Let f = ln(x + √(x ² + y ²)) ln(sin(y/x)).
Then the total differential is
[tex]\mathrm df = \dfrac{\mathrm d\left(x+\sqrt{x^2+y^2}\right)}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\mathrm d\left(\sin\left(\frac yx\right)\right)}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\mathrm dx + \frac{\mathrm d(x^2+y^2)}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}}\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}\right)\dfrac{\cos\left(\frac yx\right)\,\mathrm d\left(\frac yx\right)}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\mathrm dx + \frac{2x\,\mathrm dx+2y\,\mathrm dy}{\sqrt{x^2+y^2}}}{x+\sqrt{x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) + \ln\left(x+\sqrt{x^2+y^2}}\right)\dfrac{\cos\left(\frac yx\right)\frac{x\,\mathrm dy-y\,\mathrm dx}{x^2}}{\sin\left(\frac yx\right)}[/tex]
[tex]\mathrm df = \dfrac{\left(2x+\sqrt{x^2+y^2}\right)\,\mathrm dx +2y\,\mathrm dy}{x\sqrt{x^2+y^2}+x^2+y^2\right)\ln\left(\sin\left(\dfrac yx\right)\right) \\\\ \indent + \dfrac1{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}}\right)(x\,\mathrm dy-y\,\mathrm dx)[/tex]
[tex]\mathrm df = \left(\left(\dfrac{2x+\sqrt{x^2+y^2}}{x\sqrt{x^2+y^2}+x^2+y^2}\right)\ln\left(\sin\left(\dfrac yx\right)\right) - \dfrac y{x^2}\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dx \\\\ \indent + \left(\dfrac{2y}{x\sqrt{x^2+y^2}+x^2+y^2}\ln\left(\sin\left(\dfrac yx\right)\right)+\dfrac1x\cot\left(\dfrac yx\right)\ln\left(x+\sqrt{x^2+y^2}\right)\right)\,\mathrm dy[/tex]
Kevin's supervisor, Jill, has asked for an update on today's sales, Jill is pretty busy moving back and forth between different store locations. How can Kevin most effectively deliver an update to her ? a) Call with a quick update Ob ) Send a detailed text message c ) Book a one-hour meeting for tomorrow morning d) Send a detailed email
solve for x
8x2-5=11
Answer:
1
Explainion show in picture above
Answer:
x=6
Step-by-step explanation:
It should be 8+x+2-5=11
(-4/9)*3×(-27/20)*4=
(-4/9)*3×(-27/20)*4= 7.2
Step-by-step explanation:
here's the answer to your question
The distance between point (3,0) and (7, 2p) is √80. Find the value of p.
Distance = √[ ( 7 - 3 )^2 + ( 2p - 0 )^2 ]
Distance = √(4)^2 + ( 2p)^2
Distance = √16 + 4p^2
As the question said : Distance = √80
√80 = √16 + 4p^2
Thus :
16 + 4p^2 = 80
Subtract both sides 16
16 - 16 + 4p^2 = 80 - 16
4p^2 = 64
Divide both sides by 4
4p^2 ÷ 4 = 64 ÷ 4
p^2 = 16
Thus :
p = 4 or p = - 4
OMG!! I’m stuck on 4a) b) c)
Help please
Answer:
a) 750 cmb) 288 cmc) 2112 cmStep-by-step explanation:
Formula for getting the surface area of a rectangular prism: SA = 2 (WL + HL + HW)a) SA = 2 (WL + HL + HW) = 2(75) + 2(225) + 2(75) = 150 + 450 + 150 = 750 cm^2b) SA = 2 (WL + HL + HW)= 2(48) + 2(72) + 2(24)= 96 + 144 + 48=288 cm^2c) SA = 2 (WL + HL + HW)= 2(400) + 2(400) + 2(256)= 800 + 800 + 512= 2112 cm^2[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]
Answer:
Below in bold.
Step-by-step explanation:
(a) The surface area consists of the sum of the area of 3 sets of 2 congruent rectangles. The 2 rectangles are on opposite sides of the solid.
= 2(15*15) + 2(5*15) + 2(5&15)
= 450 + 150 + 150
= 750 unit^2.
(b). Similarly to the above:
Surface area = 2(12*6) + 2(4*12) + 2(4*6)
= 144 + 96 + 48
= 288 unit^2.
(c) Again:
Surface area = 2(25*16) + 2(25*16) + 2(16*16)
= 400 + 400 + 256
= 1056 unit^2.
Cars arrive at a toll booth according to a Poisson process with mean 90 cars per hour. Suppose the attendant makes a phone call. How long, in seconds, can the attendant's phone call last if the probability is at least 0.1 that no cars arrive during the call
Answer:
92.12 seconds
Step-by-step explanation:
According to the poisson probability relation :
P(X =x) = (e^-λ * λ^x) / x!
For no calls to be reveived during the period, x = 0
P(X = 0) = (e^-λ * λ^0) / 0!
P(X = 0) = 0.1
0.1 = (e^-λ * λ^0) / 0!
0.1 = e^-λ
Take the In of both sides
In(0.1) = - λ
-2.303 = - λ
λ = 2.303
The length of call in second, l
l = λ / r ; r = arrival rate
r = 90 per hour ; this means ;
90 / 3600 = 0.025
l = 2.303 / 0.025
l = 92.12 seconds
A common inhabitant of human intestines is the bacterium Escherichia coli, named after the German pediatrician Theodor Escherich, who identified it in 1885. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 50 cells.
Required:
a. Find the relative growth rate.
b. Find an expression for the number of cells after t hours.
c. Find the rate of growth after 6 hours. (Round your answer to the nearest integer.)
d. Find the number of cells after 6 hours.
Answer:
a. Relative Growth rate = 10% (6/60 * 100)
b. Number of cells after t hours = 50 * 1.1^t
c. Rate of growth after 6 hours = 77.2% (1.1⁶ - 1)
d. The number of cells after 6 hours is
= 89 cells
Step-by-step explanation:
A cell divides into two cells every 20 minutes
In one hour, the cell will divide into 60/20 * 2 = 6 cells
Each cell growth 6 cells per hour
Initial population of a culture = 50 cells
t = time in hours
a. Relative Growth rate = 10% (6/60 * 100)
b. Number of cells after t hours = 50 * 1.1^t
c. Rate of growth after 6 hours = 77.2% (1.1⁶ - 1)
d. The number of cells after 6 hours = initial population * growth factor
= 50 * 1.772
= 88.6
= 89 cells
Dean Halverson recently read that full-time college students study 20 hours each week. She decides to do a study at her university to see if there is evidence that students study an average of more than 20 hours each week. A random sample of 35 students were asked to keep a diary of their activities over a period of several weeks. It was found that the average number of hours that the 35 students studied each week was 21.1 hours. The sample standard deviation of 4.3 hours.
Find the p-value.
The p-value should be rounded to 4-decimal places.
Answer:
0.0698
Step-by-step explanation:
Given :
Population mean, μ = 20
Sample mean, xbar = 21.1
Sample standard deviation, s = 4.3
Sample size, n = 35
The hypothesis :
H0 : μ = 20
H0 : μ > 20
The test statistic :
(xbar - μ) ÷ (s/√(n))
T = (21.1 - 20) ÷ (4.3/√(35))
T = 1.1 ÷ 0.7268326
Test statistic = 1.513
Using the Pvalue calculator :
df = n - 1 = 35 - 1 = 34
Pvalue(1.513, 34) = 0.06976
Pvalue = 0.0698 (4 decimal places)
The p-value is 0.0698 if rounded to 4-decimal places.
It is given that students study an average of more than 20 hours each week and the random sample of 35 students was asked to keep a diary of their activities over a period of several weeks.
The average number of hours that the 35 students was 21.1 hours.
The sample standard deviation is 4.3 hours.
It is required to find the p-value.
What is the standard deviation?It is defined as the measure of data dispersement, It gives an idea about how much is the data spread out.
We can test the hypothesis using the Z test, the formula for the Z-test is given below:
[tex]\rm Z= \frac{(x-u)}{\frac{S}{\sqrt{n} } }[/tex]
Where x is the sample mean
u is the population mean
s is the standard deviation
n is the sample size.
The hypothesis are: H0 : μ = 20 V/s H1 : μ > 20
We have x = 21.1
u = 20
s = 4.3
n = 35
Putting these values in the above formula, we get:
[tex]\rm Z= \frac{(21.1-20)}{\frac{4.3}{\sqrt{35} } }\\\\\rm Z= \frac{(1.1)}{\frac{4.3}{\sqrt{35} } }\\\\[/tex]
Z = 1.513
difference or df = n -1 ⇒ 35-1 ⇒ 34
P-value at (1.513, 34) = 0.06976 (From the p-value calculator)
P-value = 0.0698 (Rounded to 4-decimal places)
Thus, the p-value is 0.0698 if rounded to 4-decimal places.
Learn more about the standard deviation here:
brainly.com/question/12402189
Differentiate the following Functions
5x^2-2xy + 4y^3= 5
Answer:
[tex]\displaystyle y' = \frac{y - 5x}{x + 6y^2}[/tex]
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringCalculus
Differentiation
DerivativesDerivative NotationImplicit DifferentiationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Derivative Rule [Product Rule]: [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]
Derivative Rule [Chain Rule]: [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle 5x^2 - 2xy + 4y^3 = 5[/tex]
Step 2: Differentiate
Implicit Differentiation: [tex]\displaystyle \frac{dy}{dx}[5x^2 - 2xy + 4y^3] = \frac{dy}{dx}[5][/tex]Rewrite [Derivative Property - Addition/Subtraction]: [tex]\displaystyle \frac{dy}{dx}[5x^2] - \frac{dy}{dx}[2xy] + \frac{dy}{dx}[4y^3] = \frac{dy}{dx}[5][/tex]Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle 5\frac{dy}{dx}[x^2] - 2\frac{dy}{dx}[xy] + 4\frac{dy}{dx}[y^3] = \frac{dy}{dx}[5][/tex]Basic Power Rule [Chain Rule]: [tex]\displaystyle 10x - 2\frac{dy}{dx}[xy] + 12y^2y' = 0[/tex]Product Rule: [tex]\displaystyle 10x - 2\bigg[ \frac{dy}{dx}[x]y + x\frac{dy}{dx}[y] \bigg] + 12y^2y' = 0[/tex]Basic Power Rule [Chain Rule]: [tex]\displaystyle 10x - 2\bigg[ y + xy' \bigg] + 12y^2y' = 0[/tex]Simplify: [tex]\displaystyle 10x - 2y + 2xy' + 12y^2y' = 0[/tex]Isolate y' terms: [tex]\displaystyle 2xy' + 12y^2y' = 2y - 10x[/tex]Factor: [tex]\displaystyle y'(2x + 12y^2) = 2y - 10x[/tex]Isolate y': [tex]\displaystyle y' = \frac{2y - 10x}{2x + 12y^2}[/tex]Factor: [tex]\displaystyle y' = \frac{2(y - 5x)}{2(x + 6y^2)}[/tex]Simplify: [tex]\displaystyle y' = \frac{y - 5x}{x + 6y^2}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
Y<3/2•x-4
Match the equation to a graph.
Answer:
Last option
Step-by-step explanation:
The slope 3/2 determines the line (although you can plot points to find (0,-4) and (4,2), connecting them, you'll get the equation of the line, and the area it covers will be to the right side, putting x = 0, y<-4, which is below the line, that's how you determine it.
Answered by GAUTHMATH
Help me please and thank you
Step-by-step explanation:
jlejej
are u using chrome os
Laura makes a sound that 80.9 dB loud. Sarah makes a sound that is 3 time as intense. What is the loudness of Sarah's sound (in dB)
Answer:
242.7 dB
Step-by-step explanation:
What is the mean of 86, 80, and 95
87 is the mean.
To find the mean, you must
- add all of the numbers
- divide by the amount of numbers given
In this case, you would want to do (86 + 80 + 95)/3. This would give you an answer of 87.
A tourist from Britain wants to exchange her British pounds for US dollar. She has 25 British pounds. How many US dollars would she get in exchange for her British pound if 1 British pound can be exchanged for 1.53 US dollars?
Answer:
$38.25 US dollars.
Step-by-step explanation:
25 / 1 = 25
To find the number of US dollars that can be exchanged for 25 British pounds, multiply 1.53 by 25 to get $38.25 US dollars.
Hope this helps!
if there is something wrong, just let me know.
Classify the following data. Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data.
A supervisor must give a summary evaluation rating from among the choices given below:
1) Poor
2) Fair
3) Good
4) Very good
5) Excellent
a. Are these data qualitative or quantitative?
b. Are these data discrete or continuous?
c. What is the highest level of measurement the data possesses?
Answer:
Qualitative data
Neither discrete or continous
Ordinal
Step-by-step explanation:
Qualitative data simply refers to Non-numeric measure, they make use of data labels which are expressed in words rather than figures or numbers.
For a data to be either discrete or continous, then it has to be numeric, since the data is qualitative and non- numeric, then it is neither continous or discrete.
This is an ordinal scale representation of data as data are ordered or ranked in terms of performance, however, there is no measure of difference between each rank or order. The highest level of performance in the scale is Excellent.
(x+7)(x-6) Find the product.ddddddddddddd
Answer:
x^2 + x - 42
Step-by-step explanation:
use the distributive property:
(x+7)(x-6) = x^2 + x - 42
Answer: x^2 + x - 42
Step-by-step explanation:
½ sejam berapa minit?
Answer:
1/2 jam 30 menit mungkin?
1/2 jam adalah 30 minit
1/2 × 60 = 30 mins
English translation
1/2 an hour is 30 minutes
1/2 × 60 = 30 mins
Answered by Gauthmath must click thanks and mark brainliest
A box contains orange balls and green The number of more four the number of orange If there 38 balls how many green balls and how balls are there in the box ?
let number of green balls= x
let number of orange balls=x+4
x+x+4=38
2x=38-4
2x=34
x=17
number of green balls=17
number of orange balls=21
Two ice cream stands are deciding where to set up along a 1-mile-long beach. The people are uniformly located along the beach, and each person sitting on the beach buys exactly 1 ice cream cone per day from the nearest stand. Each ice cream seller wants the maximum number of customers. True or False: The two stands will most likely be 1/3 mile away from each other. True
Answer:
Each ice cream seller wants the maximum number of customers:
True
The two ice cream stands will most likely be 1/3 mile away from each other.
True
Step-by-step explanation:
This distance enables the two ice cream stands to give access to the maximum number of customers at the beach, which will be almost equal at their right-hand and left-hand sides. Therefore, the two ice cream stands will most likely be 1/3 mile away from each other. Such positioning exposes the ice cream stands to almost equal number of customers since the people standing along the beach are uniformly located. Taking the extreme locations along the 1-mile-long beach will shrink location opportunities for both stands.
Using the order of operations, what is the last calculation that should be done to evaluate 4(8 - 6952 - 6+(-3)
4(8 - 6352 – 6 + (-3)
4(2)52 - 6+(-3)
4(2)(25) - 6+(-3)
200 - 6+(-3)
200 - (-2)
Answer:
200 + 2
Step-by-step explanation:
you know that two (2) negatives multiplying each other is = +
=200 +2
=202
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. He believes that the mean income is $30.8, and the standard deviation is known to be $8.2. How large of a sample would be required in order to estimate the mean per capita income at the 95% level of confidence with an error of at most $0.39
Answer:
A sample of 1699 would be required.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation is known to be $8.2.
This means that [tex]\sigma = 8.2[/tex]
How large of a sample would be required in order to estimate the mean per capita income at the 95% level of confidence with an error of at most $0.39?
This is n for which M = 0.39. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.39 = 1.96\frac{8.2}{\sqrt{n}}[/tex]
[tex]0.39\sqrt{n} = 1.96*8.2[/tex]
[tex]\sqrt{n} = \frac{1.96*8.2}{0.39}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*8.2}{0.39})^2[/tex]
[tex]n = 1698.3[/tex]
Rounding up:
A sample of 1699 would be required.
what is the value of k
Answer:
(A)
Step-by-step explanation:
M=-2
therefore
x¹=3, y¹=-12, x²=6 y²=k
M=(y²-y¹)/(x²-x¹)
-2=(k+12)/(6-3)
-2×3=k+12
-6=k+12
k=-18
If the mean of a given dataset is
42 and the standard deviation is
4, where will a majority of the
data lie?
Answer:
A majority of the data will lie between 38 and 46.
Step-by-step explanation:
It can be said that a majority of the data of a distribution lies within 1 standard deviation of the mean.
In this question:
Mean of 42, standard deviation of 4.
42 - 4 = 38
42 + 4 = 46
A majority of the data will lie between 38 and 46.
Plz this is due today help me explain the answer
Answer:
177.3 feet
This is a classic find the vertex of a parabola question.
if this was a calculus class the solution would be to take the derivative and set it equal to zero... -32t+ 105 = 0
BUT i assume that you are not in a calculus class..
so we try plan "B" the highest (or lowest) point of parabola is it's vertex
the vertex formula is [-b/2a,f(-b/2a)]
in your problem a = -16, b=105, c= 5
so the "X" (TIME) is located at -(105)/(2*-16) = 3.28
plug in 3.28 into -16(3.28)^2 + 105(3.28) + 5 = 177.27
and you will get
Step-by-step explanation:
The length of a rectangle is 5 ft less than three times the width, and the area of the rectangle is 28 ft^2. Find the dimensions of the rectangle.
Answer:
7 x 4
Step-by-step explanation:
Let the width be x, length will be 3x-5. ATQ, x(3x-5)=28. x=4 and x=-7/3, since length isn't negative, x=4. Width=4 and length=7
Urgent need the answers plz help.
Answer:
(a) [tex]P" = (-4,-3)[/tex]
(b) [tex](x,y) \to (4,-8)[/tex]
Step-by-step explanation:
Given
[tex]P = (4,3)[/tex]
Solving (a): Reflect across x and y-axis.
Reflection across x-axis has the following rules
[tex](x,y) \to (x,-y)[/tex]
So, we have:
[tex]P' = (4,-3)[/tex]
Reflection across y-axis has the following rules
[tex](x,y) \to (-x,y)[/tex]
So, we have:
[tex]P" = (-4,-3)[/tex]
Hence, the new point is: (-4,-3)
Solving (b): Rx . Do,2 (2,4)
[tex]R_x \to[/tex] reflect across the x-axis
Reflection across x-axis has the following rules
[tex](x,y) \to (x,-y)[/tex]
So, we have:
[tex](2,4) = (2,-4)[/tex] ---- when P is reflected across the x-axis
[tex]D_{o,2} \to[/tex] dilate by a scale factor of 2
The rule is:
[tex](x,y) \to 2 * (x,y)[/tex]
So, we have
[tex](x,y) \to 2 * (2,-4)[/tex]
Open bracket
[tex](x,y) \to (4,-8)[/tex]
b) An achievement test was administered to a class of 20,000 students. The mean score was 80 and the standard deviation was 11. If Lingard scored 72 in the test, how many students did better than him
Answer: 15328
Step-by-step explanation:
The following can be deduced from the information given:
N = 20000
μ = 80
σ = 11
P(X>72) = 1 - P (X<72)
= 1 - P(Z < 72-80/11)
= 1 - P(Z < -8/11)
= 1 - P(Z < 0.7272)
= 1 - 0.2336 = 0.7664
Therefore, the number of students that were better than Lingard n(X > 72) will be:
= 20000 × 0.7664
= 15328
a car completes a journey in 8hours it covers half the distance at 40kms per hours and the rest at 60 km per hour. what is the total distance of the journey?
Answer:
384 kmph
Step-by-step explanation:
h is a trigonometric function of the form h(x)=a sin(bx+c)+d. Below is the graph h(x). The function intersects its midline at (-pi,-8) and has a maximum point at (pi/4, "-1.5)." Find a formula for h(x). Give an exact expression.
Answer:
6.5sin(.04x+.4pi)-8
The function intersects its midline at (-pi,-8) and has a maximum point at (pi/4, "-1.5). The final equation is h(x) = 4 sin(2x + π /2) + 3.
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
The function intersects its midline at (3π/4, 3) then the midline is d= 3.
The amplitude is just the positive distance between the maximum/minimum and the midline,
so the amplitude a = 7 - 3 = 4
Also, given that period is 2π/b and the fact that the period is π from our given maximum,
we have the equation 2π/b= π where b = 2
we know that the phase shift, -c/b is - π/4 (or to the left)
since -π /4. Therefore, c = π /2.
our final equation is
h(x) = 4 sin(2x + π /2) + 3.
Learn more about function;
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the incenter of a triangle is formed by the intersection of the of a triangle
Answer:
angle bisectors
Step-by-step explanation:
The incentre is where a triangle's three angle bisectors intersect ( an angle bisector is a ray that cuts an angle in half ). The incentre is the centre of a triangle drawn inside the triangle.
