The surface integral of the given surface [tex]z=\frac{2}{3}(x^\frac{3}{2}+y^\frac{3}{2})[/tex] in the intervals 0 ≤ x ≤ 4, 0 ≤ y ≤ 1 is 7.36615.
How to evaluate the surface integral?To evaluate the surface integral, the formula applied is
[tex]S=\int\limits^b_a\int\limits^d_c {f(x,y)} \ dy\ dx[/tex]
⇒ S = [tex]\int\limits^b_a \int\limits^d_c {\sqrt{1+(\frac{dz}{dx})^2+(\frac{dz}{dy})^2 } } \, dy \, dx[/tex]
Where the differentiation is partial differentiation and f(x, y) = z.
Calculation:The given function is
f(x, y) = [tex]z=\frac{2}{3}(x^\frac{3}{2}+y^\frac{3}{2})[/tex]
Then, applying the partial differentiation w.r.t x and y respectively,
dz/dx = [tex]\frac{2}{3}(\frac{3}{2})x^{1/2}[/tex] = [tex]x^{1/2}[/tex]
dz/dy = [tex]\frac{2}{3}(\frac{3}{2})y^{1/2}[/tex] = [tex]y^{1/2}[/tex]
Then,
we have surface integral formula as
S = [tex]\int\limits^b_a \int\limits^d_c {\sqrt{1+(\frac{dz}{dx})^2+(\frac{dz}{dy})^2 } } \, dy \, dx[/tex]
On substituting,
⇒ S = [tex]\int\limits^4_0 {\int\limits^1_0 {\sqrt{1+(x^{1/2})^2+(y^{1/2})^2} \, dy } \, dx[/tex]
⇒ S = [tex]\int\limits^4_0 {\int\limits^1_0 {\sqrt{1+x+y} \, dy } \, dx[/tex]
On integrating w.r.t y
⇒ S = [tex]\int\limits^4_0 {\frac{2}{3}(1+x+y)^{3/2}} \,|_0^1 dx[/tex]
Applying limits,
⇒ S = [tex]\int\limits^4_0 {\frac{2}{3}[(1+x+1)^{3/2}-(1+x+0)^{3/2} } \, dx[/tex]
⇒ S = [tex]\frac{2}{3} \int\limits^4_0 {[(x+2)^{3/2}-(x+1)^{3/2}}] \, dx[/tex]
Again applying the integration w.r.t x
⇒ S = [tex]\frac{2}{3}[\frac{2}{5}(x+2)^{5/2}-\frac{2}{5}(x+1)^{5/2}]|_0^4[/tex]
Applying the limits and simplifying,
⇒ S = [tex]\frac{4}{15}[(4+2)^{5/2}-(4+1)^{5/2}-(0+2)^{5/2}+(0+1)^{5/2}][/tex]
⇒ S = [tex]\frac{4}{15}[1+36\sqrt{6}-25\sqrt{5}-4\sqrt{2}][/tex]
∴ S = 7.36615
Therefore, the surface integral of the given function is 7.36615.
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Write the first five terms of the recursively defined sequence. a1 = 6, ak 1 = 1 3 ak2
The first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608
For given question,
We have been given the recursive formula of a sequence.
[tex]a_{k+1}=\frac{1}{3}{a_k}^2[/tex]
Also, the first term of the sequence is,
a1 = 6
Substitute k = 1 in given recursive formula.
⇒ [tex]a_{1+1}=\frac{1}{3}{a_1}^2[/tex]
⇒ a2 = 1/3 (6)²
⇒ a2 = (1/3) × 36
⇒ a2 = 12
Substitute k = 2 in given recursive formula.
⇒ [tex]a_{2+1}=\frac{1}{3}{a_2}^2[/tex]
⇒ a3 = (1/3) × (12)²
⇒ a3 = (1/3) × 144
⇒ a3 = 48
Substitute k = 3 in given recursive formula.
⇒ [tex]a_{3+1}=\frac{1}{3}{a_3}^2[/tex]
⇒ a4 = (1/3) × (48)²
⇒ a4 = (1/3) × 2304
⇒ a4 = 768
Substitute k = 4 in given recursive formula.
⇒ [tex]a_{4+1}=\frac{1}{3}{a_4}^2[/tex]
⇒ a5 = (1/3) × (768)²
⇒ a5 = (1/3) × 589824
⇒ a5 = 196608
Therefore, the first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608
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I don’t understand what I did wrong
Step-by-step explanation:
You got your fraction messed up
It should be -3/2 or -1.5
PLS HELP PLS
Figure B is a scaled copy of Figure A.
What is the scale factor from Figure A to Figure B?
The scale factor from Figure A to Figure B is 4
How to determine the scale factor from Figure A to Figure B?From the question, we have the following statement:
Figure B is a scaled copy of Figure A.
The corresponding side lengths of figure A and figure B are:
Figure A = 10
Figure B = 40
The scale factor from Figure A to Figure B is then calculated as:
Scale factor = Figure B/Figure A
Substitute the known values in the above equation
Scale factor = 40/10
Evaluate the quotient
Scale factor = 4
Hence, the scale factor from Figure A to Figure B is 4
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y=–6x+2
–12x – 2y=–4
How many solutions does this linear system have?
The linear equation y = -6x + 2; -12x - 2y = -4 has no solution
Linear equationy = -6x + 2
-12x - 2y = -4
Substitute y = -6x + 2 into (2)-12x - 2y = -4
-12x - 2(-6x + 2) = -4
-12x + 12x -4 = -4
-12x + 12x = - 4 + 4
0 = 0
Solve for xy = -6x + 2
y - 2 = -6x
x = (y - 2) / -6
Substitute into (2)-12x - 2y = -4
-12(y- 2)/ 6 - 2y = -4
(-12y + 24) / 6 - 2y = -4
-2y + 4 - 2y = 4
0 = 0
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Marika is training for a track race. She start sprinting by 100 yards. She gradually increases her distance, adding 4 yards a day for 21 days. the explicit formula that models this situation is an=100+(n-1)4. how far does seh sprint on day 21
Answer:
180 yards
Step-by-step explanation:
The number of yards she sprints on day 21 can be found by evaluating the formula with n=21.
Solutiona21 = 100 +(21 -1)4 = 100 +(20)(4) = 100 +80 . . . . . use 21 in place of n
a21 = 180
Marika sprints 180 yards on day 21.
Me and mrs corrino can complete a job in 5 hours if mr corrino works twice as long as mrs corrino if each foes the job alone how long does it take mrs corrubi to complete the job alone
Mrs. Corrubi takes 7.5 hours to complete the job alone.
Directly proportional: as one amount increases, another amount increases at the same rate. Direct variation means when one quantity changes, the other quantity also changes in direct proportion
Inversely Proportional: when one value decreases at the same rate that the other increases. An increase in the quantity A leads to a decrease in quantity B and vice versa.
Let the number of hours taken by Mrs Corrubi to do a particular work be x.
∴ The number of hours taken by Mr Corrubi to do a particular work will be 2x.
So according to the condition,
1/x + 1/2x = 1/5
(2+1)/2x = 1/5
3/2x = 1/5
2x = 15
x = 7.5 hours.
Thus Mrs. Corrubi takes 7.5 hours to complete the job alone.
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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match each solid cone to its surface area. Answers are rounded to the nearest square unit.
829 square units
628 square units
444 square units
996 square units
8 units
12 units
525 square units
>
758 square units
Rounded to the nearest square units, the surface area of the cone, is: 524 square units.
How to Find the Surface Area of a Cone?The surface area of a cone = πr(r + l), where:
r is the radius of the cone
l is the length of the cone.
Given the following:
Radius of the cone (r) = 12/2 = 6 units
Slant height of the cone (l) = √(21² + 6²) [Pythagorean theorem]
Slant height of the cone (l) = 21.8 units.
Plug in the values into πr(r + l):
Surface area of the cone = π × 6(6 + 21.8)
Surface area of the cone = 3.14 × 6(27.8)
Surface area of the cone ≈ 525 square units
The surface area of the cone, approximated to the nearest square units, we have: 524 square units.
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Subtract the given fraction:-
[tex] \frac{3}{5} - \frac{5}{3} = [/tex]
Please help with 54 :(
Answer:
A is the answer
[tex]x = \frac{1}{48} [/tex]
Select the correct answer. the data manager for a state political party gathered data to determine how many citizens would support the party’s senate candidate. he polled citizens in 30 similarly sized senate districts and found a sample mean of 70,438 citizens. statewide data shows that the population standard deviation is 645.3. what is the approximate 90% confidence interval for this situation? a. 70,134 and 70,742 b. 70,207 and 70,669 c. 70,403 and 70,473 d. 70,244 and 70,632
Answer:
D. 70,244 and 70,632
Step-by-step explanation:
Got it right on PLATO/EDMENTUM
70,244 and 70,632 is the approximate 90% confidence interval for this situation.
A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.
A confidence interval displays the probability that a parameter will fall between a pair of values around the mean.Confidence intervals measure the degree of uncertainty or certainty in a sampling method.They are most often constructed using confidence levels of 95% or 99%.Confidence intervals measure the degree of uncertainty or certainty in a sampling method. They can take any number of probability limits, with the most common being a 95% or 99% confidence level. Confidence intervals are conducted using statistical methods.
Statisticians use confidence intervals to measure uncertainty in a sample variable. For example, a researcher selects different samples randomly from the same population and computes a confidence interval for each sample to see how it may represent the true value of the population variable. The resulting datasets are all different; some intervals include the true population parameter and others do not.
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d. If you double a certain number and subtrack 7 you get the same answer as when you add 5 to the number, Determine the number
Answer:
12
Step-by-step explanation:
Let n = the number.
2n - 7 = n + 5
n = 12
Let’s check if we got the right answer by substituting 12 for n into the original equation.
2*12 - 7 = 12 + 5
24 - 7 = 17
17 = 17
PLS HELP ASAP....i need to finish this soon
A GDP per capita of $13,000 would correspond to the following corruption score of: B. 42.
What is a scatter plot?A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.
Based on the information provided in the table above, we can logically deduce that the situation can be modeled by this linear function:
y = 511x - 8540
Where:
x is the corruption score.
y is GDP per capita in dollars.
How to calculate the corruption score?Based on the model, a GDP per capita of $13,000 would correspond to the following corruption score:
y = 511x - 8540
13,000 = 511x - 8540
511x = 13,000 + 8540
511x = 21,540
x = 21,540/511
x = 42.1 ≈ 42.
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Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
The range of the quadratic function y = (2 / 3) · x² - 6 is {- 6, 0, 18, 48}.
What is the range of a quadratic equation?
In this case we have a quadratic equation whose domain is stated. The domain of a function is the set of x-values associated to only an element of the range of the function, that is, the set of y-values of the function. We proceed to evaluate the function at each element of the domain and check if the results are in the choices available.
x = - 9
y = (2 / 3) · (- 9)² - 6
y = 48
x = - 6
y = (2 / 3) · (- 6)² - 6
y = 18
x = - 3
y = (2 / 3) · (- 3)² - 6
y = 0
x = 0
y = (2 / 3) · 0² - 6
y = - 6
x = 3
y = (2 / 3) · 3² - 6
y = 0
x = 6
y = (2 / 3) · 6² - 6
y = 18
x = 9
y = (2 / 3) · 9² - 6
y = 48
The range of the quadratic function y = (2 / 3) · x² - 6 is {- 6, 0, 18, 48}.
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pls help with math rn neeedddd
Answer:
40° to the left and 3/2 units down
Step-by-step explanation:
See attached image.
o trees are growing in a clearing. The first tree is 5.6 feet tall and casts a 4.2-foot shadow. The second tree casts a 42.3-foot shadow. How tall is the second tree to the nearest tenth of a foot?
The second tree is 56.4 ft tall.
Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are identical, their respective sides are equal in number and their corresponding angles are congruent.
Let the length of the tall tree be x. Thus by similarity of triangles we get,
Length of small tree/ Shadow Length of small tree =
Length of Tall tree/ Shadow Length of tall tree
Substituting the values we get,
5.6/4.2 = x/42.3
x = 56.4
Thus the second tree is 56.4 ft tall.
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A sine function has an amplitude of 3, a period of pi, and a phase shift of pi/2. What is the y-intercept of the function?
A. 3
B.0
C.-3
D. pi/4
Based on the calculations, we can logically deduce that the y-intercept of this sine function is equal to: A. 3.
Given the following data:
Amplitude = 3Period = πPhase shift = π/2How to determine the y-intercept of this function?Mathematically, a sine function is modeled by this equation:
y = Asin(ωt + ø)
Where:
A represents the amplitude.ω represents angular velocity.t represents the period.ø represents the phase shift.Also, the period of a sine wave is given by:
t = 2π/ω
2 = 2π/ω
ω = 2
Substituting the given parameters into the equation, we have;
y = 3sin(2t + π/2)
At t = 0, we have:
y = 3sin(2(0) + π/2)
y = 3sin(π/2)
y = 3sin(90)
y = 3 × 1
y = 3.
In conclusion, we can logically deduce that the y-intercept of this sine function is equal to 3.
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Which description best fits this picture?
Answer:
Accurate AND Precise
WILL GIVE CROWN
What is the remainder of 2x^2+7x-39/x-7
show work
On dividing we get 69/2 or 34.5 as remainder.
In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial f(x) has a factor if and only if f=0.
Long division is best suited for such expressions:-
On applying long division and factor theorem we get
2x²+7x-39 = (2x - 1/2)(x-7) + 69/2
Thus on dividing we get 69/2 or 34.5 as remainder.
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HELPPPP WITH ALL OF THE 3 PLSSS
Answer:
See picture.
C is the point that does not move because it is on the line of reflection
Yes, a reflection is a rigid motion. It does not change size. A dilation changes the size.
Step-by-step explanation:
In the picture, you will see that I traced the triangle on tracing paper and then folded (flipped) the drawing over the line of reflection.
Please help me with these questions. Thank you!
Answer:
382.19cm²
Step-by-step explanation:
a / sin(A) = b / sin(B)
a / sin(68) = 53 / sin(95)
a = (53 x sin(68)) / sin(95)
a = 49.33
area = ½absin(C)
C = 180 - (95 + 68)
C = 180 - 163
C = 17°
area = ½(53)(49.33)sin(17)
area = 382.19cm²
determine o vértice da função quadrática y=16x²-6x-10
Can someone help me out please
By just adding the given areas, we conclude that the definite integral is equal to 3.026
How to calculate the definite integral?
The integral will be equal to the sum of the four areas between points a and c.
The areas above the horizontal axis are positive areas, these are A and C.
While the areas below the horizontal axis are negative areas, these are B and D.
Then the definite integral will be:
I = A - B + C - D
Here we know that:
A = 1.311
B = 2.229
C = 5.545
D = 1.601
Replacing that, we conclude that the definite integral is
I = 1.311 - 2.229 +5.545 - 1.601 = 3.026
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If a random variable is characterized by (infinitely) uncountable values within any interval, it is known as ________ variable
Answer:
Step-by-step explanation:
i doont know
Find the Z-scores that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution.
The z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.
Given that the z score separates the 56% of the distribution from the area in the tails of the standard normal distribution.
In a normal distribution in with mean μ and standard deviation σ, the z score of a measure X is as under:
Z=(X-μ)/σ
It is used to measure how many standard deviations the measure is from the mean.
After finding the z score we have to look at the z score table and find the p value associated with this z score, which is the percentile of X.
The normal distribution is symmetric which means that the middle 56% is between the 11th and 67th percentile. Looking at the z table the z scores are Z=±0.77.
Hence the z score that separate the middle 56% of the distribution from the area in the tails of the standard normal distribution is ±0.77.
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Two trains leave the station at the same time, one heading west and the other east. The westbound train travels at miles per hour. The eastbound train travels at miles per hour. How long will it take for the two trains to be miles apart
Answer:
one hour
Step-by-step explanation:
if they are going the same speed going differnet directions they will be 2 miles apart after one hour
Write and solve a system of equations. Be sure to label the variables. The sum of two numbers is fourteen. Two times the first number plus three times the second number is nine. What are the two numbers? Show and Explain all work.
Answer:
First number = 33, Second number = -19
Step-by-step explanation:
We can use F to represent the first number and S to represent the second number.
Our two equations then are F + S = 14 and 2F + 3S = 9
We can use substitution:
[tex]F+S = 14\\2F+3S=9\\F=14-S\\2(14-S)+3S=9\\28-2S+3S=9\\28+S=9\\S=-19\\\\F-19=14\\F=33[/tex]
if a car is moving at 52mph, how fast is the car moving in m/s?
**Disclaimer** Hi there! I assumed the unit [ mph ] represents miles per hour and [ m/s ] represents meters per second. The following answer will be according to this understanding. If I am wrong, please let me know and I will modify my answer.
Answer: [tex]\Large\boxed{23~m/s}[/tex]
Step-by-step explanation:
Given information
Speed = 52 mph
Given conversion factors
1 mile ≈ 1609 meters
1 hour = 3600 seconds
Convert the unit from mph to m/s using conversion factors
The basic idea is that you utilize the factors and cancel out unnecessary units
[tex]\dfrac{52~miles}{1~hour} \times\dfrac{1~hour}{3600~seconds} \times\dfrac{1609~meters}{1~miles}[/tex]
Simplify by multiplication
[tex]=\dfrac{52~miles}{3600~Seconds} \times\dfrac{1609~meters}{1~miles}[/tex]
[tex]=\dfrac{52\times 1609~meters}{3600~Seconds}[/tex]
Simplify the fraction
[tex]=\dfrac{83668~meters}{3600~Seconds}[/tex]
[tex]\Large\boxed{\approx23~m/s}[/tex]
Hope this helps!! :)
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sketch the graph: y=1/3x+2
The slope of the line is 1/3and the y-intercept is at the (0, 2) as shown in the graph below.
Graph of a linear functionA linear function is a function that has a leading degree of 1. The standard equation for a linear function is expressed as:
y = mx + b
where
m is the slope which is equal to the rate of change of y coordinate to x-coordinates.
b is the y-intercept
Given the following equation
y= 1/3x + 2
The slope of the line is 1/3 and the y-intercept is at the(0,2) as shown in the graph below.
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Study island
Need help on this question fast pls help
Answer:
D is correct
Step-by-step explanation:
Since you have 2 parallel lines cut by a transversal, <BAC and <BDE are corresponding angels. Corresponding angles are congruent. You are able to prove that 2 pairs of angles are congruent so the triangles are similar. All of the answers show that the 2 triangles share angle B as the first part of the answer.
Marissa is selling paintings for $15 each and bracelets for $7 each. Her goal is to sell at least $800 in products, and she must sell at least 60 bracelets. Which of the following combinations will satisfy these constraints?
The first inequality is represented by the purple area seen in the picture and the second inequality by the black area seen in the picture, the solutions set is the region where the two areas overlap each other.
How to find posible solutions from a system of inequalities
In this question we have two inequalities representing constraints that Marissa should satisfy, provided that she wants to make a profit in selling paintings and bracelets.
The first inequality represents the minimum profit required from the sales of paintings (x) and bracelets (y) and the second one represents the minimum number required of sold bracelets. The two inequalities are described below:
15 · x + 7 · y ≥ 800 (1)
y ≥ 60 (2)
Since there are more than one solution, we decided to define a solutions set with the help of graphing tool. The first inequality is represented by the purple area seen in the picture and the second inequality by the black area seen in the picture, the solutions set is the region where the two areas overlap each other.
Remark
The statement is incomplete and such issue cannot be resolved. We decided to modify the statement as follows:
Marissa is selling paintings for $ 15 each and bracelets for $ 7 each. Her goal is to sell at least $ 800 in products, and she must sell at least 60 bracelets. Please show the set of all possible solution that will satisfy these constraints?
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Answer:
26 paintings and 61 bracelets
Step-by-step explanation:
if you do 26x15=390 and 61x7=427
390+427=817
so the answer is 26 paintings and 61 bracelets
also, I took the test so I know its right