Let $s$ be the set of points with polar coordinates $(r,\theta)$ such that $ 2 \le r \le 6$ and $\frac{\pi}{3} \le \theta \le \frac{5 \pi}{6} $. find the area of $s$.
Answers
2 ≤ r ≤ 6 and π/3 ≤ θ ≤ (5π)/6 is shown in the figure below.
An element of area is
dA = r dr dθ
Therefore the total area is
[tex]A=\int _{ \frac{ \pi }{3}} ^{ \frac{5 \pi }{6} } \,d\theta \int_{2}^{6} \,rdr \\ A= [ \frac{5 \pi }{6}- \frac{ \pi }{3}]*[ \frac{6^{2}}{2} - \frac{2^{2}}{2}] = 8 \pi [/tex]
Answer: 8π
Related Questions
Identify the coefficient of 2xy3
Answers
Please help me on this one
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south America = 2.2%
2.2% = 0.022
0.022 = 22/1000 which reduces to 11/500
Write the standard form of the line that contains a slope of 2/3 and passes through the point (1, 1)
Answers
y - 1 = 2/3x - 2/3
2/3x - y = -1 + 2/3
2/3x - y = -1/3
2x - 3y = -1
A sequence is defined recursively using the formula f(n+1)=-0.5f(n). If the first term on the sequence is 120, what is f(5)
Answers
F(n+1)=-0.5f(n) 120 f (5)
A real estate agent received a 6% commission on the selling price of a house. If his commission was $8,880, what was the selling price of the house?
Answers
106 % = x + 8,800 where x is the selling price
100 % = x
so 106 / 100 = 1.06 = (x + 8800) / x
1.06x = x + 8800
0.06x = 8800
x = 8800 / 0.06 = $146,666.67
Which positive integers less than 12 are relatively prime to 12?
Answers
Final answer:
To find the positive integers less than 12 that are relatively prime to 12, we need to find the positive integers that do not share any common factors with 12 other than 1. The positive integers less than 12 that are relatively prime to 12 are 1, 5, 7, and 11.
Explanation:
Two positive integers are relatively prime if their greatest common divisor (GCD) is 1. To find the positive integers less than 12 that are relatively prime to 12, we need to find the positive integers that do not share any common factors with 12 other than 1.
The prime factors of 12 are 2 and 3. Therefore, any positive integer less than 12 that is not divisible by 2 or 3 will be relatively prime to 12.
Therefore, the positive integers less than 12 that are relatively prime to 12 are 1, 5, 7, and 11.
The height of a cone is equal to the diameter of the base. what expression represents the volume of the cone, in cubic units? πx3 πx2 2πx3 4πx3
Answers
The formula for a cone is given as:
V = π r^2 h / 3 ---> 1
Where,
V = volume of the cone
r = radius of the circle base of the cone
h = is the perpendicular length from the center of the base of the cone to the tip at the top
It was given that:
h = d
but d = 2 r, therefore:
h = 2 r
Substituting this to equation 1:
V = π r^2 (2 r) / 3
V = 2 π r^3 / 3
Since r = x, the answer from the choices is:
2πx3
The expression representing the volume of the cone is (2/3)πx^3, where x represents the cone's radius.
Step 1: Identify Key Information
We are given that the height (h) of the cone is equal to the diameter (d) of the base. The diameter is twice the radius (r).
Step 2: Apply Formula and Substitute
The formula for the volume of a cone is:Volume (V) = (1/3) * π * r^2 * h
Since h = d = 2r, we can substitute:V = (1/3) * π * r^2 * (2r)
Step 3: Simplify the Expression
V = (1/3) * π * r^2 * 2rV = (2/3) * π * r^3Oq is a diagonal of quadrilateral nopq. if noq=pqo, no = 5x + 12, and pq = 7x – 8, find the length of no for which nopq is a parallelogram.
a. 10
b. 24
c. 47
d. 62
Answers
NO = PQ
5 x + 12 = 7 x - 8
12 + 8 = 7 x - 5 x
20 = 2 x
x = 20 : 2
x = 10
NO = 5 * 10 + 12 = 50 + 12 = 62
Answer: d. 62
Since it is a parallelogram, NO = PQ
5 x + 12 = 7 x - 8
12 + 8 = 7 x - 5 x
20 = 2 x
x = 20 : 2
x = 10
NO = 5 * 10 + 12 = 50 + 12 = 62
Answer: 62
Hope this helps, have a BLESSED and wonderful day, as well as a safe one! Also, have a merry Christmas! :-)
-Cutiepatutie
The probability that a train leaves on time is 0.4. The probability that the train arrives on time and leaves on time is 0.28. What is the probability that the train arrives on time, given that it leaves on time?
0.4
0.12
0.28
0.7
Answers
P(A|B) = P(A∩B) / P(B)
Key:
P(A|B): Probability of A given B
P(A∩B): Probability of A and B
If we say A is the event that the train arrives on time and B is the event that the train leaves on time, then according to the information:
P(B) = 0.4
P(A∩B) = 0.28
Just insert into the formula:
P(A|B) = 0.28 / 0.4 = 0.7
(or 70% as a percentage).
The probability that the train arrives on time, given that it leaves on time is 0.7
Explanation:The question asks for the probability that the train arrives on time, given that it leaves on time. This is a conditional probability problem, and we can use the formula for conditional probability, which is P(A|B) = P(A and B)/P(B).
In this case, event A is the train arrives on time, event B is the train leaves on time. We know that P(A and B) = 0.28 (the probability that the train arrives on time and leaves on time) and P(B) = 0.4 (the probability that the train leaves on time).
By substituting these values into the formula, we get P(A|B) = 0.28/0.4 = 0.7. So, the probability that the train arrives on time, given that it leaves on time is 0.7.
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Use the student's t distribution to find tc for a 0.95 confidence level when the sample is 29. (round your answer to three decimal places.)
Answers
Using a t distribution table you can easily find the t critical value in a very easy way just look for the confidence level which is 95% or the 5% significance level and look for the degrees of freedom which is 28 (just to remind you degrees of freedom is always -1, so if you have 29 – 1 you will get 28 and it is the degrees of freedom), then the t distribution should give you 2.048 for your t critical value. When you use the significance level here you need to subtract the 100% by your confidence level of 95% you will get the 5% then you should divide it to 2, you will get the .025 if it only a two-tailed test you will use the significance level.
What is the simplified form of the quantity y−squared minus y minus 12 over the quantity y−squared plus 8y plus 15?
PLEASE EXTRA POINTS
Answers
(y-4)(y+3)/(y+3)(y+5)=
The y+3 cancel out. Therefore: (y-4)/(y+5)
How many different id cards can be made if there are 5 digits on a card and no digit can be repeated?
Answers
if no numbers can repeat then you have
1st digit = 10 numbers
2nd digit = 9 numbers
3rd digit = 8 numbers
4th digit = 7 numbers
5th digit = 6 numbers
10 * 9 * 8 * 7 *6 =30,240 different combinations
There are 30,240 different ID cards that can be made with 5 digits where no digit can be repeated, calculated as a permutation of 10 choices taken 5 at a time without replacement.
Explanation:The question asks us to determine how many different ID cards can be made with 5 digits where no digit can be repeated. This is a problem of permutations where the order of the digits matters. We have 10 possible digits (0-9), and we need to choose 5 of them without repetition.
For the first digit, we have 10 choices (0-9). Once we choose the first digit, we have 9 choices left for the second digit (since one digit is already used and can't be repeated). Continuing this pattern, we have 8 choices for the third digit, 7 choices for the fourth digit, and 6 choices for the fifth digit.
The total number of different ID cards is calculated by multiplying these choices:
10 choices for the first digit9 choices for the second digit8 choices for the third digit7 choices for the fourth digit6 choices for the fifth digitThe calculation is 10 x 9 x 8 x 7 x 6, which equals 30,240 different ID cards.
Find the truth set of each of these predicates where the domain is the set of integers.
a.p(x): x3 ≥ 1
b.q(x): x2 =2
c.r(x): x < x2
Answers
x^3 ≥ 1 => x ≥ 1 => all the integers equal or greater than 1 = { x ∈ Z | x ≥ 1} = {1, 2, 3, 4, 5, 6, ...}
That is the same that the natural numbers except 0 = N - {0}.
b.q(x): x2 = 2
x^2 = 2 => x = +/- √2, which is not an integer, so the truth set is the empty set = { } =∅
c.r(x): x < x2
x < x^2 => x^2 - x > 0
=> x (x - 1) > 0
=>
1) x > 0 and x - 1 > 0
=> x > 0 and x > 1
=> x > 1
2) x < 0 and x - 1 < 0
=> x < 0 and x < 1 => x < 0
=> the solution is the union of the two sets: x > 1 ∪ x < 0
That is all the integers except 0 and 1.
=> the truth set is { x ∈ Z | x < 0 or x > 1} = Z - { 0,1}
Is 202.98% greater than 1 or is 67.14% greater than 1?
Answers
Answer:
202.98% > 167.14% < 1Step-by-step explanation:
100% = 1
202.98% is more than 100%, so is more than 1.
67.14% is less than 100%, so is less than 1.
Angelo family drove 254.6 miles their car used 19 gallons of gasoline describe the cars gas mileage
Answers
Gas mileage = 254.6 miles/19 gallons
Gas mileage = 13.4 miles/gal
The Angelo family's car has a gas mileage of approximately 13.4 miles per gallon, calculated by dividing the total miles driven (254.6 miles) by the gasoline used (19 gallons).
Explanation:A car's gas mileage is calculated by dividing the total number of miles driven by the amount of gasoline used. In this case, the Angelo family drove 254.6 miles and used 19 gallons of gasoline. So, to figure out their car's gas mileage, you would divide 254.6 miles by 19 gallons.
254.6 miles ÷ 19 gallons = 13.4 miles per gallon
Therefore, the gas mileage of the Angelo family's car is approximately 13.4 miles per gallon.
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Let f( x)= sin(x) Let g(x)=cos(x) a) Sketch the graph of f^2 b) Sketch the graph of g^2 c) Sketch the graph of f^2+g^2
Answers
To sketch the graphs, square the y-values of sin(x) and cos(x) to get f^2(x) and g^2(x), respectively. Then, add the squared y-values of f(x) and g(x) to get f^2(x)+g^2(x). Plot the points obtained for each function and sketch the graphs.
Explanation:a) To sketch the graph of f^2, we need to square every y-value of the function f(x)=sin(x). This means finding the square of the sine of each angle. For example, f^2(0)=sin^2(0)=0^2=0. By repeating this process for multiple angles, we can plot the points and sketch the graph.
b) Similarly, to sketch the graph of g^2, we need to square every y-value of the function g(x)=cos(x). This means finding the square of the cosine of each angle. For example, g^2(0)=cos^2(0)=1^2=1. By repeating this process for multiple angles, we can plot the points and sketch the graph.
c) To sketch the graph of f^2+g^2, we need to add the squared y-values of f(x) and g(x) at each angle. For example, f^2+g^2(0)=sin^2(0)+cos^2(0)=0^2+1^2=1. By repeating this process for multiple angles, we can plot the points and sketch the graph.
A seamstress is paid $9.55 for every pair of pants made. how many pants would have to be made to receive $525.00 a week?
Answers
So,
9.55 * x = 525.00
x = [tex] \frac{525}{9.55} [/tex] ≈ 54.97
Thus, the number of pants have to be made are 54.
To receive $525.00 a week, a seamstress being paid $9.55 per pair of pants made would need to make approximately 55 pairs of pants.
Let’s denote the number of pairs of pants that need to be made as x.
The seamstress is paid $9.55 for every pair of pants.
We want to find the number of pairs of pants needed to earn $525.00, so we set up the equation:
[tex]9.55 \times x = 525.00[/tex]
Solve for x:
[tex]x = \frac{525.00}{9.55} \approx 54.97[/tex]
Since we can’t make a fraction of a pair, we round up to the nearest whole number:
The seamstress would need to make 55 pairs of pants (which means a total of 110 pants) to receive $525.00 a week.
The lengths of the sides of a triangle are in the extended ratio 1:2:5. The perimeter of the triangle is 32 ft. The length of the longest side is?
Answers
1+2+5=8
1/8*32=4 ft
2/8*32=8 ft
5/8*32=20 ft
Therefore we conclude that the longest side is 20 ft
The sum of three consecutive odd integers is forty five written as an algebraic equation would be:
x + (x+1) + (x+3) = 45
True or False
Answers
False,
the equation should be
x+ (x+2) +(x+4) = 45
PLEASE HELP! (8)/(5x) - (4)/(x^2) Show your work :)
Answers
You accidentally dropped a coin from the top of 7 stairs. What is the probability that it will land below the sixth step and heads up?
Answers
1/2 because there is a 50/50% chance its either heads or tails
Answer:
The probability that it will land below the sixth step and heads up is [tex]\frac{1}{14}[/tex]
Step-by-step explanation:
Given : You accidentally dropped a coin from the top of 7 stairs.
To find : What is the probability that it will land below the sixth step and heads up?
Solution :
A coin has two sides - head and tail.
Probability of getting head is
[tex]P(H)=\frac{1}{2}[/tex]
Total stairs are 7.
Coin will land below the sixth step i.e. it land on 7th step.
So, Probability of landing coin on below the sixth step is
[tex]P(L)=\frac{1}{7}[/tex]
Now, The probability that it will land below the sixth step and heads up is
[tex]P=\frac{1}{2}\times \frac{1}{7}[/tex]
[tex]P=\frac{1}{14}[/tex]
Therefore, The probability that it will land below the sixth step and heads up is [tex]\frac{1}{14}[/tex]
Grace and Jamal each bought notebooks for school. Grace bought 3 notebooks for $3.90 while Jamal bought 2 notebooks for $2.20. What was the unit price of each student's notebooks?
Answers
2.2/2=$1.10
The unit prices are $1.30 and $1.10.
Hope this help!
Use the arc length formula and the given information to find r. Show your work for full credit. s = 8.1 ft θ = (3.14/3)rad r = ?
Answers
s=θ(r)
arc length = angle x radius
2.46888m(or 8.1 ft) = (π/3) x r
[tex]r = (\pi /3)/2.46888[/tex]
[tex]r = .425m [/tex]
Answer:
The length of the radius is 7.74 ft.
Step-by-step explanation:
It is given that the length of arc is s=8.1 and central angle of arc is [tex]\theta=\frac{3.14}{3}[/tex] in radian.
The formula for arc length is
[tex]s=r\theta[/tex]
Where, s is length of arc, θ is central angle of arc in radian and r is the radius of the circle.
Substitute s=8.1 and [tex]\theta=\frac{3.14}{3}[/tex] in the above formula.
[tex]8.1=r\times \frac{3.14}{3}[/tex]
[tex]8.1=r\times 1.0467[/tex]
Divide both sides by 1.0467.
[tex]\frac{8.1}{1.0467}=r[/tex]
[tex]7.73860705073=r[/tex]
[tex]r\approx 7.74[/tex]
Therefore the value of r is 7.74 ft.
Jorani flips two standard American quarters. How many ways can she get at least one head?
Answers
one head, one tails
one tails, one head
one head, one head
A farmer owns 30 acres of land. Of the 30 acres, only 65% can be farmed. How many acres are available for farming?
Answers
Final answer:
To calculate the available farming land, 65% of the total 30 acres is determined, resulting in 19.5 acres available for farming.
Explanation:
To find out how many acres are available for farming, we need to calculate 65% of the total 30 acres of land the farmer owns.
The calculation is as follows:
Convert the percentage to a decimal by dividing by 100: 65% / 100 = 0.65.Multiply the total acres by the decimal: 30 acres × 0.65 = 19.5 acres.Therefore, 19.5 acres of the farmer's land can be used for farming.
find the sum of the measures of the interior angles of a convex 20-gon
Answers
If you'd like to know more, it is the number of sides - 2 multiplied by 180 degrees
eight more than the product of two and a number x
Answers
hope this helps
18 thousands times 10=
Answers
Answer:
180,000.
Step-by-step explanation:
Given : 18 thousands times 10.
To find : Solve .
Solution : We have given
18 thousands times 10.
According to question :
18 thousand = 18000.
10 Times of 18 thousand .
18000 *10 .
180,000.
Number would be 180,000
Therefore, 180,000.
The empty gas tank of a truck needs to be completely filled. The tank is shaped like a cylinder that is 3 ft long with a diameter of 2.4 ft . Suppose gas is poured into the tank at a rate of 2.5 ft 3 per minute. How many minutes does it take to fill the empty tank? Use the value 3.14 for π , and round your answer to the nearest minute. Do not round any intermediate computations.
Answers
now, the tank is filling up at 2.5 ft³/min
how many times is 2.5 into V?
[tex]\bf V=\pi ft \cdot 1.2^2 ft\cdot 3 ft\implies 4.32\pi\ ft^3 \\\\\\ \textit{the rate is filling up is }2.5\frac{ft^3}{min} \\\\\\ \cfrac{4.32\pi \ ft^3}{\frac{2.5\ ft^3}{min}}\implies \cfrac{\frac{4.32\pi \ ft^3}{1}}{\frac{2.5\ ft^3}{min}}\implies \cfrac{4.32\pi \ ft^3}{1}\cdot \cfrac{min}{2.5\ ft^3}\implies \cfrac{4.32\pi }{2.5}min[/tex]
that many minutes, round it away.
(Solve for x) -8 = -7 + x
Answers
-8 + 7 = x
-1 = x <==
-8 + -7 +x
add 7 to both sides
-1=x
so x = -1