The volume V of the solid is (248/3)π cubic units.
To find the volume of the solid below the cone z = √(x² + y²) and above the ring 1 ≤ x² + y² ≤ 25, we can use polar coordinates to simplify the calculation.
In polar coordinates, we have x = rcos(θ) and y = rsin(θ), where r represents the distance from the origin to a point and θ represents the angle between the positive x-axis and the line connecting the origin to the point.
The given inequalities in terms of polar coordinates become:
1 ≤ x² + y² ≤ 25
1 ≤ r² ≤ 25
Since z = √(x² + y²), we can express it in terms of polar coordinates as z = √(r²cos²(θ) + r²sin²(θ)) = √(r²) = r.
So, the height of the solid at any point is equal to the radius r in polar coordinates to find the volume.
Now, we need to determine the limits of integration for r and θ.
For r, the lower limit is 1, and the upper limit is the radius of the ring, which is √25 = 5.
For θ, we need to consider a full circle, so the lower limit is 0, and the upper limit is 2π.
Therefore, the volume V of the solid can be calculated as:
V = ∫∫∫ r dz dr dθ
V = ∫[θ=0 to 2π] ∫[r=1 to 5] ∫[z=0 to r] r dz dr dθ
To evaluate the volume of the solid below the cone z = √(x² + y²) and above the ring 1 ≤ x² + y² ≤ 25, we'll integrate the expression as mentioned earlier:
V = ∫[θ=0 to 2π] ∫[r=1 to 5] ∫[z=0 to r] r dz dr dθ
Let's evaluate this integral step by step:
∫[z=0 to r] r dz = r[z] evaluated from z=0 to r = r(r-0) = r²
∫[r=1 to 5] r² dr = [(1/3)r³] evaluated from r=1 to 5 = (1/3)(5³ - 1³) = (1/3)(125 - 1) = (1/3)(124) = 124/3
∫[θ=0 to 2π] (124/3) dθ = (124/3)[θ] evaluated from θ=0 to 2π = (124/3)(2π - 0) = (124/3)(2π) = (248/3)π
Therefore, the volume V of the solid is (248/3)π cubic units.
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Does anyone know this one?
Answer:
-3
Step-by-step explanation:
(-5) - (-2) = (-3)
hope it helps
Answer:
there is a three degree difference between san Diego and Los Angeles
Use the method of undetermined coefficients to solve the initial value problem below. y'' + 7y=7 sin (√7t), y(0) = 8, y'(0)=√7 19 2 y =
The general solution to the initial value problem is:
y(t) = y_c(t) + y_p(t)
= 8 cos(√7t) + cos(√7t)
To solve the initial value problem using the method of undetermined coefficients, we assume a particular solution of the form:
y_p(t) = A sin(√7t) + B cos(√7t)
where A and B are constants to be determined.
Taking the first and second derivatives of y_p(t), we have:
y'_p(t) = A√7 cos(√7t) - B√7 sin(√7t)
y''_p(t) = -A(√7)^2 sin(√7t) - B(√7)^2 cos(√7t)
Substituting these derivatives back into the differential equation, we get:
(-A(√7)^2 sin(√7t) - B(√7)^2 cos(√7t)) + 7(A sin(√7t) + B cos(√7t)) = 7 sin(√7t)
Simplifying, we have:
(-A(√7)^2 + 7A) sin(√7t) + (-B(√7)^2 + 7B) cos(√7t) = 7 sin(√7t)
To satisfy this equation for all t, the coefficients of sin(√7t) and cos(√7t) must be equal to the corresponding coefficients on the right side.
Therefore, we have the following system of equations:
-A(√7)^2 + 7A = 0 (coefficient of sin(√7t))
-B(√7)^2 + 7B = 7 (coefficient of cos(√7t))
Solving these equations, we find:
A = 0
B = 1
So, the particular solution is:
y_p(t) = cos(√7t)
To find the general solution, we need to find the complementary solution by solving the homogeneous equation:
y'' + 7y = 0
The characteristic equation is:
r^2 + 7 = 0
Solving this quadratic equation, we find two complex roots:
r₁ = √7i
r₂ = -√7i
The complementary solution is then:
y_c(t) = C₁ cos(√7t) + C₂ sin(√7t)
where C₁ and C₂ are constants to be determined.
Using the initial conditions y(0) = 8 and y'(0) = √7, we can substitute these values into the general solution and solve for C₁ and C₂.
y(0) = C₁ cos(0) + C₂ sin(0) = C₁ = 8
y'(0) = -C₁√7 sin(0) + C₂√7 cos(0) = C₂√7 = √7
Therefore, C₁ = 8 and C₂ = 1.
The general solution to the initial value problem is:
y(t) = y_c(t) + y_p(t)
= 8 cos(√7t) + cos(√7t)
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#1 someone help me with this question pls ??
Answer:
58-51
why to have the speed of a cucumber you need a potato on a skateboard at 1000kmh, ok?
Answer: 4 I think
on each side it has 4
The cook at the Elmview School cafeteria made grilled chicken and fried chicken yesterday for lunch. He made 5 pieces of grilled chicken for every 2 pieces of fried chicken.
Pick the diagram that models the ratio in the story.
If the cook made 80 pieces of fried chicken, how many pieces of chicken did he make altogether?
The cook made 280 pieces of chicken altogether.
the diagram is like this :
Grilled chicken: [#####] [#####] [#####] [#####] [#####] ,
Fried chicken: [##] [##]
The ratio of grilled chicken to fried chicken is 5:2, which means for every 5 pieces of grilled chicken, the cook made 2 pieces of fried chicken.
To model this ratio, we can use a bar diagram with five sections for the grilled chicken and two sections for the fried chicken,
If the cook made 80 pieces of fried chicken, we can use this ratio to calculate the number of pieces of grilled chicken.
First, we need to find out how many sets of 5:2 there are in 80. We can do this by dividing 80 by 2 and then multiplying by 5:
80 ÷ 2 = 40
40 × 5 = 200
So the cook made 200 pieces of grilled chicken.
To find the total number of pieces of chicken, we just need to add the grilled and fried chicken together: 200 + 80 = 280 .
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QUICK! WHOEVER GIVES CORRECT ANSWER GETS BRAINLIEST
Please awnser correctly! I will mark you as Brainliest!
-12 x (1/3)? what is this equal to!
Answer:
-4
Step-by-step explanation:
Answer:
-4
Step-by-step explanation:
-12 times 1/3.
It's pretty much just -12x1, then divided by 3.
-12x1 is equal to -12.
Your equation is now simplified, making it easier to solve.
Your equation is: [tex]\frac{-12}{3}[/tex]
-12 divided by 3 is -4, because when a negative number is divided (or multiplied) by a positive number, the quotient (or product) is negative.
-12 x (1/3) = -12/3 = -4.
Find the area of a circle if the diameter is l6 meters.
PLEASE EXPLAIN AND DO THE PROBLEM IN THE ANSWER!!!!
Answer:
Step-by-step explanation:
the formula for a circle is pi(r^2) where r is the radius. the diameter is 16 so 16/2 =8. substitute 8 for the radius to get pi(8^2). 8^2=64 so you have pi(64).
pi(64)= approximately 201.06
A biweekly compounding will generate a higher annual percentage yield ( APY )
than a monthly compounding .
True
False
True. A biweekly compounding will generate a higher annual percentage yield (APY) than a monthly compounding.
True. A biweekly compounding frequency will generate a higher annual percentage yield (APY) compared to a monthly compounding frequency. The APY takes into account the effect of compounding on the total return of an investment over a year.
Biweekly compounding means that interest is calculated and added to the account balance every two weeks, resulting in more frequent compounding periods throughout the year. This more frequent compounding leads to the accumulation of interest on a larger balance, thus generating a higher APY.
On the other hand, monthly compounding occurs once a month, resulting in fewer compounding periods and a lower overall APY. Therefore, for the same nominal interest rate, a biweekly compounding schedule will yield a higher APY compared to a monthly compounding schedule.
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A coach ordered 20 practice jerseys for her soccer team. Six of the jerseys she ordered arrived late. What decimal represents the fraction of jerseys that arrived late?
Answer: 0.3
Step-by-step explanation:
There are 20 practice jerseys in total.
Six of those 20 jerseys arrived late.
The fraction of jerseys that arrived late is therefore:
= 6 / 20 jerseys
Convert them to decimal form by dividing the numerator with the denominator:
= 6 ÷ 20
= 0.3
Here's a easy one
Not accepting links!
If JKLM is a rectangle, solve for x.
(6/-7)/(3/11)
6/-7 divided by 3/11
Answer:
-22/7
Step-by-step explanation:
To divide fractions, we multiply by the reciprocal:
(6/-7)/(3/11)
(6/-7)(11/3)
66/-21
22/-7
-22/7
Therefore, your simplifed answer is -22/7
Answer:
36/49
Step-by-step explanation:
108/49/3
=108/147
=36/49
3333 divided by 77. i really need help
Answer:
43.2857142857
plz mark me as brainliest
Answer:
476.142857143
Step-by-step explanation:
Plz help I’ll mark brainliest:$
(1) x = -2 y = -8
(2) x = -1 y = -4
(3) x = 0 y = 0
(4) x = 1 y = 4
(5) x = 2 y = 8
Those are the answers for what y is so now i think you have to plug it in to the right side of the chart
it is 20 miles from the airport to the hotel. The driver says that there is 1/8 of the total distance left to travel. What distance has already been driven?
Answer:
2.5mi
Step-by-step explanation:
?/20 = 1/8
^ If you turn into a percentage you get 1/8 = 12.5%
so now the question is v
what is 12.5 percent of 20?
which is 2.5
I WOULD CHECK FIRST, NOT 100 PERCENT SURE
Hila found the data at the left that shows the number of ways that each sum can be obtained when rolling three dice. a) Determine the mean and the standard deviation. b) Draw a frequency polygon to show the data. c) Does the data have a normal distribution? Explain. Rolling 3 Dice Sum Frequency 3 1 4 3 5 0 6 6 10 7 15 8 21 9 25 10 27 11 27 12 25 13 21 14 15 15 10 16 6 17 3 18 1
a) The mean and standard deviation need to be determined for the given data on the number of ways each sum can be obtained when rolling three dice.
b) A frequency polygon can be drawn to represent the data.
c) Whether the data has a normal distribution or not needs to be determined, and an explanation is required.
a) Mean and Standard Deviation: The mean can be calculated by summing up the products of each value and its corresponding frequency, then dividing by the total frequency. The standard deviation can be calculated by finding the square root of the variance, where the variance is the sum of the squared differences between each value and the mean, divided by the total frequency.
b) Frequency Polygon: A frequency polygon can be plotted by taking the sum values on the x-axis and the corresponding frequencies on the y-axis. Points are plotted for each sum value, and then lines are drawn to connect these points to form the polygon.
c) Normal Distribution: To determine if the data follows a normal distribution, one can visually analyze the frequency polygon. If the polygon displays a symmetric, bell-shaped curve, it suggests a normal distribution. However, if the polygon is skewed or does not exhibit a bell shape, the data is unlikely to have a normal distribution.
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Just need the answer thank you
Answer:
The multiplicative rate of change is 3/4
Step-by-step explanation:
Here, we want to get the multiplicative rate of change
In this case, by dividing the succeeding term by the preceding term, we will get the multiplicative rate of change
mathematically, we have this as;
81/128 divided 27/32
= 81/128 * 32/27
= 3/4
Find the value of $x$ .
A circle with center Q has four points L, M, N, and P lie on the circle. Diameter L N and chord M P intersect perpendicularly. The diameter divides the chord M P into two parts with measures 5 x minus 6 and 2 x plus 9.
Answer:
What
Step-by-step explanation:
I dont understand what you are asking
There are 244 seventh grade students. The number of students enrolled in P.E. Is 8 fewer than three times the number of students enrolled in health
Answer:
No. of students enrolled in Health = 63
No. of students enrolled in P.E. = 181
Step-by-step explanation:
Given,
Total students in grade seven = 244 students
A.T.Q.
Let the number of students enrolled in Health be x
so, The number of students enrolled in P.E. = 3x - 8
As we know,
x + (3x - 8) = 244
4x = 244 + 8
x = 252/4
x = 63
Thus, the number of students enrolled in Health = 63
The number of students enrolled in P.E. = 3x - 8
= 3 * 63 - 8
= 189 - 8
= 181 students
_______1. What is 22% of 10?
_______2. 16% of 30 is ______.
_______3. 25 percent of 50 is ______.
_______4. What is 65% of 300
_______5. Find 10% of 450
A. 195
B. 45
C. 4.8
D. 12.5
E. 2.2
Pa sagot po pls
Answer:
1. 22% of 10 = 2.2
2. 16% of 30 = 4.8
3. 25% of 50 is 12.5
4. 65% of 300 = 195
5. 10% of 450 = 45
HAHA, I KNEW IT!!!
HOPE THIS HELPS!!!!
MARK AS BRAINLIEST (probably)
GIVE 5 STARS PLEASE
Answer:
E - 2.2C - 4.8D - 12.5A - 195B - 45Step-by-step explanation:
For each questions, multiply the whole number by the percentage.
Or, change each percentage by getting rid of the percentage sign and dividing by 100.
EX : 65% = .65 or 22% = .22
10 x .22 = 2.2
A study was run to determine if more than 30% of Cal State East Bay students work full-time. A random sample of 100 Cal State East Bay students had 36 work full-time. The p-value was found to be 0.0952. Group of answer choices There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than our sample's 36 working full-time. There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than our sample's 36 working full-time if exactly 30% of Cal State East Bay students work full-time. There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have the same as our sample's 36 working full-time if exactly 30% of Cal State East Bay students work full-time. There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than 30% working full-time.
The correct option id D. There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than our sample's 36 working full-time
A study was conducted to determine if more than 30% of Cal State East Bay students work full-time.
The sample of Cal State East Bay students selected was random.
Out of 100 students, 36 were found to be working full-time.
The p-value was calculated to be 0.0952.
The probability of having more than 36 Cal State East Bay students working full-time out of a random sample of 100 students is 9.52% if exactly 30% of Cal State East Bay students work full-time.
Therefore, it is concluded that the null hypothesis cannot be rejected.
The p-value is greater than 0.05 which shows the significance level.
Hence, we accept the null hypothesis.
The null hypothesis states that the proportion of Cal State East Bay students who work full-time is not greater than 30%.
The alternate hypothesis states that the proportion of Cal State East Bay students who work full-time is greater than 30%.
The test is a right-tailed test.
The sample proportion is p = 0.36. The test statistic is given as Z = (p - P0) / √ [P0 (1 - P0) / n]Z = (0.36 - 0.30) / √ [(0.30) (0.70) / 100] = 1.76The p-value is given as 0.0392.
Since the p-value is less than 0.05, we can reject the null hypothesis.
Thus, we can conclude that more than 30% of Cal State East Bay students work full-time.
Hence, option D is the correct answer.
There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than 30% working full-time.
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John flew a kite. He started flying the cat at 2:20 p.m. and ended at 3:14 p.m. How many minutes did John fly a kite?
A. 47 minutes
B. 50 minutes
C. 54 minutes
D. 55 minutes
Answer:
54 minutes
Step-by-step explanation:
3:14 = 3 × 60 = 180 + 14
= 194
2:20 = 2 × 60 = 120 + 20
= 140
194 - 140
= 54
Solve by completing the square.
x2 - 4x – 20 = 0
A. x = {-2±6√2}
B. x = {2+6√2}
C. x = {2+2√6}
D. x = {-2±2√6}
Show your work.
Step-by-step explanation:
Subtract
20
from both sides of the equation.
x
2
−
4
x
=
−
20
To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of
b
.
(
b
2
)
2
=
(
−
2
)
2
Add the term to each side of the equation.
x
2
−
4
x
+
(
−
2
)
2
=
−
20
+
(
−
2
)
2
Simplify the equation.
Tap for more steps...
x
2
−
4
x
+
4
=
−
16
Factor the perfect trinomial square into
(
x
−
2
)
2
.
(
x
−
2
)
2
=
−
16
Solve the equation for
x
.
Tap for more steps...
x
=
2
±
4
i
You have two unknown integers. Double the larger integer increased by triple the smaller integer is 46. Squaring the larger number and increasing it by four times itself gives the same result as multiplying the smaller number by 20 and adding 5. Use a system to solve for the integers by graphing
The two unknown integers can be found by graphing the given equations. The larger integer is 10, and the smaller integer is 8.
Let's represent the larger integer as 'x' and the smaller integer as 'y.' According to the given information, we have two equations:
Equation 1: 2x + 3y = 46
Equation 2: x^2 + 4x = 20y + 5
To solve this system of equations, we can graph both equations on the same coordinate plane. The point where the two graphs intersect will give us the values of 'x' and 'y' that satisfy both equations simultaneously.
For equation 1, we rearrange it to y = (46 - 2x)/3. Plotting this equation on the graph, we see a straight line.
For equation 2, we rearrange it to x^2 + 4x - 20y - 5 = 0. Plotting this equation, we get a quadratic curve.
By examining the graph, we can see that the two lines intersect at a point where 'x' is approximately 10 and 'y' is approximately 8. Therefore, the larger integer is 10, and the smaller integer is 8.
By substituting these values back into the original equations, we can verify that they satisfy both equations.
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How can this expression be written another way?
32k + 24
Factor using the distributive property and the greatest common factor to write an equivalent expression
Enter your answer by filling in the boxes
32k + 24 = __ (__)
Kora and Wallace planted a garden bed the size of the red square. How big is their garden bed? (Finding the area)
Answer: no sol
Step-by-step explanation:
bro there is no pic to do so im just going to say...
Find a curve that passes through the point (1,5) and has an arc length on the interval [2,6] given by:
6
S2 V1 + 16x dx.
6∫[2,6] (1 + (f'(x))²) dx + 16∫[2,6] x dx = 6S²V1 + 16x dx. To solve this equation, we need additional information about the curve, such as a boundary condition or another equation that relates f(x) and f'(x).
To find a curve that passes through the point (1, 5) and has an arc length on the interval [2, 6] defined by the expression 6S²V1 + 16x dx, we can follow these steps:
Step 1: Determine the general form of the curve equation.
Step 2: Use the arc length formula to obtain an equation involving the curve's equation.
Step 3: Solve the resulting equation to find the specific curve.
Let's proceed with each step:
Step 1: Determine the general form of the curve equation.
Let's assume the curve equation is y = f(x), where f(x) represents the unknown function describing the curve.
Step 2: Use the arc length formula to obtain an equation involving the curve's equation.
The arc length formula for a curve defined by y = f(x) is given by:
S = ∫[a,b] √(1 + (f'(x))²) dx
We are given that the arc length on the interval [2, 6] is defined by the expression 6S²V1 + 16x dx. Substituting the formula for arc length, we have:
6∫[2,6] (√(1 + (f'(x))²))²dx + 16∫[2,6] x dx
Simplifying, we get:
6∫[2,6] (1 + (f'(x))²) dx + 16∫[2,6] x dx
Step 3: Solve the resulting equation to find the specific curve.
Since the expression 6S²V1 + 16x dx represents the arc length on the interval [2, 6], we need to equate it to the arc length formula obtained in Step 2.
6∫[2,6] (1 + (f'(x))²) dx + 16∫[2,6] x dx = 6S²V1 + 16x dx
To solve this equation, we need additional information about the curve, such as a boundary condition or another equation that relates f(x) and f'(x). Without such information, it is not possible to determine the specific curve. Please provide additional constraints or information if available to proceed further in finding the specific curve.
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Mr. Piper's plumbing needed
repairs. The plumber charged
$98 for parts plus $45 per hour
for labor. If the bill totaled $458,
how many hours of labor were
required?
Answer:
8 hours of labor at 45 dollars an hour, plus the 98 dollars for parts equal 458
Convert 13,000,000,000,000,000,000,000,000 to scientific notation.
Answer:
1.3 times 10 to the 25th power
Step-by-step explanation:
Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the
10
. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.
Answer:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
Hi! The answer to your question is 1.3 x [tex]10^{25}[/tex]
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!
- Brooklynn Deka