[tex]xe^y+4\ln y=x^2[/tex]
Differentiate both sides with respect to x, assuming y = y(x).
[tex]\dfrac{\mathrm d(xe^y+4\ln y)}{\mathrm dx}=\dfrac{\mathrm d(x^2)}{\mathrm dx}[/tex]
[tex]\dfrac{\mathrm d(xe^y)}{\mathrm dx}+\dfrac{\mathrm d(4\ln y)}{\mathrm dx}=2x[/tex]
[tex]\dfrac{\mathrm d(x)}{\mathrm dx}e^y+x\dfrac{\mathrm d(e^y)}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x[/tex]
[tex]e^y+xe^y\dfrac{\mathrm dy}{\mathrm dx}+\dfrac4y\dfrac{\mathrm dy}{\mathrm dx}=2x[/tex]
Solve for dy/dx :
[tex]e^y+\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x[/tex]
[tex]\left(xe^y+\dfrac4y\right)\dfrac{\mathrm dy}{\mathrm dx}=2x-e^y[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x-e^y}{xe^y+\frac4y}[/tex]
If y ≠ 0, we can write
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2xy-ye^y}{xye^y+4}[/tex]
At the point (1, 1), the derivative is
[tex]\dfrac{\mathrm dy}{\mathrm dx}\bigg|_{x=1,y=1}=\boxed{\dfrac{2-e}{e+4}}[/tex]
(6 points) which answer describe the shape below? Check all that apply
20 - (+7) + - (6) = whats the answer
20 - (+7) + - (6)
Answer: 7
Answer:
Answer is 7
20-(+7)+(-6)= ?
(20-7)-6
13-6
7
Cube the following numbers.
a. 1
b. 2
c. 4
d. 8
Answer:
I need to know the equation, but if you have to cube them then you will find your answer right away if you google how to cube numbers.
Step-by-step explanation:
Sorry for the bad answer.
What is the slope of the line that passes through the points (-8, -6) and (-8,4)?
Write your answer in simplest form.
[tex]\\ \rm\rightarrowtail m=\dfrac{4+6}{-8+8}[/tex]
[tex]\\ \rm\rightarrowtail m=10/0[/tex]
Parallel to x axis[tex]\\ \rm\rightarrowtail m=\infty[/tex]
On a coordinate plane, a straight line and a parallelogram are shown. The straight line has a negative slope and has a formula of y = negative x. The parallelogram has points G (negative 2, negative 3), F (1, negative 3), E (negative 1, negative 5), and H (2, negative 5).
What are the coordinates of the image of vertex F after a reflection across the line
y = –x?
A. (–1, –3)
B. (3, –1)
C. (1, 3)
D. (–3, 1)
Answer:
B. (3, –1)
Step-by-step explanation:
Reflection in the line y=-x is described by the transformation ...
(x, y) ⇒ (-y, -x)
Then the point of interest becomes ...
F(1, -3) ⇒ F'(3, -1) . . . . matches choice B
Answer:
The correct answer is B
Step-by-step explanation:
This is correct because it is correct
9x-8y= 1
18x - 16y= 2
Answer:
all real numbers.
Step-by-step explanation:
9x - 8y = 1
18x - 16y = 2
if you look at the first equation, you can figure out what y equals.
9x - 8y = 1
add 8y to both sides
9x = 1 + 8y
subtract 1 from both sides
9x - 1 = 8y
divide both sides by 8
[tex]\frac{9x - 1}{8}[/tex] = y
now, substitute y in the second equation.
18x - 16y = 2
18x - 16([tex]\frac{9x - 1}{8}[/tex]) = 2
18x - 2(9x - 1) = 2
18x - 18x +2 = 2
2 = 2
the answer is all real numbers, because regardless of what x equals, 2 will always equal 2.
please help on number 5 and 6 i’ll give 15 points
If y(x) = 4x, what is x when y(x) = 4?
Replace y(x) with 4:
4 = 4x
Divide both sides by 4:
x = 1
find the area of a triangle if do math problem 5 stars and brainly points
Answer:
24
Step-by-step explanation:
area of a triangle = 1/2 ( base length * height )
given base length : 6
given height : 8
area of triangle = 1/2(8*6)
==> multiply 8 and 6
area of triangle = 1/2(48)
==> multiply 1/2 and 48
area of triangle = 24 square units
Simplify the following expression
Answer:
25
Step-by-step explanation:
On her way home from work, Sandra fills up her car. She likes the idea of using gasoline with ethanol, but thinks her car can only handle 30% ethanol. At the gas station, she can use regular gas with 10% ethanol or E70 fuel with 70% ethanol.
How many gallons of each type of fuel should Sandra use if she wants to fill up her car with 9 gallons of fuel containing 30% ethanol?
Answer:
6 gallons of 10% ethanol gas and 3 gallons of the E70 fuel.
Step-by-step explanation:
Let the volume of 10% ethanol gas be x gallons and the volume of 70% be y gallons.
The resulting mixture ( 9 gallons) must have a strength of 30% ethanol.
SO WE HAVE THE SYSTEM:
x + y = 9
0.10x + 0.70y = 0.30 * 9
0.10x + 0.70y = 2.7
Multiplying the first equation by -0.10:
-0.10x - 0.10y = -0.9
Adding the last 2 equations:
0 + 0.60y = 1.8
y = 1.8 / 0.6 = 3 gallons.
So x = 9 - 3 = 6 gallons.
6 gallons of 10% ethanol gas and 3 gallons of the E70 fuel.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Let the volume of 10% ethanol gas be x gallons and the volume of 70% be y gallons.
The resulting mixture ( 9 gallons) must have a strength of 30% ethanol.
x + y = 9
0.10x + 0.70y = 0.30 * 9
0.10x + 0.70y = 2.7
Multiplying the first equation by -0.10:
-0.10x - 0.10y = -0.9
Adding the last 2 equations:
0 + 0.60y = 1.8
y = 1.8 / 0.6 = 3 gallons.
So x = 9 - 3 = 6 gallons.
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Given f(x) = 3x - 5 and g(x) = -2x + 1, find h(x) = f(x) - g(x)
Answer:
h(X)=5x-6
Step-by-step explanation:
Fill in variables with corresponding equations.
h(X)=(3X-5)-(-2X+1)
Distribute the - sign to (-2X+1)
h(X)=3X-5+2X-1
Add and subtract values together to find answer
h(X)=5X-6
Your teacher asks the class to evaluate the expression (3³)¹. Your classmate gives an incorrect answer of 81. Evaluate the expression. Then find the likely error.
The most likely error is that, the student multiplied 27 by 3, after the first computation
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the error in the calculation?The expression is given as
(3^3)^1
As a general rule, we start by evaluating the expression in the inner bracket
So, we have
(3^3)^1 = (3 x 3 x 3)^1
Evaluate the products
So, we have
(3^3)^1 = (27)^1
Next, we evaluate the exponent
So, we have
(3^3)^1 = 27
The above implies that the value of the expression is 27 and not 81 as the student solved
The most likely error is that, the student multiplied 27 by 3, after the first computation
Hence, the value of the expression is 27 and not 81 and the most likely error is that, the student multiplied 27 by 3, after the first computation
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A vertical wall AB which is 5m high was built on level ground. The distance of a point C on the ground from the base of the wall is 12m. Calculate the distance from the top of the wall to the point C..
13. Find the area of the triangle given a = 14, b = 9, and C = 66 degrees. Round your answer to the nearest tenth.
14. Find the area of the triangle given a = 38, b = 31, and C = 29 degrees. Round your answer to the nearest tenth.
15. Find the area of the triangle given b = 17, c = 19, and A = 135 degrees. Round your answer to the nearest tenth.
Answer:
13) 57.6 units²
14) 285.6 units²
15) 114.2 units²
(All answers rounded off to the nearest tenth)
Step-by-step explanation:
Please see the attached picture for the full solution.
The formula of the diameter, radius, and area of a circle.
Answer:
Step-by-step explanation:
diameter = 2r
radius = C/2π
area = πr^2
(HELP) What is the length of xy in xyz?
Answer:
xy=6
Step-by-step explanation:
sin θ= opposite side÷ hypotenuse
sin 30°= xy÷12
sin 30°=1/2
Therefore,
1/2=xy÷12
1/2×12=xy
xy=6
A graduate student is performing a study on a new anti-anxiety drug. The drug is supposed to reduce anxiety, but the graduate student realizes that it may do nothing or even increase anxiety, so he decides to formulate non directional hypotheses and conduct a two-tailed test. He knows that the average score for all anxious people is μ₀ = 100, with a standard deviation of σ = 14. If he designates the mean for the population of anxious people who take the anti-anxiety drug as μ anti-anxiety drug anti-anxiety drug , he can identify the null and alternative hypotheses as:
Answer:
hello your question is incomplete attached below is the complete question
Answer : The standard deviation of the scores on the anxiety inventory is the same for those who take the anti-anxiety drug and those who don't
Step-by-step explanation:
average score for anxious people = 100
standard deviation = 14
mean of anxious people who take the anti-anxiety drug
null hypothesis ( H ) =
Alternate hypothesis ( H1 ) ≠
using the z- test ( hypothesis test ) the condition that is not required is the condition that
The standard deviation of the scores on the anxiety inventory is the same for those who take the anti-anxiety drug and those who don't
What is the slope between the points (–2, 1) and (2, 6)?
5/4
-4/5
4/5
-5/4
To find the slope, we must know the equation
--> [tex]slope = \frac{y2-y1}{x2-x1}\\[/tex]
Now using the information given, (-2,1) and (2,6), let's plug that into the equation
--> [tex]slope = \frac{6-1}{2--2} = \frac{5}{4}[/tex]
In this case, the slope is 5/4
Hope that helped!
Answer:
[tex]\rn\hookrightarrow 5/4[/tex]
Step-by-step explanation:
[tex]Solution,\\\\Let,\\(x_1,y_1)=(-2,1)\\\\(x_2,y_2)=(2,6)\\\\Now,\\\\\rn\hookrightarrow Slope=\frac{y_2-y_1}{x_2-x_1}\\\\\rn\hookrightarrow Slope=\frac{6-1}{2-(-2)} \\\\\rn\hookrightarrow Slope=\frac{5}{4}[/tex]
A population of beetles are growing according to a linear growth model. The initial population (week 0) is
P
0
=
5
, and the population after 7 weeks is
P
7
=
47
.
After how many weeks will the beetle population reach 113?
9514 1404 393
Answer:
18 weeks
Step-by-step explanation:
We are given the (time, population) pairs (0, 5) and (7, 47). With these values, we can use the two-point form of the equation of a line to write the equation of the linear model.
p = (p2 -p1)/(t2 -t1)(t -t1) +p1
p = (47 -5)/(7 -0)(t -0) +5
p = 6t +5 . . . . . the linear model matching the given points.
For p = 113, the time (number of weeks) is ...
113 = 6t +5
108 = 6t . . . . . . subtract 5
18 = t . . . . . . . . . divide by 6
After 18 weeks, the beetle population will reach 113.
help me please if that's okay , thank you sm
Answer:
9. is true
10. is false
hope this helps
Step-by-step explanation:
Step-by-step explanation:
9 is true and 10 is true as well
Frank owed Alan $30. One week he paid him $14. Another week he paid him $8.50 What percentage of the $30 does Frank still owe to Alan?
Need help with math probelm if do 5 stars and brainly points
Answer:
63 units^2
Step-by-step explanation:
the area of the rectangle is 48 units^2
l*h=a
6*8=a
48=a
The area of the triangle is 15 units^2
b*h/2=a
6*5/2=a
30/2=a
15=a
Let me know if you have any further questions, hope this helped!
a) Write down the value of angle x.
b) Write down the value of angle y.
HELP PLS
Answer:
A) is 49 degrees and B) is 63
Step-by-step explanation:
they are kinda like mirrors
the length of a rectangle is 4 times it’s width. The rectangle has an area of 1024cm squared
[tex]Your answer it W^2 = 1024/4 = 256.[/tex]
Step-by-step explanation:
What is the distance from m(-1,6) to n(11,1)
Soln:
Let m(-1,6) be (x1, y1) & n(11,1) be (x2, y2).
Now,
Use distance formula and calculate it
Rendell cycles 42 km at an average speed of 18 km/hr. Find the time taken, giving your
answer as a fraction of an hour in its simplest form.
Answer:
[tex]\frac{7}{3}[/tex]
Step-by-step explanation:
42/18=[tex]\frac{7}{3}[/tex]
Rendell took 2.34 hr to cycle 42 km.
Rendell cycles 42 km at an average speed of 18 km/hr.
Distance = 42 km
Speed = 18 km/hr
Speed is define as the distance covered per unit time,
Here,
Time = Distance / speed
= 42 / 18
= 2.34 hr
Thus, Rendell took 2.34 hr to cycle 42 km.
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Try This question out and I’ll give you brainliest
Answer:
7/12ths
Step-by-step explanation:
2/3rds of the way full would be 8/12. Since she started at 1/12th of a tank, 7/12ths was added. (:
ts
Find the quotient.
5
14)154
O 10
O 10.5
O 11
O 11.7
Answer:11/c
Step-by-step explanation:
Help help math math ASAP
Answer:
y equals to x plus 9
Step-by-step explanation:
-x+y=9
so, y=x+9