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]
What is the area of the figure?
A) 18 yd2
B) 54 yd2
C) 72 yd2
D) 90 yd2
Answer:
72 yd²
Step-by-step explanation:
area of this figure = area of 1st rectangle + area of 2nd rectangle
= l×b + L×B
= 6 × 5 + 14 × 3
=30 + 42
= 72 yd²
Answer:
the answer c 72 yd2
Step-by-step explanation:
Which persons dues are cheaper per month? explain. (please help)
Answer:
Claire
Step-by-step explanation:
Evaluate the expression 8-5xy3 for x=3 and y=-2.
Answer:
-54
Step-by-step explanation:
8-5xy3 x=3 y=-2
3xy3
3(3)(-2)3
9(-2)3
-18*3
-54
are these lines parallel or perpendicular? 2y=-3x=5 and y=3/2-6
Answer:
perpendicular because they have a positive and negative slope meaning on a graph they would be crossing each other.
the Area of the circles
Answer:
254.4 in²
Step-by-step explanation:
Area of a circle is given by the formula:
[tex]\pi r^{2}[/tex]
Our radius is 9 so we substitute this into the equation:
π(9)² = 81π
81π = 254.4 in²
Answer:
254 cm^2.
Explain:
The area of a circle is given by pi r squared. Pi has a constant value of 3.14. And the radius of the circle is 9 cm. The area equals pi R² equals 3.14 × 9² CM squared. 3.14 × 81 = 2.54.34cm^2 equals 254cm^2.
What is the volume of a cube with an edge length of 7.3 cm?
Enter your answer in the box
Answer:
389.017 cm³
Step-by-step explanation:
Given:
Side length of cube = 7.3 cmThe volume of a cube is the cube of the side length.
V = (side length)³Substitute the side length of the cube to determine the volume of the cube.
⇒ V = (s)³
⇒ V = (7.3)³
⇒ V = (7.3)(7.3)(7.3) = 389.017 cm³
Answer: 389.017
Step-by-step explanation: I just took the test.
Samir also picks pumpkins from his garden. He picked 6 7/10 kg, but 2.6 of pumpkins were spoiled and could not be used for decoration. How many kilograms of pumpkins were not spoiled? Write an equation that shows how you reached your answer.
Answer:
6.7kg - 2.6kg = 4.1kg
Step-by-step explanation:
6 7/10 is equal to 6.7. If we have 6.7kg of pumpkins, but we can't use 2.6kg, then we subtract to find the amount that we can use.
Help I don't understand this math. Whoever gets the right answer gets Brainlist! :)
Answer:
1200 more beats in 3 seconds or
400 more beats in 1 second
Step-by-step explanation:
A Mosquito beats its wings at a rate of 600 times per second.
A honey bee beats its wings at a rate of 200 times per second.
600 - 200 = 400
The mosquito beats 400 more times per second
400 X 3 = 1200
1. Abe and Malik both stayed after school on
Wednesday to practice their instruments. Abe
practiced for 30 minutes. Malik practiced 10
minutes longer than Abe. Select all the ratios
that compare Abe's practice time to Malik's practice time
Answer:
Step-by-step explanation:
If Abe practiced 30 minutes,
Malik practiced 40 minutes.
It's 30:40 minutes;
3:4
If the two spinners below are spun, what is the probability that the numbers will match? 1/4 1/6 1/12 1/3
Answer:
1/4
Step-by-step explanation:
Probability of getting a number on Spinner 1 = 1/3Probability of getting a number on Spinner 2 = 1/4Sample Space = 12 entriesSample Space
{(1,1)(1,2)(1,3)(1,4)(2,1)(2,2)(2,3)(2,4)(3,1)(3,2)(3,3)(3,4)}Probability of getting the same number = 3/12 = 1/4Which fractions are equivalent to 5/8?
Select each correct answer.
20/32
25/64
10/16
50/80
10/13
Solve the following system of equations algebraically:
x + 5y = -19
3x - y=-9
Answer:
x= -4, y=-3
Step-by-step explanation:
solving the two equations simultaneously you'll get x to be-4 and y to be -3
x+ 5y= -19
3x-y=-9
multiplying the second equation by5
15x-5y=-45
adding eqn 1 and eqn 3
16x= -64
x= -4
substituting into eqn 2
3(-4)-y= -9
-y= -9+12
-y= 3
y=-3
help pls quick i need the answer pls
Answer:
multicultural
Step-by-step explanation:
Answer:
A. Multicultural
Step-by-step explanation:
It shows later in the sentence that they ate Thai noodles and Egyptian falafel those come from different cultures so it must be multicultural
Vani bought snacks for her team's practice. She bought a bag of popcorn for $3.39
and a 18-pack of juice bottles. The total cost before tax was $26.61. Write and solve
an equation which can be used to determine x, how much each bottle of juice costs.
Equation:
Answer: x=
Answer:
x= (26.61-3.39)/18
Step-by-step explanation:
Can some help me I will mark u brilliant
Answer:
The answer is C
Step-by-step explanation:
The formula of a circle is pie radius ^2. Its asking for the surface area. So I got C because you do pie 18^2 and gets you approximately 1017. Although A also says 18 as the radius, it says meters. After you solve a surface area problem you do square meters or square units. For volume you have to use units cubed or units ^3. Make sure to always do this or your teacher might count you as wrong.
Answer:
Let's first try to find the radius before finding the diameter because when you find the radius, you double it to get the diameter.
To find the radius, use the area for a circle formula and plug in the values you know so far, so the formula is;
A = π[tex]r^{2}[/tex]
What we know:
1,017 is the area.Plug that area in our equation:-
A = π[tex]r^{2}[/tex]
1,017 = 3.14[tex]r^{2}[/tex]
Solve for r;
÷3.14 ÷3.14
324(approximate) = [tex]r^{2}[/tex]
√324 = r
18 = r, the radius is around 18 square meters (do not mistake the unit for some other unit).
Therefore, your answer is C.Another alternative way;Plug in your options' numbers into the equation;
A = π[tex]r^{2}[/tex]
And by looking at the options, we can see the only number here being used is 18, so we use 18 in the formula for the area of a circle to check if it'll result in 1,017 as the area.
Also: Notice if it says diameter or radius when using this solution, you are looking for the radius first.
help me pls guys guys
Answer:
1.TRUE
2.TRUE
3.TRUE
4.TRUE
5.TRUE
Step-by-step explanation:
THATS MY ANSWER ON MY MODULES
hope it helps as
Identify the indicated angles as Adjacent, vertical, linear, or complimentary
Which of the following rational functions is graphed below
Answer:
option B
Step-by-step explanation:
[tex]f(x) = \frac{x + 2}{x + 1} [/tex]
If f is a second-degree polynomial function such that f(3)=5, f'(3)=6, and f''(3)=4, what is the value of f(2) ?
so let's say the equation is y = ax² + bx + c, where a,b,c are constants.
we know that f(3) = 5, or namely when x = 3 , y = 5.
we also know that f'(3) = 6, or namely the slope at the point (3,5) is 6.
we also know that at (3,5) the 2nd derivative is 4, so a positive number simply tell us its concavity, is up, so is a parabola opening upwards.
[tex]y=ax^2+bx+c\implies \left. \cfrac{dy}{dx}=2ax+b \right|_{x=3}~~ = ~~ 6\implies 6=2ax+b \\\\\\ 6=2a(\stackrel{x}{3})+b\implies 6=6a+b\implies 6-6a=b\implies \boxed{6(1-a)=b} \\\\[-0.35em] ~\dotfill\\\\ \left. \cfrac{d^2y}{dx^2}=2a \right|_{x=3}~~ = ~~4\implies 2a=4\implies a=\cfrac{4}{2}\implies \boxed{a=2}~\hfill \boxed{-6=b} \\\\[-0.35em] ~\dotfill[/tex]
[tex]y=2x^2-6x+c\qquad \begin{cases} x=3\\ y = 5 \end{cases}\implies 5=2(3)^2-6(3)+c\implies \boxed{5=c} \\\\\\ y=2x^2-6x+5~\hfill y(2)=2(2)^2-6(2)+5\implies \blacktriangleright y(2)=1 \blacktriangleleft[/tex]
how do you do Mean Absolute Deviation with 35 42,41,32,30?
Answer:
The numbers added up together is 180, and divide 180 by 5 is 36.
1,6,5,4,6=22.
22/5=4.4
Step-by-step explanation:
You can look it online but as quoted,
"Take each number in the data set, subtract the mean, and take the absolute value. Then take the sum of the absolute values. Now compute the mean absolute deviation by dividing the sum above by the total number of values in the data set. Finally, round to the nearest tenth." -IXL
A stone is projected vertically upward from a platform that is 18ft high at a rate of 114ft/sec. Use h=−16t^2+v0t+h0.
Using the vertex of the quadratic equation, it is found that the stone reaches a maximum height of 221.0625 ft after 3.5625 s.
What is the vertex of a quadratic equation?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The vertex is given by:
[tex](x_v, y_v)[/tex]
In which:
[tex]x_v = -\frac{b}{2a}[/tex]
[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]
Considering the coefficient a, we have that:
If a < 0, the vertex is a maximum point.If a > 0, the vertex is a minimum point.In this problem, considering initial velocity of v(0) = 114 and an initial height of h(0) = 18, the equation is:
h(t) = -16t² + 114t + 18.
Which is a quadratic equation with coefficients a = -16, b = 114, c = 18.
Hence:
[tex]x_v = -\frac{114}{2(-16)} = 3.5625[/tex]
[tex]y_v = -\frac{114^2 - 4(-16)(18)}{4(-16)} = 221.0625[/tex]
Hence, the stone reaches a maximum height of 221.0625 ft after 3.5625 s.
More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967
Read the sentence.
When my cousin Jason suddenly showed up out of the blue, it was an unexpected surprise because we had no idea that he was coming to the special event that our family had planned ahead of time.
Which revision most effectively shortens the sentence to make it less repetitive and more precise?
Drag the revision into the box.
The first sentence is correct.
Answer: We were surprised when my cousin jason attended our family reunion.
Step-by-step explanation: I took the k12 quiz and got it right.
Find the area of the figure
answer:
178.5398mm²
explanation:
attached
--
if this helped, please consider giving brainliest !
the vertex of this parabola is at (4, -3). when the x-value is 5, the y-value is -6. what is the coefficient of the squared expression in the parabola's equation?*sorry edited now
Answer:
- 3
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here (h, k ) = (4, - 3 ) , then
y = a(x - 4)² - 3
to find a substitute x = 5, y = - 6 into the equation
- 6 = a(5 - 4)² - 3 ( add 3 to both sides )
- 3 = a(1)² = a
y = - 3(x - 4)² - 3 ← expand factor using FOIL
y = - 3(x² - 8x + 16) - 3
= - 3x² + 24x - 48 - 3
= - 3x² - 24x - 51 ← in standard form
coefficient of the x² term is - 3
Find the length of the midsegment of the trapezoid.
Answer:
MN=66.5
Step-by-step explanation:
Add 57 and 76, then divide by 2.
What is cosK?
(25)/(7)
(25)/(24)
(7)/(25)
(24)/(25)
Step-by-step explanation:
7/25
we need to remember this triangle with 90° 7, 24, 25
Which of the following rational functions is graphed below?
Step-by-step explanation:
There is a vertical asymptote x=3 and x=-1 so our rational function will contain
(x-3)(x+1).
Since we have a horinzintal asymptote, our numerator will be either a constant function, or linear function.
we have a zero at approximately, at 1 so our numerator will include
[tex] \frac{x - 1}[/tex]
So our rational function is
[tex] \frac{x - 1}{(x - 3)(x + 1)} [/tex]
There is a vertical asymptote x=3 and x=-1 so our rational function will contain option C [tex]f(x) = \dfrac{x-1}{(x-3)(x+1)}[/tex].
When do we get horizontal asymptote for a function?The line y = a is a horizontal asymptote if the function f(x) tends to 'a' from the upside of that line y = a, or from downside of that line.
Since we have a horizontal asymptote, our numerator will be either a constant function or a linear function.
We have given a zero at approximately, 1 so our numerator will include (x-1).
So our rational function is
[tex]f(x) = \dfrac{x-1}{(x-3)(x+1)}[/tex]
Learn more about horizontal asymptotes here:
https://brainly.com/question/2513623
#SPJ5
A rectangular prism is a
Choose...
two-dimensional, three dimensional or one dimensional.
Answer: Three dimensional
Step-by-step explanation:
A rectangular prism is a three-dimensional shape.
[] A one-dimensional shape is a line
[] A two-dimensional shape is a rectangle, circle, etc
[] This means that a rectangular prism is a three-dimensional shape
A rectangular prism is a
Two dimensionalThree dimensional Four dimensional Explanation -:A rectangular prism is three dimensional.
One dimensional -:
Lines that have length in at least one direction.Two dimensional -:
Shapes that are flat and have two dimensions i.e. length and breadthThree dimensional -:
A solid figure that has three dimensions i.e. length, breadth and height.[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \tiny \rm{spbankingandsscseries}[/tex]
[tex] \rule{75mm}{6pt}[/tex]
There are 5 cups of oatmeal in a container stella eats 1/3 of oatmeal every day for breakfast in how many days will stella finish all the oatmeal in the container
Answer:
15 days
Step-by-step explanation:
if she eats 1/3 cup of outmeal each day then in 3days she will have eaten 1 cup so to get to 2cups he will have to eat for 3 more days so it goes 3 days by 3 days this will be easy to do on a number line but you could also just multiplying the 3days times the 5 cups because thats how many cups you want to get to finish so it will be 15 the 15 days it took me time to understand hope this was helpful
The number of days is 15 days.
What is unit rate?A rate is a ratio that compares two quantities of DIFFERENT. kinds of UNITS. A unit rate has a denominator of 1 unit when the rate is written as a fraction. To write a rate as a unit rate: divide the numerator and the denominator of the rate by the denominator.
here, we have,
to determine the number of days
From the question, we have the following parameters that can be used in our computation:
Size = 5 cups
Rate = 1/3 cup per day
The question illustrates unit rates
A unit rate is a rate in which the denominator of a ratio is 1 unit.
In other words, it is the amount of something per one unit of another thing.
Using the above as a guide, we have the following:
Number of days = 5/(1/3)
Evaluate the quotient
Number of days = 15/1 days
This gives
Number of days = 15 days
Hence, the number of days is 15
Read more about unit rates at
brainly.com/question/26059245
#SPJ2
please add these number togeather
Answer:
314.00+200.96+113.04+78.50+63.59+38.47+28.26+3.14+.79
=840.75
