Answer:
[tex]\mathbf{\dfrac{\pi}{6}[5 \sqrt{5}-1]}[/tex]
Step-by-step explanation:
Given that:
The surface area (S.A) [tex]z = x^2 +y^2[/tex]
Hence the S.A is of form z = f(x,y)
Then the S.A can be represented with the equation
[tex]A(S) = \iint _D \sqrt{1+ (\dfrac{\partial z}{\partial x})^2+ (\dfrac{\partial z}{\partial y})^2} \ dA[/tex]
where :
D = cylinder [tex]x^2 +y^2 =1[/tex]
In polar co-ordinates:
D = {(r, θ): 0≤ r ≤ 1, 0 ≤ θ ≤ 2π)
Similarly, [tex]\dfrac{\partial z}{\partial x} = 2x[/tex] and [tex]\dfrac{\partial z}{\partial y} = 2y[/tex]
Therefore;
[tex]S.A = \iint_D \sqrt{1+4x^2+4y^2} \ dA[/tex]
[tex]= \iint_D \sqrt{1+4(x^2+y^2)} \ dA[/tex]
[tex]= \int^{2 \pi}_{0} \int^{1}_{0} \sqrt{1+4r^2} \ r \ dr \d \theta[/tex]
[tex]= [\theta]^{2 \pi}_{0} \dfrac{1}{8}\times \dfrac{2}{3}\begin {bmatrix} (1+4r^2)^{\dfrac{3}{2}}\end {bmatrix}^1_0[/tex]
[tex]= 2 \pi \times \dfrac{1}{12}[5^{\dfrac{3}{2}} - 1][/tex]
[tex]\mathbf{=\dfrac{\pi}{6}[5 \sqrt{5}-1]}[/tex]
Evaluate the intergal F•dr where F (x,y,z)=xyi+yzj+zxk and c is the twisted cubic given by x=t, y=t^2 ,z=t^3, 0<=t=<1
The integral can be evaluated by substituting everything you know:
[tex]\displaystyle\int_C\mathbf F\cdot\mathrm d\mathbf r=\int_C\mathbf F(x(t),y(t),z(t))\cdot\dfrac{\mathrm d\mathbf r}{\mathrm dt}\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1(t^3\,\mathbf i+t^5\,\mathbf j+t^4\,\mathbf k)\cdot(\mathbf i+2t\,\mathbf j+3t^2\,\mathbf k)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1(t^3+5t^6)\,\mathrm dt[/tex]
[tex]=\dfrac{t^4}4+\dfrac{5t^7}7\bigg|_0^1=\dfrac14+\dfrac57=\boxed{\dfrac{27}{28}}[/tex]
The line integral ∫F · dr along the curve is 9/10.
To evaluate the line integral ∫F · dr along the curve C, where F(x, y, z) = xyi + yzj + zxk and C is the twisted cubic given by x = t, y = t², z = t³ for 0 ≤ t ≤ 1, we need to parameterize the curve C and compute the dot product between F and the tangent vector dr.
The parameterization of C is:
r(t) = ti + t²j + t³k
To compute dr, we take the derivative of r(t) with respect to t:
dr = (dx/dt)i + (dy/dt)j + (dz/dt)k
dr = i + 2tj + 3t²k
Now we can compute the dot product between F and dr:
F · dr = (xy)(dx/dt) + (yz)(dy/dt) + (zx)(dz/dt)
F · dr = (t)(i) + (t²)(2t)(j) + (t)(t³)(3t²)(k)
F · dr = ti + 2t³j + 3t⁴k
To evaluate the line integral, we integrate F · dr with respect to t over the interval [0, 1]:
∫[0,1] F · dr = ∫[0,1] (ti + 2t³j + 3t⁴k) dt
Integrating each component separately:
∫[0,1] ti dt = (1/2)t² ∣[0,1] = (1/2)(1)² - (1/2)(0)² = 1/2
∫[0,1] 2t³j dt = (1/4)t⁴ ∣[0,1] = (1/4)(1)⁴ - (1/4)(0)⁴ = 1/4
∫[0,1] 3t⁴k dt = (1/5)t⁵ ∣[0,1] = (1/5)(1)⁵ - (1/5)(0)⁵ = 1/5
Adding the results together:
∫[0,1] F · dr = (1/2) + (1/4) + (1/5) = 5/10 + 2/10 + 2/10 = 9/10
Learn more about line integral here:
brainly.com/question/29850528
#SPJ2
To you divide fractions, you have to ______ by the reciprocal
halo edwin perkenalkan saya elto saya minta maaf atas kejadian ini disini ada edam yang warna merah era yang orange itu ekut yang ceria ya eria....
hahay
When dividing fractions, you have to multiply by the reciprocal.
Step-by-step explanation:
by punith Reddy
If DM = 25, what is the value of r?
A.10
B.12
C.14
D.15
Step-by-step explanation:
DG+GM=DM
r+2+2r-13=25
combine like terms
3r-11=25
3r=36
r=12
Which of the following is equal to -5/4?
A. -5/-4
B. -(-5/4)
C. -(5/-4)
D. -(-5/-4)
Answer:
C. -(5/-4)
Step-by-step explanation:
[tex] - \bigg(\frac{5}{ - 4} \bigg) \\ \\ = \frac{ - 5}{ - ( - 4)} \\ \\ = \frac{ - 5}{4} \\ [/tex]
How does the graph change between point A and point B?
The graph increases.
The graph decreases.
The graph remains constant.
the graph increases
Step-by-step explanation:
because its moving out
*
4,781 divided by 32
Answer:
149.40625 approximately
Step-by-step explanation:
There isn't really an explanation, you can just use a calculator ;)
Answer:
Step-by-step explanation:
4781/32
without using calculator you can configure this.
AS
32√4781 ║ 149.40625
- 32
1581
- 128
301
- 288
1 30 (put decimal above to add zero in reminder)
- 128
200 (one 0 is from decimal and to add another one add 0 abov)
-192
80
-64
160
- 160
X
The volume, in cubic feet, of a right cylindrical silo of height h and radius r is V = πr2h. The height of the silo is h(r) = 3.5r.
Answer:
2,4,5
Step-by-step explanation:
Please help me please
Answer:
Step-by-step explanation:
2n + 8.5 = 23
2n = 14.5
2n = 7.25 or 7 1/4 feet
Please help! Sorry about the crack.
Answer:
[tex] - 18 \\ - 13 \\ 12 \\ 22 \\ 27[/tex]
Step-by-step explanation:
just replace the x by the number given, it's simple calculation
is -18.75 rational or irrational number
Answer:
-18.75 is a rational number. A rational number is any number that has either a repeating decimal or one that ends. It doesn’t no go on, so it is considered rational. Hopefully this helps! Feel free to mark brainliest!
-18.75 is a rational number
Rational numbers are numbers that can be expressed as the fractions of two integers
That is, R is a rational number if it can be expression as:
R = p/q
where p and q are integers
-18.75 can be expressed as -1875/100 where both -1875 and 1000 are integers.
Since -18.75 can be expressed as the fraction of two integers, it is a rational number.
Learn more here: https://brainly.com/question/17471044
Will vote brainliest!!!!!!!! Thank you!!!!!!!!!!!!
Answer:
[tex]\frac{2x+2}{x}\ge \:0[/tex]
Step-by-step explanation:
[tex]3+\frac{4}{x}\ge \frac{x+2}{x}[/tex]
Subtract [tex]\frac{x+2}{x}[/tex] from both sides:
[tex]3+\frac{4}{x}-\frac{x+2}{x}\ge \frac{x+2}{x}-\frac{x+2}{x}[/tex]
[tex]3+\frac{4}{x}-\frac{x+2}{x}\ge \:0[/tex]
[tex]\frac{3x}{x} +\frac{-x+2}{x}[/tex]
[tex]\frac{2x+2}{x}\ge \:0[/tex]
What is the distance between-21 and 6 on a number line in units
Answer: 27
Step-by-step explanation:
-21 to 6= 27
The difference between the numbers -21 and 6 is 27.
What is a number line?A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R." It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
Given that the two numbers are -21 and 6. The distance between the two numbers will be calculated as,
Distance = 6 - ( -21 )
Distance = 6 + 21
Distance = 27
Hence, the difference is 27.
To know more about number lines follow
https://brainly.com/question/24644930
#SPJ2
What is an equation of the line that passes through the points (5,0) and (-5, -8)?
Answer:
y = 4/5 x - 4
Step-by-step explanation:
If 1/6x + 3 = 7 what is x
Answer:
x = 24
Step-by-step explanation:
1/6 x + 3 = 7
1/6 x = 4
x = 24
Step-by-step explanation:
The expression is 1/6x+3=7
1/6x+3=7
First, you subtract 3 from both sides
1/6x=4
Then you divide 1/6 from both sides
Dividing fractions is confusing, so I will show you how to do it
4/1 / 1/6
Because you can't divide 1 by 6, you KCF, or keep change flip.
You keep the 4/1, you change the operation to multiplication, and flip 1/6 to make it 6/1.
Now the problem is 4x6=24
So x=24
The value of coins in the pockets of several students is recorded. What is the mean of the values: 10, 20, 35, 35, 35, 40, 45, 45, 50, 60. A. 10 cents B. 35 cents C. 37.5 cents D. 50 cents
Answer:
C. 37.5
Step-by-step explanation:
10 10 + 20 + 35 + 35 + 35 + 40 + 45 + 45 + 60 + 50=375
375÷10=37.5
The mean of the given data set 10, 20, 35, 35, 35, 40, 45, 45, 50, 60 is 37.5 so option (C) will be correct.
What is mean?The mean is the average of a data set. Mean gives us the idea of that how much amount of overall data have.
In other words, the mean is the foundation of the deviation of data from all data sets.
Mean = sum of data / Number of data
For example, if you have marks in 5 subjects like 40,45,44,46,48 then the mean will be
( 40 + 45+ 44 + 46 + 48) /5 = 44.6.
Given the data set,
10, 20, 35, 35, 35, 40, 45, 45, 50, 60
Now mean is given as
Mean = sum of data / Number of data
So,
Mean = (10+20+35+35+35+40+45+45+50+60)/10
Mean = 37.5
Hence "The mean of the given data set 10, 20, 35, 35, 35, 40, 45, 45, 50, 60 is 37.5".
For more about the mean,
https://brainly.com/question/17060266
#SPJ2
Write a ratio in simplest form to express 8 inches over 3 feet
Answer:
Step-by-step explanation:
8 inches : 3 feet
12 x 3 = 36 inches
8 inches: 36 inches = 2 inches: 9 inches
The ratio in simplest form to express 8 inches over 3 feet is 2:9.
To express the ratio of 8 inches to 3 feet in simplest form, we need to convert the measurements to a common unit.
Since both measurements involve length, we can convert inches to feet or feet to inches.
We know that 1 foot = 12 inches
So 3 feet = 12×3
=36 inches.
Now the ratio 8 inches over 3 feet is equal to 8 inches over 36 inches.
8/36
Divide numerator and denominator by 4:
2/9
Hence, the ratio in simplest form to express 8 inches over 3 feet is 2:9.
To learn more on Ratios click here:
https://brainly.com/question/1504221
#SPJ4
If
f(x) = 2x2 - 5
and
g(x) = 5x +7
Find
g(f(x)) = [? ]x2 +
Help pls
The composite function g(f(x)) is equivalent to 10x^2 - 1
Composite functionsThis are also referred to as function of a function. Given the following functions;
f(x) = 2x^2 - 5
g(x) = 5x + 7
In order to determine the composite function g(f(x))
g(f(x)) = g(2x^2 - 5)
Replace x with 2x^2 - 5 in g(x) to have;
g(f(x)) = 5(2x^2 - 5) + 7
g(f(x)) = 10x^2 - 18
Hence the composite function g(f(x)) is equivalent to 10x^2 - 1
Learn more on composite function here: https://brainly.com/question/10687170
#SPJ1
Solve x to the second power =36
Answer: 6x6 =36
Step-by-step explanation:
Sorry if it's wrong, but should be right cause it makes sense.
12. The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 253.4 and a standard
deviation of 62.3. (All units are 1000 cellsfuL) Using the empirical rule, find each approximate percentage below.
a. What is the approximate percentage of women with platelet counts within 1 standard deviation of the mean, or
between 191.1 and 315.7?
b. What is the approximate percentage of women with platelet counts between 128.8 and 378.0?
a. Approximately
% of women in this group have platelet counts within 1 standard deviation of the mean,
or between 191.1 and 315.7.
(Type an integer or a decimal. Do not round.)
b. Approximately
% of women in this group have platelet counts between 128.8 and 378.0.
(Type an integer or a decimal. Do not round.)
Answer:
a. What is the approximate percentage of women with platelet counts within 1 standard deviation of the mean, or
between 191.1 and 315.7?
68%
b. What is the approximate percentage of women with platelet counts between 128.8 and 378.0?
95%
Step-by-step explanation:
The Empirical rule formula states that:
1) 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .
2) 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
a. What is the approximate percentage of women with platelet counts within 1 standard deviation of the mean, or
between 191.1 and 315.7?
μ = mean = 253.4
σ = standard deviation = 62.3.
μ - σ
= 253.4 - 62.3
= 191.1
μ + σ
= 253.4 + 62.3
= 315.7
Therefore, the first empirical rule holds for Question a. This states that 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ .
Therefore, the approximate percentage of women with platelet counts between 191.1 and 315.7 is 68%
b. What is the approximate percentage of women with platelet counts between 128.8 and 378.0?
μ = mean = 253.4
σ = standard deviation = 62.3.
Applying the second rule of the empirical rule: this states that: 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .
For x = 128.8
μ - 2σ
= 253.4 - 2 × 62.3
= 128.8
μ + 2σ
= 253.4 + 2 × 62.3
= 378
Therefore, the approximate percentage of women with platelet counts between 128.8 and 378.0 is 95%
Simplify 6.920? need help asap a) −1 b)0 c)1 d)6.92
Answer:
C.) 1
Step-by-step explanation: Any number raised to the zeroth power will always be 1.
If Mike bikes at a speed 10 mph for half an hour, how far would he go? What was Mike's speed (in average) if he covered the distance of 18 miles in 2 hours?
Step-by-step explanation:
Answer:
A: 5 miles
B: 9 mph
Step-by-step explanation:
A:
since the speed is constant, in half an hour, Mike would travel 5 miles.
this is because: 10 miles/1 hour = 5 miles / 0.5 hours (multiply top and bottom by 1/2)
B:
[tex]\frac{18 miles}{2 hours}[/tex] = [tex]\frac{9 miles}{1 hour}[/tex] = 9 mph
Assume that we are interested in the average length of 1015 fishes in Square Lake, WI. Also assume that all information for all 1015 fishes in this lake is known. Suppose, the average length of all 1015 fishes in Square Lake is 98.06 mm. Derek randomly selects 50 fishes from the Square Lake and obtains and average length of 101.04 mm. Using this information, describe the Individual, Variable, Parameter and Statistic.
Answer is given below
Step-by-step explanation:
given data
average length of all 1015 fishes = 98.06 mm
randomly selects 50 fishes average length = 101.04 mm
solution
When we get here, we mean to measure, so here we measure a fish in a square lake. And the variable means that a fish varies from fish to fish, so the length of the fish in the squares parameter mean that all individuals in the population so the parameter is average length of all 1015 fish in square lakestatics is selct of individual in sample so statistic is average length of random sected so fish in square lakeQUICK, which graph is proportional ?
Solve for X if X +127 equals 185
Answer:X=58
Step-by-step explanation:
Answer:
58
Step-by-step explanation:
2x + 5y = 13
-x + 4y = 13
solve by elimination
Answer:
i think x=-1 and y=3. ....
Answer:
x = -1 , y = 3
Step-by-step explanation:
2x+5y = 13
-x+4y = 13
Decide whether to add or subtract the two equations by using Different Add Same Subtract (DASS) or in case below as its SUBTRACT
i apply (SDSS).
We subtract 5y as this is easier equation either positive prioritises or if both positive then easier number becomes priory.
Results to SDSS before substituting Y if 5y etc was subtracted
2x+5y = 13 Subtract -5
2x+5y -5y = 13 -5y
2x= 13 - 5y then Divide by 2
2x / 2 = 13/2 - 5y/2 Show then
x = 13 - 5y / 2 + 4y = 13 Simplify
simplify 13 - 13y / 2 as y = 3
as 13/2 = 6.5 and 2.5 +4 = 6.5
y = 3
Substitute y = 3
13-5y )3) / 2
13-5 (3) / 2
BODMAS Brackets first Multiplying only for y substitute 5y = 5 x 3
-5 (3) = 15
13-15 = -2
-2/2 = -1
x = -1
Every day, you take the elevator from the basement parking lot that is at level-3. The elevator takes two
seconds per level and you find that it takes 46 seconds to reach your floor.
Which floor do you live on?
Write an negative number whose absolute value is greater than 3
Answer:
4+is the absolute value is greater than 3
Use a stem-and-leaf plot to display the data, which represent the thickness (in centimeters) of ice measured at 20 different locations on a frozen lake. Describe any
patterns.
5.8 6.5 6.9 7.2 5.1 4.9 4.3 5.8 7.0 6.8
8.7 7.5 7.2 5.8 7.2 8.0 7.2 6.9 5.9 7.9
Determine the leaves in the stem-and-leaf plot below.
Key: 3|3= 3.3
Ice Thickness
4|
5|
6|
7|
8|
Answer/Step-by-step explanation:
To represent the data given on a stem and leaf plot, the whole number in a given value would be used as the stem, while the number after the decimal point is the leaf. (Key: 3|3 = 3.3).
For example, in the first stem in the first row, we have 4 as the stem. All values that starts with 4 point would be represented in this row. The digit after 4 point for each of the values would be written on the leaf column in the first row, from the least to the largest. For the first row we have: 4 | 3 9.
Same applies to the rest rows.
The stem plot would look like the one below:
Ice Thickness:
Stem | Leaf
4 | 3 9
5 | 1 8 8 8 9
6 | 5 8 9 9
7 | 0 2 2 2 2 5 9
8 | 0 7
The data of the stem-and-leaf plot shows a bell-shaped pattern with majority of the ice thickness for the 20 locations clustering around the center of the data distribution.
Leon bought a dozen daisies for $3.75. To the nearest hundredth, approximately how much did Leon pay for each daisy?
Answer: $0.31
Step-by-step explanation:
A dozen = 12
Cost of 12 daises = 3.75
Cost of one daisy = 3.75/12 = 0.3125
0.3125 to the nearest hundredth = 0.31
At age six, Kylie is 50 inches tall. Her height has a z-score of 1.8. At age four, Hannah is 48 inches tall. Her height has a z-score of 2.1. Relative to girls their ages, who is taller? Kylie is taller because her z-score is lower than Hannah’s z-score. Hannah is taller because her z-score is higher than Kylie’s z-score. Kylie is taller because her z-score is closer to the mean than Hannah’s z-score. Hannah is taller because her z-score is closer to the mean than Kylie’s z-score.
Answer:
Hannah is taller because her z-score is higher than Kylie’s z-score.
Step-by-step explanation:
