Compute [tex]\frac{\mathrm dy}{\mathrm dx}[/tex] using implicit differentiation:
[tex]x^2-(xy)^{1/2}=2y^2+3x[/tex]
[tex]\dfrac{\mathrm d(x^2)}{\mathrm dx}-\dfrac{\mathrm d(xy)^{1/2}}{\mathrm dx}=\dfrac{\mathrm d(2y^2)}{\mathrm dx}+\dfrac{\mathrm d(3x)}{\mathrm dx}[/tex]
[tex]2x-\dfrac1{2(xy)^{1/2}}\left(\dfrac{\mathrm dx}{\mathrm dx}y+x\dfrac{\mathrm dy}{\mathrm dx}\right)=4y\dfrac{\mathrm dy}{\mathrm dx}+3[/tex]
[tex]2x-\dfrac1{2(xy)^{1/2}}\left(y+x\dfrac{\mathrm dy}{\mathrm dx}\right)=4y\dfrac{\mathrm dy}{\mathrm dx}+3[/tex]
[tex]2x-\dfrac12\left(\dfrac yx\right)^{1/2}-\dfrac12\left(\dfrac xy\right)^{1/2}\dfrac{\mathrm dy}{\mathrm dx}=4y\dfrac{\mathrm dy}{\mathrm dx}+3[/tex]
[tex]2x-3-\dfrac12\left(\dfrac yx\right)^{1/2}=\left(4y+\dfrac12\left(\dfrac xy\right)^{1/2}\right)\right)\dfrac{\mathrm dy}{\mathrm dx}[/tex]
[tex]4x-6-\left(\dfrac yx\right)^{1/2}=\left(8y+\left(\dfrac xy\right)^{1/2}\right)\right)\dfrac{\mathrm dy}{\mathrm dx}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4x-6-\left(\frac yx\right)^{1/2}}{8y+\left(\frac xy\right)^{1/2}}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4x(xy)^{1/2}-6(xy)^{1/2}-y}{8y(xy)^{1/2}+x}[/tex]
Plug in x = 4 and y = 1 to find that the tangent line's slope is 19/20.
Select all the statements that are true.
Answer:
Sqrt(7) is irrational because 7 is not a perfect square.
7.1234... is irrational because it is a nonterminating nonrepeating decimal.
Step-by-step explanation:
A rational number is a number that can be expressed in terms of fractions which result in terminating decimals, repeating decimals, or integer values.
An irrational number is a number that cannot be expressed in terms of fractions resulting in nonrepreating nonterminating decimals.
All options other than the two selected do not make sense. Pi is irrational because it is a nonrepeating nonterminating decimal.
Cheers.
pls help me pls pls
Hope it helped
Thank You4. What do your measurements in #3 tell you about the lengths of PR and QS ? Explain your thinking and then
measure to verify your conjecture. Be sure to state your measurements.
Answer:mn
Step-by-snbtep explanation:
ANSWER = MY ETERNAL LOVE determine an equation of the line which is the perpendicular bisector of the segment whose endpoints are (-5,3) and (7,2). make sure to show all work.
Answer:
Perpendicular Bisector Equation: y = 12x - 9.500
Step-by-step explanation:
Let find out the midpoint for given coordinates as follows:
[(-5+7)/2, (3 +2)/2]
= (2/2, 5/2)
= (1,5/2)
The midpoint coordinates are (1,5/2) means (x1 , y2)
2. Find the slop of line for given coordinates as follows:
(2-3)/(7-(-5)
= -1/12
3. Find the negative reciprocal as follows
-1/12
= 12 (m)
4. Now find the perpendicular bisector equation as follows:
y – y1 = m ( x – x1)
y – 3 = 12 (x – (-5)
y = 12x - 9.5
The required equation of the line is x + 12y = 41 which is the perpendicular bisector of the segment whose endpoints are (-5,3) and (7,2).
What is a perpendicular bisector?A perpendicular bisector is defined as a line that divides an angle into two equal angles.
The perpendicular bisector of the segment whose endpoints are (-5,3) and (7,2).
We have to determine the equation of the line
Let x₁ = -5, y₁ = 3 and x₂ = 7, y₂ = 2
The required of equation line is:
y - y₁ = (y₂ - y₁ )/( x₂ - x₁ )( x - x₁ )
Substitute the values in the formula to get the line,
y - 3 = (2 - 3)/(7 - (-5))(x - (-5))
y - 3 = (-1/12)(x+5)
12y - 36 = -x -5
x + 12y = 41
Thus, the required equation of the line is x + 12y = 41.
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Please help!!!!!!!!!!!!!
Answer:
r=8
Step-by-step explanation:
r*4=32
32/4=8
Therefore, r=8
Answer:
r = 8
Step-by-step explanation:
Ok don't worry. This question is not as hard as it should be.
It states it's a balanced equation. So that means 32 is equal to the other side.
there are 4 r's on the other side
32=4r
Divide 4 on both sides so the variable is independent
32/4=4r/4
8=r
Hope this helps!
Brighton Company launched a new gaming console. They sold 200 consoles prior to the launch.
The number of consoles sold each day after the launch is shown by the graph below.
Answer: in the domain of this situation, there is no asymptote.
Step-by-step explanation:
Asymptote would be on the left where x is negative but this function only shows all positive values of X
The value of k is -0.25. The graph shows that the actual number of consoles sold is slightly higher than the predicted number of consoles sold.
The graph shows that the number of consoles sold each day after the launch of the Brighton Company gaming console follows an exponential decay pattern. This means that the number of consoles sold each day is decreasing at a rate that is proportional to the number of consoles that have already been sold.
The equation that can be used to model this exponential decay pattern is:
N = A * [tex]e^{-kt[/tex]
where:
N is the number of consoles sold on day t
A is the initial number of consoles sold (200 consoles)
k is a constant that determines the rate of decay
e is the base of the natural logarithm
We can use the data from the graph to estimate the value of k. The first day after the launch, 180 consoles were sold. This means that on day 1, N = 180. The initial number of consoles sold, A, is known to be 200 consoles. Therefore, we can write the following equation:
180 = 200 * [tex]e^{-kt[/tex]
Solving for k, we get:
k = -ln(1.8) / 1
≈ -0.25
The value of k is approximately -0.25. This means that the number of consoles sold each day is decreasing at a rate of 25%.
We can use the equation to predict the number of consoles sold on future days. For example, on day 2, we would predict that 150 consoles would be sold. On day 3, we would predict that 120 consoles would be sold.
The graph shows that the actual number of consoles sold is slightly higher than the predicted number of consoles sold. This is because the exponential decay pattern is not perfect. There are other factors that can affect the number of consoles sold, such as the availability of the console and the price of the console.
To learn more about graph here:
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What is 503.782 to the nearest then tenth
Answer: 503.8
Step-by-step explanation: 503.782 is the original fraction. To round up the number has to be 5, 6, 7, 8, or 9. The number in the hundredths place is 8. so that means the number in the tenths place can be moved up to 8 since 7+1=8.
The cost (y) to rent a car is $45 per day plus 22 cents per mile. Which is the constant value in this situation?
A)
0.22x
B)
45
х
D)
у
Answer: is b andrea
Step-by-step explanation: i just took the same test
Answer:
Thy answer is B my queen
Step-by-step explanation:
NEED HELP NOW!!!! find the measure of the angle BXE using the figure below
Answer:
bxe is a triangle
Step-by-step explanation:
A truck can be rented from Company A for $110 a day plus $0.40 per mile. Company B charges $80 a day plus $0.60 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same. PLZ HELP
Answer: i am also looking for the answer so far i’ve gotten x=200 but it told me it was wrong feel free to try it i guess
is 3 by 3=9 rational or inrational and why
Answer:
KCC off KCC off off egg LLC
Answer:
rational
Step-by-step explanation:
3by3=3/3
= 1
1 is not eq. to 9
and 3/3 is 1
and 1 is rational no.
8. John is in a club that collects annual dues. In the first year that he was a member, he paid $20 in club dues. However, the club dues increase by $2 each year. Identify the function that describes the relationship between the number of years that John has been a member of the club and the dues he pays that year.
options:
A. f(n) = 20 + 2(n – 2)
B. f(n) = 20 + 2(n + 1)
C. f(n) = 20 + 2(n – 1)
D. f(n) = 20 + 2n
Answer: C) f(n) = 20 + 2(n - 1)
Step-by-step explanation:
The explicit formula is: [tex]a_n=a_1+d(n-1)[/tex] where
[tex]a_1[/tex] is the first termd is the difference between consecutive termsGiven: In the first year he paid $20 --> [tex]a_1[/tex] = 20
Dues increase $2 each year --> d = 2
[tex]a_n[/tex] = 20 + 2(n - 1)
Answer:
C f(n) = 20 + 2(n – 1)
Step-by-step explanation:
got it right on test
Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent
variable.)
Vertex: (-1/2,0)
point:
(-3/2,-16/3)
Answer:
[tex]y = \frac{16}{3} x^{2} + 16x + \frac{20}{3}[/tex]
Russell runs 910 mile in 5 minutes. At this rate, how many miles can he run in one minute?
Russell would run 182 miles for 1 minute.
The drama club spent $8.50 per person on food for a cast party. The total cost of the flood was $229.50. How many people were at the cast party?
Answer:
229.50 ÷ 8.50= 27 people
Need help -5(1+2k)-8(-4+5k)
Answer:
27 - 50k
Simplify
1. Distribute
-5 ( 1 + 2k ) - 8 ( -4 + 5k )
-5 - 10k - 8 ( -4 + 5k )
2. Distribute
-5 - 10k - 8 ( -4 + 5k )
-5 - 10k + 32 - 40k
3. Add the numbers
-5 - 10k + 32 - 40k
27 - 10k - 40k
4. Add the same term to both sides of the equation
27 - 10k - 40k
27 - 50k
Marty drew a model of the school library. The total area of the floor is 132 square
centimeters. What is the area of the shaded part of the model shown below?
10 centimeters
6 centimeters
Answer:
Step-by-step explanatio11n:
116
Cheri paid $6.50 for the bunch of grapes with the weight of 2.5 pounds. What is the price per pound?
You have a band concert coming up. You need to make sure that everyone in the audience has a seat. 70 people bought tickets. You set 6 rows of 11 chairs. Is that enough chairs? Why or why not? Show Work!
no this is not enough chairs!
if you have 6 rows of 11 chairs it would look like this
xxxxxx
xxxxxx
xxxxxx
xxxxxx
xxxxxx
(each x is a chair)
this would mean to figure out the amount of chairs you set down you would do 6 x 11 which is 66. so you would need 4 more chairs to fit all 70 people.
A bag contains colored tiles.
• 3 tiles are red
• 6 tiles are green
• 3 tiles are blue
A tile will be randomly selected from the bag.What is the probability in decimal form that the tile selected will
be green?
0.5 or 50% because there are 12 tiles and 6 are green. 6/12 probability simplifies to 1/2 = 0.5 = 50%
An open box is constructed of 3500 cm2 of cardboard. The box is a cuboid, with height h cm and square base of side x cm. What is the value of x which maximises the volume of the box? Give your answer in cm correct to 3 significant figures.
Answer:
this is confusing and my head hurts
Step-by-step explanation:
The square of a number is that number ___________________________________. The square of an integer is a _________________________.
The square of negative 12 is written as _______________. The opposite of the square of 12 is written as ______________.
2 • 2 = 4. Another number that can be multiplied by itself to equal 4 is _______.
2. Fill in the blanks with square root or principal square root.
A ___________________________________ is a number that produces a given number when it is multiplied by itself.
The ___________________________________ is the positive square root of a number and is shown using the radical symbol, √.
3. Complete the table to describe perfect cubes.
Definition A number multiplied by itself _______ times.
Examples 13 = 1 • 1 • 1 = _____
23 = _____ • _____ • _____ = 8
_____3 = 4 • 4 • 4 = _____
4. Answer the questions about cube roots.
What is a cube root?
Use the radical symbol to represent the cube root of 8.
What is the cube root of –8?
Main idea: Solving equations by taking the square root
5. Complete the steps to show how to solve x2 = 36.
6. Answer the questions about Ally's web page icons as you work through the problem in the study.
Each icon contains 1024 pixels arranged in rows. What does p represent in the equation p2 = 1024?
What is the first step in solving p2 = 1024?
Why doesn't the solution p = –32 make sense for this problem?
Main idea: Solving equations by taking the cube root
7. Solving an equation in the form x3 = p is similar to solving equations with squared terms. Complete the table to show the differences.
x2 = p x3 = p
To solve: Take the square root.
Number of solutions and their sign(s): Two solutions. One is positive and one is negative.
Example:
8. Answer the questions about Tanisha's baking supply container as you work through the problem in the study.
The volume of the salt container is 125 cm3. What does x represent in the equation x3 = 125?
What is the first step in solving x3 = 125?
Is x = –5 a solution to the equation? Why or why not?
Key Terms
Use this table to write definitions for the key terms from this activity in your own words. If you're confident you know a term, put a check mark next to it and move on.
Key Term Definition
cube
cube root
integer
inverse operations
perfect square
principal square root
square
square root
I
Did you just copy and paste your assignment??
If yes, please do not do such a thing and give it in a question by question basis, sorry but I can't type such a big one. Suggestion!!
The coordinates of three of the vertices of parallelogram ABCD are A(2, 0), B(4, 3), C(3, 1). How many possibilities are there for the position of the fourth vertex? What are coordinates of the fourth vertex?
Answer:
probability is one for the position of the fourth vertex
it's co ordinates will be (2,2)
There are 128 ounces in a gallon. There are 4 quarts in a gallon. How many ounces are in a quart
32 ounces.
128/4 = 32
Please see picture
What type(s) of symmetry does this figure have?
A. Both rotational and reflectional
B. This figure is not symmetrical.
C. Rotational
D. Reflectional
Given that the 3rd term in an arithmetic sequence is -2 and the 7th term is -10, tell me what the 1st term in the sequence is. Explain how you know.
Answer:
2
Step-by-step explanation:
a₃ = -2
a₇ = -10
The nth term of an arithmetic sequence is:
a = a₁ + d (n − 1)
Therefore:
-2 = a₁ + d (3 − 1) = a₁ + 2d
-10 = a₁ + d (7 − 1) = a₁ + 6d
Subtract the equations:
8 = -4d
d = -2
Plug into either equation to find the first term.
-2 = a₁ + 2(-2)
a₁ = 2
Multiply. 3 2/3 x 3/4 Express your answer in simplest form
A car rental agency advertised renting a car for $26.95 per day and $0.24 per mile. If Kevin rents this car for 3 days, how many whole miles can he drive on a $250 budget?
miles (Round down to the nearest whole mile.)
Answer: 26.95 * 3 = 80.85
250/0.24 = 60
This year omar watched 80 movies. He thought that 54 of them were very good. of the movies he watched, what percentage did he rate as very good
Answer:
percentage flim rated very good = 54/80*100%
= 67.5%
Step-by-step explanation:
The triangle below is an equilateral triangle. What is the perimeter of the triangle?
Answer:
[tex]5.4x+15[/tex] inches
Step-by-step explanation:
This is an equilateral triangle.
Therefore, all sides are equal to each other. This means that we don't need to go through the whole hassle of adding up all the sides together. We can just take the easiest side and multiply it by 3 (as the perimeter of an equilateral triangle is [tex]3s[/tex], s being the side length.)
In my opinion, the side [tex]1.8x+5[/tex] is the easiest to work with.
Let's multiply this by 3.
[tex]3(1.8x+5)[/tex]
We can apply the distributive property - multiply all terms inside the parentheses by 3.
[tex]1.8\cdot 3 = 5.4\\5\cdot3 = 15\\\\5.4x+15[/tex]
Hope this helped!