(i) The triple integral that gives the volume of the right circular cylinder enclosed by the surfaces x^2 + y^2 = 4 , z=-10 and z=0 is:
∫∫∫dV = ∫∫∫dx dy dzwhere the limits of the integration are:
0 ≤ x ≤ 2*sqrt(2), -2*sqrt(2) ≤ y ≤ 2*sqrt(2), 0 ≤ z ≤ -10.
This triple integral gives the volume of the right circular cylinder which is enclosed by the given surfaces and extends from z = 0 to z = -10.
(ii) The triple integral that gives the volume of the right circular cylinder with a hemisphere sitting atop the cylinder is:
∫∫∫dV = ∫∫∫dx dy dzwhere the limits of the integration are:
0 ≤ x ≤ 2*sqrt(2), -2*sqrt(2) ≤ y ≤ 2*sqrt(2), 0 ≤ z ≤ -10, and 0 ≤ r ≤ sqrt(x^2 + y^2).
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When the length of each edge of a cube is increased by 1 cm, the volume is increased by 37 cm3.
What is the length (in centimeters) of each edge of the original cube?
original length =3cm
Answer:
solution given;
let length be x
its
volume be x ³
we have when length is increased by 1cm volume increased by 37cm³ so
(x+1)³=x³+37cm³
x³+1³+3x²+3x=x³+37
3x²+3x-36=0
3(x²+x-12)=0
x²+4x-3x-12=0
x(x+4)-3(x+4)=0
(x+4)(x-3)=0
either
x=-4 rejected
or
x=3cm
The length (in centimeters) of each edge of the original cube will be 3.
How do you calculate the volume of a cube?Assume the side length of the cube under consideration is L units. The volume of the cube is then equal to L³ cubic units.
We have when length is increased by 1 cm volume increased by 37 cm³, so from the given condition the equation formed as;
(L+1)³=L³+37 cm³
Open the bracket and apply the necessary identities;
L³+1³+3L²+3L=L³+37
3L²+3L-36=0
3(x²+x-12)=0
Applying the factorization method;
L²+4L-3L-12=0
L(L+4)-3(L+4)=0
(L+4)(L-3)=0
L=-4 cm (Negative length is not possible.)
L=3cm
Hence,the length (in centimeters) of each edge of the original cube will be 3.
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You have one type of nut that sells for $4.50/lb and another type of nut that sells for $8.00/lb. You would like to have 28 lbs of a nut mixture that sells for $7.80/lb. How much of each nut will you need to obtain the desired mixture?
You will need
lbs of the cheaper nut
and
lbs of the expensive nut.
Answer:
I will need 26.4 pounds of the expensive nuts and 1.6 pounds of the cheap nuts.
Step-by-step explanation:
Since I have one type of nut that sells for $ 4.50 / lb and another type of nut that sells for $ 8.00 / lb, and I would like to have 28 lbs of a nut mixture that sells for $ 7.80 / lb, to determine how much of each nut will I need to obtain the desired mixture, the following calculation must be performed:
8 x 0.95 + 4.5 x 0.05 = 7.825
8 x 0.94 + 4.5 x 0.06 = 7.79
0.94 x 28 = 26.32
26.4 x 8 + 1.6 x 4.5 = 218.4
218.4 / 28 = 7.8
Thus, I will need 26.4 pounds of the expensive nuts and 1.6 pounds of the cheap nuts.
please help and show work
What are a and b when you write √-16 in the form a+bi, when a and b are real number?
A) a=0, b=-4
B) a=0, b=4
C) a=-4, b=0
D) a=4, b=0
On comparing, we get {a} = 0 and {b} = 4.
What is the general form of a complex number?The general form of a complex number is -
z = a + ib
Given is the number as -
√-16
We can write the number √-16 in the form of (a + ib) as follows. We have -
√-16
√(- 1 x 16)
√(i² x 16)
√i² x √16
i√16
0 + i√16
0 + 4i
Therefore, on comparing, we get {a} = 0 and {b} = 4.
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A representative sample of 50 students from a high school is surveyed. Each student is asked what science class he or she
is taking
This table shows the responses.
Science Class
Physics
Chemistry
Blology
Earth Science
Health Science
Number of
Students
6
10
18
4
12
Select all of the statements that are valid based on the survey results..
The statements that are valid based on the survey results are:
About 20% of the students are taking chemistry.
About twice as many students are taking health science than are taking physics.
For every 150 students we could predict that at least 18 of the students are taking physics.
Option A, B, and C are correct answer.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
About 20% of the students are taking chemistry:
To calculate the percentage of students taking chemistry, we divide the number of students taking chemistry by the total number of students surveyed and multiply by 100:
10/50 x 100% = 20%
Therefore, the statement "About 20% of the students are taking chemistry" is valid based on the survey results.
About twice as many students are taking health science than are taking physics:
The number of students taking health science is 12, and the number of students taking physics is 6. To see if twice as many students are taking health science than physics, we can compare the ratios:
Health science : Physics = 12 : 6 = 2 : 1
Since the ratio is 2:1, we can conclude that the statement "About twice as many students are taking health science than are taking physics" is valid based on the survey results.
For every 150 students, we could predict that at least 18 of the students are taking physics:
To make this prediction, we need to calculate the proportion of students taking physics based on the survey results:
6/50 = 0.12
To predict how many students are taking physics in a larger population, we can multiply the proportion by the size of the population:
0.12 x 150 = 18
Therefore, the statement "For every 150 students we could predict that at least 18 of the students are taking physics" is valid based on the survey results.
For every 25 students, we could predict that at least 4 of the students are taking Earth Science:
To make this prediction, we need to calculate the proportion of students taking Earth Science based on the survey results:
4/50 = 0.08
To predict how many students are taking Earth Science in a larger population, we can multiply the proportion by the size of the population:
0.08 x 25 = 2
Therefore, the statement "For every 25 students we could predict that at least 4 of the students are taking Earth Science" is not valid based on the survey results, as we would predict that at least 2 students are taking Earth Science, not 4.
Therefore,
The statements that are valid based on the survey results are:
About 20% of the students are taking chemistry.
About twice as many students are taking health science than are taking physics.
For every 150 students we could predict that at least 18 of the students are taking physics.
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Pretty face cosmetics earned $(1.26 x 10^6) in sales last year. write this number in standard form
Answer:
1,260,000
Explanation:
Using the calculator on any Windows computer, first put "1.26" in. After doing so, press the "exp" button that should be there if you're using the calculator on a Windows computer. After pressing that, put in "6", then press equals. After doing it correctly, you should get this answer.
wyoming electric coop owns a steam-turbine power-generating plant. because wyoming is rich in coal deposits, the plant generates its steam from coal. this, however, may result in emission that does not meet the environmental protection agency (epa) standards. epa regulations limit sulfur dioxide discharge to 2000 parts per million per ton of cual burned and smoke discharge from the plant stacks to 20 ib per hour. the coop receives two grades of pulverized coal, c1 and c2, for use in the steam plant. the two grades are usually mixed together before burning. for simplicity, it can be assumed that the amount of sulfur pollutant discharged (in parts per million) is a weighted average of the proportion of each grade used in the mixture. the following data is based on the consumption of 1 ton per hr of each of the two coal grades. sulfur discharge smoke discharge steam generated coal grade in parts per million in ih per hour in ib per hour cl 1800 2.1 12,000 c2 2100 3 9,000 (a) determine the optimal ratio for mixing the two coal grades. (b) determine the effect of relaxing the smoke discharge limit by 1 ib on the amount of generated steam ner hour.
5. A bag contains 21 red marbles and 29 blue marbles. A marble is picked at
random from the bag. What is the probability of picking a red marble?
Answer:
i dont know
Step-by-step explanation:
uhhh
Answer:
42% chance
Step-by-step explanation:
Since there are 21 red marbles and 29 blues ones, the total amount of marbles is 50. There are only 21 red marbles out of 50 marbles so there is a 21/50 chance that you will pick a red marble.
mhairi invest 1000 for 5 years at 4% compound interest p.a calculate how much interest she has gained over the 5 years
Answer:
Step-by-step explanation:
$1000×1.04⁵ ≅ $1216.65
interest ≅ $216.65
You have $400,000.00 saved in a retirement account paying 4% interest compounded monthly and are ready to start your retirement. You have to figure out how much money you can safely take out of your account every month because you don't want to run out of money before you die.
How much money can you take out each month if you expect to live another 25 years?
9514 1404 393
Answer:
$2,104.33 at the beginning of the month, or
$2,111.35 at the end of the month
Step-by-step explanation:
The amount you can withdraw at the end of the month is given by the annuity formula ...
A = P(r/12)/(1 -(1 +r/12)^(-12t))
where principal P is earning annual rate r for t years
A = $400,000(0.04/12)/(1 -(1 +0.04/12)^(-12·25)) ≈ $2,111.35
If the withdrawal is at the beginning of the month, then the amount is less by a factor of (1+0.04/12) ≈ 1.003333. It will be $2,104.33.
PLEASE HELP ACED + +++++++++
If 55% of a number is 209 and 35% of the same number is 133, find 90% of that number.
Answer:
205 is 55% of 372 and is 335 90% of 372
Step-by-step explanation:
Identify the need coordinates of the line segment M (10,5) and N (5,5) when it is rotated about 270 degrees clockwise
Answer:
280? srry if i wrong
Step-by-step explanation:
Which list shows the numbers NOT in order from least to greatest?
4.036 < 4.08 < 42<4.201
3.09 < 3.1 < 3.507 < 3.9
6.4 < 6.51 < 6.387 < 6.995
7.315 < 7.38 < 7.406 < 7.5
Find the measure of angle B.
Step-by-step explanation:
C = 180 - 112 = 68°
A = 180 - 68 - 51 = 61°
B = 180 - 61 = 119°
Another way :
We know that B = C + 51 ==> B = 68 + 51 = 119°
The reverse of adding 6 is:
A. dividing by 6
B. adding 1/6
C. subtracting 6
D. adding 6
E. multiplying by 6
F. subtracting 1/6
Answer:
C. subtracting 6
Step-by-step explanation:
If you add 6 to a number then subtract t you get the same number because they are inverse operations
Hope I helped! (p.s. maybe brainliest answer)
la masa de un camión de 45000000
Explicación:
conversión de 45.000.000 gr a kg
45.000.000 gr ( 1 kg / 1000 gr) = 45.000 kg
conversión de 45.000 kg a toneladas
45.000 kg ( 1 ton / 1000 kg) = 45 ton
Respuesta: Espero te sirva...
Please help thank you
Answer:
x = 140
Step-by-step explanation:
Using the exterior angle rule ( an exterior angle of a triangle is equal to the opposite interior angles of a triangle )
x is the interior angle and the given angles ( 50 and 90 ) are the opposite interior angles
So
x = 50 + 90
50 + 90 = 140
x = 140
Note: there is a right angle ( indicated by the little square. A right angle has a measure of 90 degrees so that's where the 90 came from)
what is is distance between (0,2) and (5,2)
PLEASE HELP!!! I GIVE 15 POINTS!
Flaws in a carpet tend to occur randomly and independently at a rate of one every 260 square feet. What is the probability that a carpet that is 7 feet by 14 feet contains no flaws?
Probability =
Enter your answer in terms of e.
Answer:
The probability that a carpet that is 7 feet by 14 feet contains no flaws is 99.996%.
Step-by-step explanation:
Given that flaws in a carpet tend to occur randomly and independently at a rate of one every 260 square feet, to determine what is the probability that a carpet that is 7 feet by 14 feet contains no flaws, the following calculation must be performed:
7 x 14 = 98
1/260 = 0.003
98 = 100
0.003 = X
0.003 x 100/98 = X
0.0039 = X
100 - 0.0039 = 99.996
Thus, the probability that a carpet that is 7 feet by 14 feet contains no flaws is 99.996%.
Joel went to the market to buy a juicy watermelon and found the volume was 523.6 mm. what is the radius of the watermelon? round to the nearest whole number.
Answer:
The radius of the watermelon was 5 milimeters.
Step-by-step explanation:
Since Joel went to the market to buy a juicy watermelon and found the volume was 523.6 square mm., To determine what is the radius of the watermelon, the following calculation must be performed, knowing that the volume of a sphere is equal to four thirds multiplied by pi, multiplied by the radius cubed:
4/3 x 3.14 x X^3 = 523.6
4.186 x X^3 = 523.6
X^3 = 523.6 / 4.186
X = 3√ 125.06
X = 5
Therefore, the radius of the watermelon was 5 milimeters.
What is 4 1/7 in simplest form ??
Answer:28
Step-by-step explanation:
Answer:
29/7 or in decimal form: 4.1428...
Please answer quickly! Will mark brainliest
Answer: C) 1/a^12•b^8
Step-by-step explanation:
A scale drawing of an NFL god post uses a
scale of 2 inches = 5 feet. If the actual width
of the goal post is 182 feet, what is the width
of the goal post on the drawing?
Ann took a taxi home from the airport. The taxi fare was $2.10 per mile, and she gave the driver a tip of
$5. Ann paid a total of $49.10.
Answer:
Ann went 21 miles in the taxi
Step-by-step explanation:
-7.66666, \sqrt(50,) -(157)/(20), -7.64 list these from least to greatest.
Answer:
From least to greatest, the correct order is: [tex]-\frac{157}{20}[/tex]; -7.666....; -7.64; and [tex]\sqrt{50}[/tex].
Step-by-step explanation:
Since [tex]\sqrt{50}[/tex] is the only positive number, that means that it will be the greatest number on the list. [tex]-\frac{157}{20}[/tex] is equivalent to -7.85, which makes it the smallest number. So you can conclude that the correct order is [tex]-\frac{157}{20}[/tex]; -7.666...; -7.64; and [tex]\sqrt{50}[/tex].
B= R/E - T, solve for E
A ball is thrown directly upward from a height of 5 ft with an initial velocity of 24 ft/sec. The function s(t) = -16t^2+24t+5 gives the height of the ball, in feet, t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height and find the maximum height.
Answer:
The maximum height is 14 feet and it will take 0.75 s to reach there.
Step-by-step explanation:
A ball is thrown directly upward from a height of 5 ft with an initial velocity of 24 ft/sec.
The function is :
[tex]s(t) = -16t^2+24t+5[/tex] ....(1)
It gives the height of the ball, in feet, t seconds after it has been thrown.
For maximum height,
s'(t) = 0
So,
-32t+24 = 0
t = 0.75 s
It will take 0.75 s to reach the maximum height.
Put t = 0.75 s in equation (1). So,
[tex]s(0.75) = -16(0.75)^2+24(0.75)+5\\\\s=14\ feet[/tex]
So, the maximum height is 14 feet and it will take 0.75 s to reach there.
Need the answer for x and y
Answer:
How many molecules of water are there in 10 lbs of water?
Step-by-step explanation:
Answer:
x = 15
AC = 95
Step-by-step explanation:
6x + 5 = 8x - 25
combine like terms:
2x = 30
x = 15
AC = 95
Please help will give brainliest
Answer:
One-third of the volume
Step-by-step explanation:
Volume of cylinder = πr²h
Volume of cone = (1/3)πr²h