For ∬∂WF⋅dS differentiable each of the following regions is 0, [tex]\frac{18 \sqrt{2}}{15}, -\frac{16 \sqrt{2}}{15}[/tex]
Let the f=[tex]\left(y^2+z^3, x^3+z^2, x z\right) \\[/tex],
Differentiability of Function: For a function to be differentiable at any point x=a in its domain, it must be continuous at that particular point but vice-versa is not always true. In complex analysis, complex-differentiability is defined using the same definition as single-variable real functions. This is allowed by the possibility of dividing complex numbers
Solution: For checking the continuity, we need to check the left hand and right-hand limits and the value of the function at a point x=a.
This means that f'(a) must exist, or equivalently:
[tex]$$\lim _{x \rightarrow a^{+}} f^{\prime}(x)=\lim _{x \rightarrow a^{-}} f^{\prime}(x)=\lim _{x \rightarrow a} f^{\prime}(x)=f^{\prime}(a)$$[/tex]
(A).
[tex]& x^{2 / t} y^2 \leq z \leq 2 \\\\& \int_{\theta=0}^{2 \pi} \int_{\gamma=0}^{\sqrt{2}} \int_{z=\gamma^2}^2 \gamma \cos \theta d z d \gamma d \theta \\\\&=\int_{\theta=0}^{2 \pi} \int_{\gamma=0}^{\sqrt{2}}[\gamma \cos \theta][z]_{\gamma^2}^2 d \gamma d \theta \\[/tex]
[tex]&=\int_{\theta=0}^{2 \pi} \int_{\gamma=0}^{\sqrt{2}}\left(2-\gamma^2\right) \gamma \cos \theta d \gamma d \theta \\\\&=\int_{\theta=0}^{2 \pi}\left[\gamma^2-\frac{\gamma^4}{4}\right]_0^{\sqrt{2}} \cos \theta d \theta \\\\&=\int_{\theta=0}^{2 \pi} \cos \theta d \theta \\\\&=[\sin \theta]_0^{2 \pi} \\&=0[/tex]
(B).
[tex]& \ x^2+y^2 \leq 2 \leq 2 . \quad, x \geqslant 0 \\[/tex]
[tex]& \int_{0=-\frac{\pi}{2}}^{\frac{\pi}{2}} \int_{\gamma=0}^{\sqrt{2}} \int_{z=\gamma^2}^2 \gamma^2 \cos \theta d z d \gamma d \theta . \\\\& =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \int_0^{\sqrt{2}} \gamma^2 \cos \theta[z]^2 \gamma^2 \cdot d \gamma d \theta \text {. } \\[/tex]
[tex]& =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \int_0^{\sqrt{2}} \cos \theta\left(2-\gamma^2\right) \gamma^2 d \gamma d \theta . \\\\& =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos \theta\left[\frac{2}{3} \gamma^3-\frac{\gamma^5}{5}\right]_0^{\sqrt{2}} d \theta \text {. } \\[/tex]
[tex]& =\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \cos \theta\left[\frac{4}{3} \sqrt{2}-\frac{4 \sqrt{2}}{5}\right] d \theta . \\\\& =[\sin \theta]_{-\frac{\pi}{2}}^{\frac{\pi}{2}} d \theta\left[\frac{4}{4} \sqrt{2}-\frac{4 \sqrt{2}}{5}\right] \\\\& =\left[\frac{4 \sqrt{2}}{3}-\frac{4 \sqrt{2}}{5}\right] \\[/tex]
[tex]& =\left[\frac{4 \sqrt{2}}{3}-\frac{4 \sqrt{2}}{5}\right] \\\\& =\left[\frac{20 \sqrt{2}-12 \sqrt{2}}{15}\right]=2\left[\frac{8 \sqrt{2}}{15}\right] \\\\& =\frac{18 \sqrt{2}}{15}[/tex]
(C).
[tex]x^2+y^2 & \leqslant z \leqslant 2, x \leq 0 \\[/tex]
A+B+C
0=B+C
B=-C or C=-B
C=[tex]-\frac{16 \sqrt{2}}{15}[/tex]
Therefore, the differentiable of each function is 0, [tex]\frac{18 \sqrt{2}}{15}, -\frac{16 \sqrt{2}}{15}[/tex].
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Let F=[tex]\left(y^2+z^3, x^3+z^2, x z\right) \\[/tex]) . Evaluate ∬∂WF⋅dS for each of the following regions W:
A.[tex]& x^{2 / t} y^2 \leq z \leq 2 \\\\ \\[/tex]
B. [tex]& \ x^2+y^2 \leq 2 \leq 2 . \quad, x \geqslant 0 \\[/tex]
C. [tex]x^2+y^2 & \leqslant z \leqslant 2, x \leq 0 \\[/tex]
An office machine purchased new for $3600 loses $400 each year.
Assume the value continues to decrease the same amount
each year. If f(x) represents the value of the office machine
after x years, which linear function models the given situation?
The linear function models the given situation will be equal to f(x) = $3600 - $400(x).
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
Original price of Machine = $3600
Price lost by the machine each year = $400
Then, the equation will be,
f(x) = $3600 - $400(x)
Here, x represents the number of years.
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Answer:
f(x) = −400x + 3600
in how many ways can a committee with 4 democrats and 2 republicans be formed from a group of 7 democrats and 5 republicans?
A committee with 4 democrats and 2 republicans formed from a group of 7 democrats and 5 republicans can be created in a total of 350 ways. Therefore, the option C holds true.
The calculation of the same has been shown as below,
A group has 7 Democrats and 5 Republicans.
Committee with 4 Democrats and 2 Republicans = 7C4 x 5C2
7C4 x 5C2 = 7! / (4! 3!) x 5! / (2! 3!)
7C4 x 5C2 =(7×6×5 / 3×2×1) x (5×4 / 2×1)
7C4 x 5C2 = 35 × 10
7C4 x 5C2 = 350
Therefore, a committee can be created in 350 ways.
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Complete Question
In how many ways can a committee with 4 Democrats and 2 Republicans be formed from a group of 7 Democrats and 5 Republicans?
A 105
B 924
C 350
D 1680
Find the percent the first number is of the second.
(1.) 1.5 and 7.5,
(2.) 5ft 37.5ft
To find the percent that 1.5 is of 7.5, we need to divide 1.5 by 7.5 and multiply the result by 100% to convert it to a percentage:
1.5 / 7.5 = 0.2
0.2 * 100% = 20%
Therefore, 1.5 is 20% of 7.5.
To find the percent that 5ft is of 37.5ft, we need to divide 5 by 37.5 and multiply the result by 100% to convert it to a percentage:
5ft / 37.5ft = 0.1333
0.1333 * 100% = 13.33%
Therefore, 5ft is 13.33% of 37.5ft.
Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.
PLEASE HELP QUICK!! WILL GIVE BRAINLIEST AND 25 POINTS!!
Find the value of x, round to the nearest degree.
Answer:
7
Step-by-step explanation:
4+3=7
7-4=3
7-3=4
81 of [60-{8*7-(13-3*5)}] find simply
Answer:
Step-by-step explanation:
81 of [60-{(8*7)-(13-(3*5))}] =
81 of [60-{56}-(13-15)] =
81 of [60-{56}-(-2) =
81 of [60-{56}+2] =
81 of [6] =
81% of 6 = 4.86
The function shown in the graph below is modeled by:
a linear function.
an exponential function.
a quadratic function.
how is 15×3/5 = 9
the slash is for the fraction
Answer:15x3 /=divide 5 = 9
Step-by-step explanation:
because if you do 15x3 it is 45 then you divide it by 5 and get 9 as your answer!
you are making a cake and have already put in all of the ingredients except the eggs. you go to the refrigerator and find that there are no eggs, which results in the condition known as
The condition known as "eggless baking" is a common problem when baking cakes and other desserts.
It can be caused by not having eggs in the refrigerator or by forgetting to add them to the recipe. Without eggs, the cake batter lacks structure and will not hold together when baked. Without the proteins from the eggs, the cake will be denser and less moist.
Additionally, the cake may not rise as much as desired and the texture may be crumbly or gummy. To solve this problem, you can try substituting other ingredients such as mashed bananas, applesauce, or yogurt. However, it is best to add eggs if possible to ensure the best results.
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Use Infinite differences to write the linear function that represents the given data set.
The linear equation on the table is the one in option D.
y = 25*x + 45
How to write the linear function?
A general linear function is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know two points on the line, (x₁, y₁) and (x₂, y₂), the slope can be written as:
a = (y₂ - y₁)/(x₂ - x₁)
Using the first two points, (0, 45) and (1, 70) we can get the slope:
a = (70 - 45)/(1 - 0) = 25
And because of the point (0, 45) we know that the y-intercept is b = 45, then the linear equation is:
y = 25*x + 45
So the correct option is D.
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The U.S. Weather Bureau has a station on Mauna Loa in Hawali that has measured carbon dioxide levels since 1959. At that time , there were 312 parts per million of carbon dioxide in the atmosphere. In 2005 , the figure was 389 parts per million. Find the increase in carbon dioxide levels and the percent of increase . Percent increase:96
a) By the subtraction operation, the increase in carbon dioxide levels between 1959 and 2005 is 77 parts.
b) The percentage increase in carbon dioxide levels between 1959 and 2005 is 24.7%.
What is the percentage increase?The percentage increase is found by determining the difference between the original and final values through subtraction operation.
The difference is then divided by the original value, multiplied by 100.
The carbon dioxide levels in 1959 = 312 parts per million
The carbon dioxide levels in 2005 = 389 parts per million
The increase in dioxide levels from 1959 to 2005 = 77 parts per million (389 - 312)
The percentage increase = 24.68% (77/312 x 100)
= 24.7%
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A Web site sells baseball caps for $12 each. There's a $4 shipping charge no matter
how many hats you order. The equation c = 12h + 4 gives the total cost to buy h hats.
Which statement correctly describes what happens when h increases?
Answer:
0
Step-by-step explanation:
A dance squad needs at least $800 to buy new dance outfits. They have saved $350
already. -They are selling tickets to a dance performance for $10 each. They need to sell
x tickets to have enough money to buy the new dance outfits. Which inequality
represents the situation?
Answer:
x>=45 is the req. inequality
The inequality equation for the number of tickets to be sold is x ≥ 45
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the number of tickets to be sold be x
Let the total amount of money to be saved be = $ 800
The amount of money already saved = $ 350
So , the remaining amount of money = $ 800 - $ 350 = $ 450
The cost of each ticket = $ 10
So , the cost of x tickets = 10x
Now , the number of tickets to be sold to raise $ 450 is given by
10x ≥ 450 be equation (1)
On simplifying the equation , we get
Divide by 10 on both sides of the equation , we get
x ≥ 45
Therefore , the number of tickets to be sold is 45
Hence , the inequality is x ≥ 45
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answer these questions. ( find the variables)
1. n + 7 = 10
2. c - 2+ = 7
3. a x 3 = 15
4. a / 5 = 9
5. 9z + 2 = 38
6. 17 + 3n = 47
7. 7y - 7 = 21
8. 3x + 90 = 147
9. 26/ y + 3 = 16
10. 147 - 3x + 90
Answer:
1)3
2)9
3)5
4)45
5)4
6)10
7)4
8)19
9)2
10)unable (no equal sign?)
Step-by-step explanation:
HELPPP Determine the value of h in the equation one third plus h equals five thirds.
six thirds
fourth thirds
six over nine
four ninths
Answer:
h = [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] + h = [tex]\frac{5}{3}[/tex] ( subtract [tex]\frac{1}{3}[/tex] from both sides )
h = [tex]\frac{5}{3}[/tex] - [tex]\frac{1}{3}[/tex] = [tex]\frac{4}{3}[/tex]
The area of the figure above is
blank + 25pi/4
Answer:
Add 75 for the blank number----------------------------
Divide the figure by three parts for easy calculation of its area:
Rectangle of 5 by 10 units, Square of 5 units,Quarter-circle of 5 units radius.Find each area and add up:
A = 5*10 + 5*5 + π*5²/4 A = 50 + 25 + 25π/4A = 75 + 25π/4The blank is 75.
The weights of a pack of chewing gum for a certain brand have a mean of 47.1 grams and a standard deviation of 2.4 grams. what is the weight of a randomly selected pack of gum that has a z-score of 3.11? a. 39.6 grams b. 44.7 grams c. 49.5 grams d. 54.6 grams
Answer:
Step 1: Obtain the mean and standard deviation of the weights of packs of chewing gum. The weights of packs of chewing gum for a certain brand have a mean of 47.1 grams and a standard deviation 2.- grams. Step 2: Obtain the z-score of the randomly selected pack of gum. The z-score of the randomly selected pack of gum is 3.11. Step 3: Determine which of the following statements is true: The weight of this pack of gum is lighter than the mean weight by 3.11 standard deviations The weight of this pack Of gum is heavier than the mean weight by 3.11 standard deviations The weight of this pack Of gum is lighter than the mean weight by 2.4 standard deviations The weight of this pack Of gum is heavier than the mean weight by 2.4 standard deviations
Jamie has 2 ½ packs of sunflower seeds to cover 150 sq ft. Based on this
information, what is the number of sq ft that 1 pack of sunflower seeds will
cover?
Answer:
60 ft.^2
Step-by-step explanation:
Known area/number of packs= A / number of packs for A, where A= area of interest
150/2.5=A/1
A=60
The perimeter of a rectangle i 80 inche. The length of the rectangle i 12 inche. Which equation could repreent the width of the rectangle, w? Repone w = 2(80 – 12) w, = 2(80 – 12) w = (80 – 12) ÷ ÷ 2 w, = (80 – 12) divided by 2 w = 2(80 – 24) w , = 2(80 – 24) w = (80 – 24) ÷ ÷ 2
The perimeter of a rectangle i 80 inche. The length of the rectangle i 12 inchs then width is equal to 28 inch
What is length area and perimeter?
Firstly, the area of a shape is the surface or flat space that the shape covers whereas the perimeter of a shape represents the distance around its boundary. Secondly, the area is measured in square units, whereas the perimeter is measured in linear units.
given that the perimeter of a rectangle is 80 inch
we know that
perimeter = 2 ( L +B)
putting the values we get
80 = 2 ( 12 + B)
40= 12+B
B= 28
then the width is equal to 28inch
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1 balls and bins throw n balls into m bins, where m and n are positive integers. Let x be the number of bins with exactly one ball. Compute var(x). Your final answer should not contain any summations
Using 1 balls and bins, n balls are thrown into m bins; m and n are positive numbers. the probability of any given bin containing one ball is n/m n * (1 - (1 - 1/m)^n) / m^2
Given that n is the number of balls and m is the number of bins, the probability of any given bin containing one ball is n/m. Therefore, the variance of x is equal to the variance of a binomial random variable with n trials and probability of success p = n/m.
By the formula for the variance of a binomial random variable, the variance of x is equal to n * (1 - (1 - 1/m)^n) / m^2.
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The 2 digit number which become 5 by 6th of itelf when it digit are revered. The difference in the digit of the
number being 1, then the two digit number i
After solving the two digit number is 45.
In the given question,
The 2 digit number which become 5 by 6th of itself when it digit are revered.
The difference in the digit of the number being 1, then we have to find the two digit number.
Let the two digit number = 10y+x
When we reversed the number then the number is 10x+y
As given that;
10y+x = 5/6(10x+y)
Multiply by 6 on both side, we get
60y+6x = 50x+5y
Subtract 5y on both side, we get
55y+6x = 50x
Subtract 50x on both side, we get
55y-44x = 0
Divide by 11 on both side, we get
5y-4x = 0
4x-5y = 0......................(1)
It is given that the difference between the number is 1.
x-y = 1..................(2)
Multiply by 4 in equation 2
4x-4y = 4.........................(3)
Now subtract equation 3 and 1, we get
y = 4
Now putting the value of y in equation 2
x-4 = 1
Add 4 on both side, we get
x = 5
Since the number is 10y+x. So
10y+x = 10(4)+5
10y+x = 45
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Hamburger Heaven is having a lunch special where customers buy one 1/2-* 1 p
pound cheeseburger and get one free. If they set aside 48 pounds of meat,
how many 1/2-pound cheeseburgers can they make?
24
96
O 144
O48
Answer:
hshsjsjs
Step-by-step explanation:
shhshshsjdjdjdjdj
find the exact length of the curve. y = 3 + 4x3/2, 0 ≤ x ≤ 1
So the exact length of the curve is given by [tex]L=(1/36)*[\frac{37^{3/2}}{3/2} - 1][/tex]
Given the equation of curve:
[tex]y = 3+ 4x^\frac{3}{2}[/tex]
The length of the curve is given by [tex]L= \int\limits^a_b {\sqrt{1+(y^[/tex]
Where y^ is derivative of y with respect to x
So [tex]y= 4*(3/2) * \sqrt{x}= > 6 \sqrt{x}[/tex]
Given a=1 and b=0
So [tex]L= \int\limits^1_0 {\sqrt{1+(6\sqrt{x})^2 } } \, dx[/tex]
[tex]L= \int\limits^1_0 {\sqrt{1+36x } } \, dx[/tex]
let 1+36x be t
36dx = dt
As the value of x changes after the substitution of the value.
So now the L changes as:
[tex]L= 1/36 \int\limits{\sqrt{t } } \, dt[/tex]
[tex]L=1/36* \left \{ {{t=37} \atop {t=1}} \right. \frac{t^\frac{3}{2} }{\frac{3}{2} }[/tex]
[tex](1/36)*[\frac{37^{3/2}}{3/2} - 1][/tex]
the min value of t=1 and max value of t=37
[tex]L=(1/36)*[\frac{37^{3/2}}{3/2} - 1][/tex]
[tex]L=(1/36)*[\frac{37^{3/2}}{3/2} - 1][/tex]
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A line that includes the point (0, 0) has a slope of 2. What is its equation in slope-intercept
form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
The equation of a line that passes through (0, 0) and has a slope of 2 is y = 2x.
How to represent equation in slope intercept form?Equation of a line can be represented in slope intercept form as follows
y = mx + b
where
m = slopeb = y-interceptA line that includes the point (0, 0) has a slope of 2. The equation of the line in slope intercept form is as follows:
y = 2x + b
using (0, 0) let's find y-intercept.
0 = 2(0) + b
Hence,
b = 0
Therefore, the equation is y = 2x
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PLEASE HURRY! Brody works at the ticket booth at the movie theater and sold 25 adult tickets and several child tickets during the first hour at work. Each adult ticket costs $12, and each child ticket costs $6. Brody collected $360 during that hour.
How many child tickets did he sell?
___ child tickets
Answer:
10 Child Tickets
Step-by-step explanation:
25 x 12 = 300
So we need 60
6 x 10 = 60
Step-by-step explanation:
25 x 13 = 300
6 x 10 = 60300 + 60 = 360
Larry has decided that the above ground swimming
pools business is not the best way to earn a living
(see practice problem e). He now thinks the big
money is in rowing machines. If Larry switches jobs,
he will earn a 12% commission on all the machines he
sells. For Larry to receive $15,000 in commissions,
how many dollars worth of machines must he sell?
The amount of worth of machine Larry needs to sell to recieve 15,000 dollars is 125, 000 dollars.
How to find the worth of machine he can sell to earn a particular amount?Larry thinks the big money is in rowing machines. If Larry switches jobs,
he will earn a 12% commission on all the machines he sells. For Larry to
receive $15,000 in commissions, the worth of dollars of machines he must
sell can be computed as follows:
Therefore,
let
x = amount he will earn
Hence,
15, 000 = 12% of x
15,000 = 12 / 100 × x
15000 = 12x / 100
cross multiply
1500000 = 12x
divide both sides by 12
x = 1,500,000 / 12
x = 125,000
Therefore, he needs to sell $125, 000 worth of machine.
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If m<2 = 63°, then m<3 is:
63°.
27°
117°
None of these choices are correct.
Answer:
63°
Step-by-step explanation:
since they are in the form of vertically opposite angle.
Karen earns £12.80 an hour for a 35 hour week, time and a half on the next 6 hours and double time after that. How much does she earn for a 43 hour week?
Answer:
I hope the image helps!
M = -21 divided by 0
By using the property of division, it can be calculated that M = -21 divided by 0 is not possible
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
Anything divided by 0 is not possible.
M = -21 divided by 0 is not possible
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