I think you meant to say
[tex]\ln(x+y) = 4xy[/tex]
and not "4 times y" on the right side (which would lead to a complex value for y when x = 0). Note that when x = 0, the equation reduces to ln(y) = 0, so that y = 1.
Implicitly differentiating both sides with respect to x, taking y = y(x), and solving for dy/dx gives
[tex]\dfrac{1+\frac{dy}{dx}}{x+y} = 4y + 4x\dfrac{dy}{dx}[/tex]
[tex]\implies \dfrac{dy}{dx} = \dfrac{4xy+4y^2-1}{1-4x^2-4xy}[/tex]
Note that when x = 0 and y = 1, we have dy/dx = 3.
Differentiate both sides again with respect to x :
[tex]\dfrac{d^2y}{dx^2} = \dfrac{(1-4x^2-4xy)\left(4y+4x\frac{dy}{dx}+8y\frac{dy}{dx}\right)-(4xy+4y^2-1)\left(-8x-4y-4x\frac{dy}{dx}\right)}{(1-4x^2-4xy)^2}[/tex]
No need to simplify; just plug in x = 0, y = 1, and dy/dx = 3 to get
[tex]\dfrac{d^2y}{dx^2} \bigg|_{x=0} = \boxed{40}[/tex]
If f(x) -
X-3
and g(x) = 5x - 4, what is the domain of (f•g)(x)?
Write an equation in slope-intercept form of the line that passes through ( 7,2 ) ( 2,12 )
Answer:
y = -2x + 16
Step-by-step explanation:
Slope-intercept form is:
y = mx + bWhere m = slope
b = y-intercept
To find the slope of the line containing (7,2) and (2,12), we have to find the slope, m.
m = (y2 - y1)/ (x2 - x1)= (12 - 2)/(2 - 7) = 10/-5 = -2Now, to find the y-intercept (b), insert m = -2 into the equation and one of the given points:
y = -2x + blet's use point (7,2) to find b:
2 = -2(7) + b2 = -14 + bb = 16Now, we can find the equation of this line:
y = -2x + 16Answer:
y=-2x+16
Step-by-step explanation:
First we should find the slope.
We can use the formula (y2-y1)/(x2-x1)
(12-2)/(2-7)=10/-5=-2
So, the slope is -2.
From there, we can plug in one of the points into the standard slope-intercept equation, y=mx+b, along with the slope we already found
y=-2x+b
12=-2(2)+b
12=-4+b
b=16
So, the slope-intercept equation is y=-2x+16
Find x in each triangle
Answer:
Applying Pythagoras we get x= 9
Answer:
using the relation,
h²=p²+b²:
15²=x²+12²
x=(225-144)^0.5
x=9
therefore x equal 9 meter.
In analysis of variance, then the term factor refers to_______
a) a dependent variable
b) a treatment total
c) an independent variable (or quasi-independent) variable
d) a treatment mean
For what value of k will the relation R = {(2k+1, 3), (3k−2, −6)} not be a function?
For the relation to not to be a function we need the same value of x in (x,y) that gives off different values (y).
2k+1= 3k-22k-3k = -2-1-k = -3k = 3Now plugging in the value of k,
(2 x 3+1 ,3) =( 7,3)(3 x 3-2,-6) = (7,-6)hence , the relation won't be function if k would be equal to 3
The value of k for which the relation R = {(2k+1, 3), (3k−2, −6)} is not a function is k = 3.
What is a function?In general terms, a function is a mathematical rule or relationship that maps one set of values (the input or domain) to another set of values (the output or range). In other words, it's a specific process that takes some input and produces a corresponding output.
For the given relation R to be a function, each input in the domain should have exactly one corresponding output in the range.
We can determine whether the relation R is a function by checking if both ordered pairs have the same first coordinate. If they do, then the relation is not a function.
Let's equate the first coordinate of the ordered pairs:
2k+1 = 3k-2
Solving for k, we get:
k = 3
If we substitute k = 3 into the relation, we get:
R = {(2(3)+1, 3), (3(3)−2, −6)}
R = {(7, 3), (7, -6)}
Since both ordered pairs have the same first coordinate of 7, the relation R is not a function.
Therefore, the value of k for which the relation R = {(2k+1, 3), (3k−2, −6)} is not a function is k = 3.
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Krystal was given $3000 when she turned 2 years old. Her parents invested at a 2% interest rate compounded annually. No deposits or withdrawals were made. Determine how much money Krystal had in the account when she turned 18.
Answer:
4131.38
Step-by-step explanation:
Since it's compounded annually, and no time needs to be converted, we can use the formula [tex]y=Pe^r^t[/tex], where P is the starting amount, e is Euler's number, r is the rate in decimals, and t is time. The first task would be to find the t. The question set us a timeframe of 2 to 18, so 18-2=16, therefore our t is 16. Plugin the known into the formula and calculate:
[tex]y=3000e^0^.^0^2^*^1^6\\y=3000*e^0^.^3^2\\y=4131.38[/tex]
I don't know how to do this (don't mind the 21)
Answer:
The definition of alternate interior angles is that those two angles are the same.
Therefore because they are the same you can set them equal to eachother
3x + 24 = 78 is true
3x = 54
x = 18
Just know the definitions, for instance 3 and 4 are the same, 2 and 5 are the same, 1 and 6 are the same
Anyone can help me with this? Kinda confusing. Thank you!
Answer:
14
Step-by-step explanation:
you can do 9 x 14 and get 126
I need help with this one
which of the following ordered pairs (x y) satisfies the system of inequalities above
Just put the options in the inequalities and check if they are true or not :
A ) ( - 1 , 0 )
[tex]2x + y \leqslant 3[/tex]
[tex]2( - 1) + 0 \leqslant 3[/tex]
[tex] - 2 \leqslant 3 \: \: \: kinda \: true[/tex]
And
[tex]x - y < - 3[/tex]
[tex] - 1 - 0 < - 3[/tex]
[tex] - 1 < - 3 \: \: \: false[/tex]
Thus A is wrong
_____________________________________________
B ) ( - 1 , - 1 )
[tex]2( - 1) + ( - 1) \leqslant 3[/tex]
[tex] - 2 - 1 \leqslant 3[/tex]
[tex] - 3 \leqslant 3 \: \: kinda \: true[/tex]
And
[tex] - 1 - ( - 1) < - 3[/tex]
[tex] - 1 + 1< - 3[/tex]
[tex]0 < - 3 \: \: \: false[/tex]
Thus B is wrong
_____________________________________________
C ) ( - 2 , 4 )
[tex]2( - 2) + 4 \leqslant 3[/tex]
[tex] - 4 + 4 \leqslant 3[/tex]
[tex]0 \leqslant 3 \: \: kinda \: true[/tex]
And
[tex] - 2 - 4 < - 3[/tex]
[tex] - 6 < - 3 \: \: \: true[/tex]
Thus C is the correct option
_____________________________________________
U can do D urself ...
Have a great day ♡
How would I be able to solve all of these?
Answer:
I'm suggesting that you should read your books!!!
You should be more thoughtful...
Answer:
Part A) x = 6, 13, 22, 33
Part B)
Part ASome examples of perfect squares are 9, 16, 25, and 36. They are the squares of 3, 4, 5, and 6. To generate these values, add x to 3 and plug these numbers into an equation:
√(x + 3) = 3
√(6 + 3) = √9
x = 6
√(x + 3) = 4
√(13 + 3) = √16
x = 13
√(x + 3) = 5
√(22 + 3) = √25
x = 22
√(x + 3) = 6
√(33 + 3) = √36
x = 33
Part B
1. (6, 3)
2. (13, 4)
3. (22, 5)
4. (33, 6)
I hope this helps!
(02.01 LC) Which of the following tables represents a function?
Answer:
the answer is the third one
Step-by-step explanation:
because in a function the x value has to be unique.
Answer:
c (third one)
Step-by-step explanation:
A spherical balloon has a circumference of 25 cm.
a.) What is the approximate surface area of the balloon to the nearest square centimeter?
b.) What is the approximate volume of the balloon to the nearest cubic centimeter?
Answer:
See below ↓↓
Step-by-step explanation:
Finding the radius
C = 2πr25 = 2 x 3.14 x rr = 25 / 6.28r = 3.98 cm ≅ 4 cmSurface Area
4πr²4 x 3.14 x 4 x 43.14 x 64200.96201 cm²Volume
4/3πr³ = 4πr² x r/3201 x 4/367 x 4268 cm³Two rooms in a tiny house share a wall.
Answer:
54 + 42 = 6 (9 + 7)
Sorry if this answer is not correct, if it is or is not, please tell me in the comments!
Step-by-step explanation:
The equation already gives the 7 in the parenthesis, so we know that 7 x 6 = 42.
The 6 will be on the outside of the equation since we will be using Distributive Property to multiply the 6 and 7.
Since we already know the 6 is on the outside, your new equation is:
6 x (what number) = 54
54 divided by 6 = 9
A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find out the time at which the rocket will reach its max, to the nearest 100th of a second.
Answer:
x=5.09 seconds (times at max)
Step-by-step explanation:
CAN SOMEBODY SOLVE EQUATION IM LOST
Answer:
2
- x -1
3
Step-by-step explanation:
A demolition crew can do a job in 10 days. Another demolition crew can do the same job in 15 days. How many days would it take the two crews to do the job if they work together?
Answer:
6 days
Step-by-step explanation:
In one day, one demolition crew:
One day = [tex]\frac{1}{10} x[/tex] with x = the entire job
Other demolition crew:
One day = [tex]\frac{1}{15} x[/tex]
Together, they do it in [tex]\frac{1}{10}x\\[/tex] + [tex]\frac{1}{15}x[/tex] = [tex]\frac{3}{30}x + \frac{2}{30}x = \frac{5}{30}x[/tex] [tex]= \frac{1}{6}x[/tex] in one day
So [tex]\frac{1}{6}x[/tex] x 6 = x
so it takes 6 days to complete the work together.
Use the proof above to answer the question: What reason can be used to prove that the triangles are congruent?
A. AAS B. ASA C. AAA D. SAS E. SSS
Answer:
E. SSS
Step-by-step explanation:
AB=BC (Given)
AD=CD (Midpoint)
BD=BD (common)
Therefore answer is : SSS
Why can't the square root cancel out the exponents in the distance formula?
Let's say instead of x2-x1, we say, "The difference between x2 and x1", let's call this value A. We'll do the same for the y variables and call that difference B, for simplicity.
For (2,3) and (4,9), we're really dealing with those differences, so A should equal 2, and B should equal 6. So far so good. But this is pretty much the "rise and run" of a triangle. 2 to the right, then 6 up. But if you walk 2 miles east, then 6 north, while you, personally, have travelled 8 miles, the distance between your starting point and where you are is NOT the way you walked.
So in the case of the triangle, using 2 as the run and 6 as the rise, to get the straight line between the starting point and the ending point, we have to do Pythagorean's Theorem, or A2 + B2 = C2 to get that last direct line between the two points. Cancelling the root and exponents removes the process to get that exact distance squared. We then take the square root of that to get the exact distance.
Marlo uses 252 lb of gravel to cover a garden plot of 36 ft2.
Answer: 7lb
Step-by-step explanation:
The amount of gravel required cover each square feet of the garden obtained by dividing the total amount of gravel used and the total area of the garden is 7 lb
Total area of garden = 36 ft²
Total amount of gravel used = 252 lb
The amount of gravel used to cover each ft² of the garden can be calculated thus :
(Total amount of gravel used) ÷ (Total area of garden)
252 ÷ 36 = 7 lb
Therefore, the amount of gravel required to cover each square feet of the garden is 7 lb
Answer:
See below
Step-by-step explanation:
D o you want pounds / sq foot ?
252 lbs / 36 ft^2 = 7 pounds per square foot
Plot 1 goes from 0 to 8. There are 2 images above 5, 2 above 6, 4 above 7, and 5 above 8. Plot 2 goes from 0 to 8. there are 5 images above 1, 2 images above 2, 4 images above 3, 3 images above 4, 1 image above 5, 1 image above 6, and 1 image above 8.
Use visual clues to decide which plot has the highest measure. No calculations should be necessary, although you may use them to verify your answers.
Highest mean:
✔ Plot 1
Highest median:
✔ Plot 1
Highest range:
✔ Plot 2
Highest interquartile ranges:
✔ Plot 2
Answer: the answer is 45
Step-by-step Step-by-step explanation:
so it says a pilot goes from 0 to 8 and then two images above so you add to to eat and then you add 5 to 2:30 for me to 522 the artistic 24 + 27 + 5 then you answer 8 + 2028 and then you add 5 + 1 + 2 + 2 + 4 + 3 + 3 + 4 + 1 + 5 + 16 + 18 and you get 45
Answer:
A, A, B, B
Step-by-step explanation:
Select True or False for each statement.
Statement True False
In the ordered pair (3, 5), the number 5 is the y-coordinate.
True – In the ordered pair ( 3, 5 ) , the number 5 is the y-coordinate.
False – In the ordered pair ( 3, 5 ) , the number 5 is the y-coordinate.
The origin has coordinates (0, 0).
True – The origin has coordinates ( 0, 0 ) .
False – The origin has coordinates ( 0, 0 ) .
The horizontal axis in a coordinate plane is the y-axis.
The number 5 in the ordered pair (3, 5) is the y-coordinate (TRUE)
(0, 0) is the origin on a coordinate plane (TRUE)
y-axis is the horizontal axis on a coordinate plane (FALSE).
What is an Ordered Pair?An ordered pair is a set of numbers that represents the location of a point on a coordinate plane that has an x-axis (horizontal axis) and y-axis (vertical axis).
An ordered pair is given as (x, y). Therefore, the following statements given are matched as shown below:
The number 5 in the ordered pair (3, 5) is the y-coordinate (TRUE)(0, 0) is the origin on a coordinate plane (TRUE)y-axis is the horizontal axis on a coordinate plane (FALSE).Learn more about ordered pair on:
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There are 110 calories per 28.4 grams of Cereal X. Find how many calories are in 39.76 grams of this cereal
Step-by-step explanation:
28.4 g there are 110 calories
1 g there are 110/28.4 = 3.87 calories
39.76 g there are 3.87 × 39.76 = 153.87
Martinez and grouse swimming pool is finally finished and all this left to do is fill it with water. Martinez family decides to fill their pool using their garden hose to save money even though they know it will take a really long time the swimming pool is 10 m long and 5 m wide and Martinez family wants to the water to be 2 m deep water from the garden holes flows at a rate of 2500 l or 2.5 m³ per hour how long will it take to fill the pool
Answer:
the answer ia true
Step-by-step explanation:
hope this helps
A spinner is divided into 12 identical sectors and labeled 1 through 12.
How many spins are expected for a multiple of 5 to be spun 8 times?
Select from the drop-down menu to correctly complete the sentence.
The spinner is expected to have to spin approximately
times for a multiple of 5 has been spun 8 times.
Answer: The awnser is 48
Step-by-step explanation: I took the quiz
6.03 Quiz: Use Theoretical Probability to Predict
It is expected to take 48 spins for a multiple of 5 to be spun 8 times.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
Since there are 12 sectors, the probability of landing on a multiple of 5 is 2/12 or 1/6.
The probability of not landing on a multiple of 5 is 5/6.
We can use the geometric distribution formula to find the expected number of spins:
E(X) = 1/p, where p is the probability of success.
As per the question, the probability of success is 1/6.
Therefore, E(X) = 1/(1/6) = 6.
We need to spin a multiple of 5 8 times, so we multiply the expected number of spins by 8:
6 x 8 = 48.
Therefore, we can expect to spin a multiple of 5-8 times after 48 spins.
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T-Mobile has a family plan of four lines for $120 and additional lines are $10 each per month. If Jason wants to spend at most $175 per month on a cell phone expenses, what is the correct inequality that represents the amount of additional lines he can afford?
Answer:
Jason can afford 5 more additional lines, making 9 lines total because
175-120=55
55/10=5.5 so He can not afford more than 5 more additional lines.
Step-by-step explanation:
CO
8
6
4
N
Which function is graphed?
46
8
N
-8 -6 -4 -20
-2
-4
-6
-8
O A. y- *#4x23
[+ ,
1-x+4,52
Which set of angle measures could be the interior angles of a triangle?
Answer:
the three angles inside a triangle need to add up to 180 degrees
Step-by-step explanation:
- If the difference of 15 and a number is 5, what is the number?
Answer:
The difference of 15 and a number is 5 indeed 10 to be 15
Answer:
10
Step-by-step explanation:
In Houston, 9 bats ate 50 grams of insects in one night. At this rate, how many grams of insects could 81 bats eat in one night?
Answer:
Step-by-step explanation:
Remark
Using Algebra, this is a proportion question. A proportion is 2 equal ratios
If the of the 2 ratio parts are known, it is possible to solve for the 4th one.
Formula
9_bats/50_grams::81_bats/x grams insects
Solution
Put the three knowns in and solve for the 4th which is not known
9 bats/ 50 insects = 81 bats /x insects. Cross multiply
9 * x = 50 * 81 Combine
9x = 4050 Divide by 9
9x/9 = 4050/9
Answer: x = 450 grams
Please help me with these 2 questions, I don’t really need explanations I just need straight forward answers ! The questions are linked below. 50 points
Answer:
1. The value of 5 is fifty thousand
2. The value of 6 is six thousand
Step-by-step explanation:
1. 8.156 million - 8,156,000
2. 6,521
^ 6000