through points (8,0) and (12,0) means that 8 and 12 are its root and (x-8) and (x-12) are its factors
So we get:
f(x) = a(x - 8)(x - 12)
The parabola passes through point (13, -5) that means if x=13 then f(x)=-5
So:
-5 = a(13 - 8)(13 - 12)
-5 = a(5)(1)
-5 = 5a
a = -1 {<0 so parabola opens down}
Therefore:
f(x) = -(x - 8)(x - 12)
And expanding:
f(x) = -(x² - 12x - 8x + 96)
So the standard form equation of the parabola:
f(x) = -x² + 20x - 96
A science beaker was left under a dripping water faucet. In 3 days, the beaker filled to 2¼ mL. If the water dripped the same amount every day, how many mL dripped from the faucet each day?
Answer:
Answer: 6 3/4
Step-by-step explanation:
You have to mulitply 2 x 4 + 1 = 9 and 4 is going to be the denomiator and how much can 3 can go into 9 only 3 times and that going to be on top of the denomiator and 2 x 3 = 6
SI-
Class:
28
Graphing Review #2 (8)
Name: GO
1. The following database shows ice cream sales based on daily high temperatures.
Ice Cream Sales vs Temperature
Temperature C Ice Cream Sales
$215
14.2
16.40
$325
11.99
$185
15.2
600
$332
18.5°
$406
.
22.10
$522
$500
19.40
$412
25.1
3400
$614
15300
a) Construct a scatter plot
to compare the total sales
to the daily high temperature,
b) What type of correlation is $200
shown by the data?
100
c) Draw a line of best fit.
d) Predict what the total sales would
se if the temperature was 17°C ?
10
Ve6
Temperature
Answer:
Step-by-step explanation:
SI-
Class:
28
Graphing Review #2 (8)
Name: GO
1. The following database shows ice cream sales based on daily high temperatures.
Ice Cream Sales vs Temperature
Temperature C Ice Cream Sales
$215
14.2
16.40
$325
11.99
$185
15.2
600
$332
18.5°
$406
.
22.10
$522
$500
19.40
$412
25.1
3400
$614
15300
a) Construct a scatter plot
to compare the total sales
to the daily high temperature,
b) What type of correlation is $200
shown by the data?
100
c) Draw a line of best fit.
d) Predict what the total sales would
se if the temperature was 17°C ?
10
Ve6
Temperature
Can you help me with this? 3
Answer:
acute
Step-by-step explanation:
Naomi has earned $81 mowing lawns the past two days. She worked 2 1/2 hours yesterday and 4 1/4 hours today. If Naomi is paid the same amount for every hour she works, how much does she earn per hour to mow lawns?
Answer:
Twelve dollars per hour
Step-by-step explanation:
Add 2 1/2 and 4 1/4 together to get 6 3/4. Put it into decimal form (6.75), and divide. 81 ÷ 6.75 = 12.
Is -9.25 greater than 6 1/2
Answer:
No sir
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
Negatives are always less than positives.
Look at it on a number line:
Hope this helped!