I'll go ahead and assume you meant to say that S is the surface given by
[tex]S = \left\{(x,y,z) \mid z = \cos(y)\text{ with } 0\le y\le \pi\text{ and }0\le x\le4\right\}[/tex]
This immediately gives us a parameterization for the surface,
[tex]\vec r(x, y) = \left\langle x, y, \cos(y)\right \rangle[/tex]
The upward-pointing normal vector to this surface is then
[tex]\vec n = \dfrac{\partial\vec r}{\partial x} \times \dfrac{\partial\vec r}{\partial y} = \left\langle0,\sin(y),1\right\rangle[/tex]
Then the flux of [tex]\vec F(x,y,z) = \left\langle e^{-z}, 4z, 6xy\right\rangle[/tex] across S is
[tex]\displaystyle \iint_S \vec F(x,y,z)\cdot\mathrm d\vec s = \int_0^4\int_0^\pi \vec F(x,y,\cos(y))\cdot\vec n\,\mathrm dy\,\mathrm dx \\\\ = \int_0^4\int_0^\pi \left\langle e^{-\cos(y)},4\cos(y),6xy\right\rangle \cdot \left\langle0,\sin(y),1\right\rangle \,\mathrm dy\,\mathrm dx \\\\ = \int_0^4\int_0^\pi (4\sin(y)\cos(y)+6xy)\,\mathrm dy\,\mathrm dx \\\\ = 2 \int_0^4\int_0^\pi (\sin(2y) + 3xy)\,\mathrm dy\,\mathrm dx = \boxed{24\pi^2}[/tex]
Which one is greater 1/75 or 1/3
Answer:
1/3 is greater
Step-by-step explanation:
Mark me brainlist
Step-by-step explanation:
[tex] \frac{1}{75} \\ \frac{1}{3} = \frac{1 \times 15}{3 \times 15} = \frac{15}{75} [/tex]
Hence, 1/3 is greater.
which is better estimate for the volume of a tube of toothpaste 6 tablespoon 6 cups?
Answer:
6 tablespoons
Step-by-step explanation:
It's more logical because tubes of toothpaste do not require such a large amount of toothpaste. Look at your toothpaste tube. I'm sure that it is closer to 6 tablespoons rather than 6 cups.
The coefficient of -3x is 3 true or false?
Answer:
false
Step-by-step explanation:
The coefficient is -3 but not positive 3
Simplify the following expressions -18x2+3x-2x2+5 the first 2 is a small and the third 2 is small
Answer:
Step-by-step explanation:
well i think the answer is -32 but you did not explain the the small 2,ment so i am not 100% sure but good luck
Find the nth term for the following sequences, 100,96,90,82,72.(an^2+bn+c)
9514 1404 393
Answer:
t(n) = -n^2 -n +102
Step-by-step explanation:
We can use the first 3 terms to find a, b, c.
a(1)^2 +b(1) +c = 100
a(2)^2 +b(2) +c = 96
a(3)^2 +b(3) +c = 90
Subtract the first equation from the other two:
3a +b = -4 . . . . . . [eq4]
8a +2b = -10 . . . . [eq5]
[eq5] can be reduced to
4a +b = -5 . . . . . . [eq6]
Subtracting [eq4] from [eq6] gives ...
(4a +b) -(3a +b) = (-5) -(-4)
a = -1 . . . . . . . . simplify
Filling that into [eq4], we get
3(-1) +b = -4
b = -1 . . . . . . . add 3
Putting the values for 'a' and 'b' into the first equation gives ...
-1 +-1 +c = 100
c = 102
Then the n-th term t(n) of the sequence is ...
t(n) = -n^2 -n +102
_____
Additional comment
As you might guess, there is a generic solution for quadratic sequences. In terms of the first term (a1), first first difference (d1), and second difference (d2), the coefficients can be written as ...
a = d2/2b = d1 -3ac = a1 -d1 +d2This sequence has first differences of -4, -6, -8, -10, and second differences of -2. Putting the sequence values into the above formulas, we find ...
a = -2/2 = -1b = -4 -3(-1) = -1c = 100 -(-4) +(-2) = 102 . . . . . as above5/9 of a piece of metal has a mass of 7 kg. What is the mass of 2/7 of the piece of metal
Answer:
3.6 kg
Step-by-step explanation:
5/9 piece of metal has a mass=7kg
1 piece of metal has a mass =7/5/9 kg
=63/5 kg
Hence,
2/7 piece of metal has a mass=63/5*2/7
=18/5kg
=3.6 kg
If you have $20 and spend $12 on food, what fraction of your money do you still have?
Answer:
2/5
Step-by-step explanation:
please mark brainliest
Answer:
The fraction of the money that would be left would be 2/5. Hope this helps. :D
Step-by-step explanation:
What Is The Area Of The Rectangle: 145, 187. I AM COMPLETELY DESPRATE
Answer:
27115
Step-by-step explanation:
145 x 187 = 27115
Part A
Translate
Δ
A
B
C
6 units horizontally. How are the values in the ordered pairs affected by the translation?
Part B
Translate
Δ
A
B
C
−
3
units vertically. How are the values in the ordered pairs affected by the translation?
Part C
How could you determine the coordinates of the vertices of a translated image without using a graph?
Using translation concepts, it is found that:
a) For a translation 6 units horizontally, 6 is either added or subtracted to the x-coordinate of the ordered pairs.
b) For a translation 3 units vertically, 3 is either added or subtracted to the y-coordinate of the ordered pairs.
c) The coordinates of the vertices of the translated image will be given according to the following rule: (x,y) -> (x ± 6, y ± 3).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
For a translation 6 units horizontally, we have that:
If it is left, x -> x - 6.If it is right, x -> x + 6.Hence 6 is either added or subtracted to the x-coordinate of the ordered pairs.
For a translation 3 units vertically, we have that:
If it is down, y -> y - 3.If it is up, y -> y + 3.Hence 3 is either added or subtracted to the y-coordinate of the ordered pairs.
The coordinates of the vertices of the translated image will be given according to the following rule: (x,y) -> (x ± 6, y ± 3).
More can be learned about translations at https://brainly.com/question/4521517
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Solve equation. 7/8-2/3
Answer:
[tex] \frac{7}{8} - \frac{2}{3 } \\ \frac{7 \times 3}{8 \times 3} - \frac{2 \times 8}{3 \times 8 } \\ \frac{21 - 16}{24 } \\ = \frac{5}{24} [/tex]
Step-by-step explanation:
7/8-2/3
(7*3)/(8*3)-(2*8)/(3*8)
(21-16)/24
5/24
is the answer ...plzz add it to brainliest
Please help. Given formula, just plug it in to find answer.
Step-by-step explanation:
x = 2.5
(2.5 × 0.25 ) + 2= 0.625 +2
= 2.625
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!helpppppppp
Answer:
2W + 56 = 78 , W = 10
Step-by-step explanation:
perimeter of rectangle = 2*the Length + 2*the Width
Can someone please help me please?
9514 1404 393
Answer:
D. G(x) = (x+3)² -2
Step-by-step explanation:
G(x) is translated left 3 and down 2 from F(x). The transformation ...
G(x) = F(x -h) +k
is a translation right h units and up k units. We have h=-3 and k=-2, so the function of interest is ...
G(x) = F(x +3) -2
G(x) = (x +3)² -2
After a 90% reduction, you purchase a new clothes dryer on sale for $62. What was the original price of the clothes dryer?
Answer:
$7.20
Step-by-step explanation:
First, we would have to find out how much to subtract from $62.
We need to multiply 90% and 62 or 0.9 x 62
When we finish this equation we get 54.8, which is what we need to subtract from 62 to see what 90% off is.
62 - 54.8 = 7.2, so therefore our answer is $7.20
NEED HELP ASAP: WILL MARK BRAINLIEST: The graph of a function g is shown below.
Use the graph of the function to find its average rate of change from x=-1 to x=3.
Simplify your answer as much as possible.
Step-by-step explanation:
the change rate is expressed by y/x (like the slope of a line).
for x = -1 we get y = -3
for x = 3 we get y = 5
so, while x is changing by 4 units (-1 to +3), y changes by 8 units (-3 to +5).
the average charge rate is therefore
8/4 = 2/1 = 2
I need help with this problem please
Answer:
200
Step-by-step explanation:
15(68-60)+80
15×8=120
120+80=200
just substitute
Deshaun rented a truck for one day. There was a base fee of $18.95, and there was an additional charge of 89 cents for each mile driven.
Deshaun had to pay $171.14 when he returned the truck. For how many miles did he drive the truck?
Step-by-step explanation:
$171.14 in total.
minus the base price
171.14 - 18.95 = 152.19
this we now have to divide by the mile charge, to see how often that fits into the price paid. that will then tell us how many miles were driven.
152.19 / 0.89 = 171 miles were driven.
78. How long will it take a car travelling at an
average speed of 40 mph to cover a distance of
304 miles?
Time = distance / speed
Time = 304 miles / 40 mph
Time = 7.6 hours ( 7 hours and 36 minutes)
3.54 + 1.2 =
Explain how to get answer
PLEASE HELP WILL GIVE BRAINLIESTTTT
Answer:
B
Step-by-step explanation:
just f+g(x)
The circumference of a circle is 6inches. What is the area of the circle
Jose eamed 45 points in a video game. He lost 40 points, earned 81 points, then lost 35 more points. Enter
and evaluate an expression to find his final score in the video game.
Answer:
51 points
Step-by-step explanation:
45 - 40 + 81 - 35 = x
x = 51
Determine whether the equation is linear or not. Then graph the equation by
finding and plotting ordered-pair solutions.
y = - 2x + 3
RE
Is the equation y = - 2x + 3 linear or not?
O not linear
O linear
(Answer quickly)
on one of the snowiest days in the history of buffalo new york, nearly 5 feet of snow fell in a 24-hour period. if during this time snow fell at a consistent rate, which of the following graphs best represents the snowfall in this 24-hour period?
AnswerC
Step-by-step explanation: The reason is because if you look at the four graph you gotta make sure the Y=5 and only C has that
What is the value of the expression -11 + 24 + (-32)
Answer:
-19
Step-by-step explanation:
Just used the calculator, hope this helps
Answer:
-19
Step-by-step explanation:
You can split the equation into two steps:
1. - 11 + 24. You can also flip around the terms and get 24 - 11. 24 - 11 = 13 so - 11 + 24 = 13.
Next -
2. 13 + (-32). When you are adding a negative number, it is the same as subtracting the positive of that number, so we can turn the equation into 13 - 32. 13 - 32 = -19
:)
10+ [(50 :5+6) x 3] - 4
e 34
o 50
54
I don't know
Please help ASAP
Answer:
The third one 54
Step-by-step explanation:
I hope it helps.
Confuse with this problem
Answer:
[tex]6 \frac{2}{3} [/tex] (second option)
Step-by-step explanation:
attached
1. The physician has ordered 1000 mL of saline to infuse at 125 mL/hr. How many hours will it take to infuse the fluid?
2. The order is 0.25 g po qid. The medication is available as 125mg /5mL. How many tsps. will be given for each dose?
3. The physician has ordered ASA 650 mg p.o. Q 4 hr. for temperature higher than 101° F. The medication is supplied in 325mg tablets. What is the maximum number of tablets the patient can receive in any 12-hour period?
The physician has ordered amoxicillin 0.1 g p.o. Q8hr. Drug available is amoxicillin oral suspension, 250 mg/5mL. How many mL will the patient receive in 24 hours?
15. ____________ Order: Kanamycin (Kantrex) 1 g po Q6hr x 4 days. Available: Kanamycin capsules, 500 mg. How many capsules will the client receive in the 4 days he is to receive this medication?
16. ____________ Three liters of IV Lactated Ringer' is ordered to be given over 12 hours. The tubing drop factor is 15gtt/mL. The IV has been running for 9 hours. 1500 mL remain. How many drops per minute are needed so that the IV finishes in the required time?
17. ____________ Order: Penicillin, 350,000 U. Available: Penicillin, 400,000 U/5 mL.
How many mL will be administered to the patient per dose?
The ratio of mass required to concentration or rate gives the number of the units or time a medicine is to be administered
The quantities and time of medication are:
1. It will take 8 hours to infuse the fluid
2. The number of tsps is approximately 2 tsps
3. The maximum number of tablets is 6 tablets
4. The patient will receive 6 mL in 24 hours
5. The client will receive 32 capsules
6. 125 drops/minute per minute are needed so that the IV finishes
7. The volume of Penicillin per dose is 4.375 mL
The reason the above values are correct is as follows:
Required;
1. The volume of saline required to infuse, V = 1000 mL
The rate at which the saline is infused, r = 125 mL/hr
The number of hours it will take to infuse the fluid, t, is given as follows;
[tex]t = \mathbf{\dfrac{V}{r}}[/tex]
Therefore;
[tex]t = \mathbf{\dfrac{1000 \ mL}{125 \ \dfrac{mL}{hr} } = 8 \ hr}[/tex]
The number of hours it will take to infuse the fluid, t = 8 hours
2. The mass in the order, m = 0.25 g
The concentration of the medication, C = 125 mg/(5 mL)
[tex]V = \mathbf{\dfrac{m}{C}}[/tex]
Therefore;
The volume of the concentration required, V, is given as follows;
[tex]V = \dfrac{0.25 \, g}{125 \times 10^{-3} \ \dfrac{mg}{5 \ mL} } = 10 \, mL[/tex]
The volume of 1 tsps = 4.92892 mL
10 mL = 1 tsps/(4.92892 mL) × 10 mL ≈ 2.03 tsps
Rounding to the nearest whole number gives;
The number of tsps to be given for each dose is approximately 2 tsps
3. The quantity the physician ordered every 4 hours = 650 mg
The quantity of the medication per tablet = 325 mg/tablet
Maximum mass the patient can take in 12 hour = 650mg × 12/4 = 1,950 mg
The maximum number of tablets the patient can receive = 1,950 mg/(325 mg/tablet) = 6 tablets
4. The mass of amoxicillin to be taken every 8 hours = 0.1 g
The concentration of the oral suspension of the drug = 250 mg/(5 mL)
The volume the patient will receive per 24 hour = (24/8)× (0.1 g/(250 mg/(5 mL)) = 6 mL
The amount in mL the patient will receive in 24 hours = 6 mL
5. The mass of Kanamycin to be taken every 6 hours = 1 g
The number of days the of medication = 4 days
The quantity of Kanamycin per capsule = 500 mg
The mass of Kanamycin required for 4 days = ((24 × 4)/6) × 1 g = 16 g
The number of capsules = (16 g)/(500 mg/capsule) = 32 capsules
The number of capsules the client will receive = 32 capsules
6. The volume of Lactated Ringer to be given in 12 hours = 3 Liters
The tubing drop factor = 15 gtt/mL = 15 drops/mL
The number of hours the IV has been running = 9 hours
The volume of IV remaining = 1,500 mL
The number of drops remaining = 1,500 mL × (15 gtt/mL) = 22,500 drops
The time remaining = 12 hour - 9 hour = 3 hours
3 hours = 3 hour × 60 minutes/hour = 180 minutes
The number of drops per minute needed is therefore;
Drops per minute needed = 22,500 drops/(180 minutes) = 125 drops/minute
7. The Penicillin required = 350,000 μ
The available Penicillin = 400,000 μ/(5 mL)
The volume of Penicillin per dose = 350,000 μ/(400,000 μ/(5 mL)) = 4.375 mL
Learn more about dosage calculation here:
https://brainly.com/question/17346881
If there are a total of 20 data values, with what frequency does the data value 3 occur?
Answer:
3/20=0.15
0.15*3= 0.45
0.45*20= 9
The frequency is 9
Step-by-step explanation:
Simplify: WHAt is √100−√9
Answer:
7
Step-by-step explanation:
Since √100 is equal to 10 and √9 is equal to 3, we get 10 - 3 which equals 7.
